#### Contents

#### OVERVIEW

##### Philosophy

At Cary Christian School, we begin with the premise that ‘All truth is God’s truth’ and Jesus Christ, the Word of God, is the Source of all truth. Our purpose in mathematics is to reveal our glorious Creator and Sustainer to our students and for them to know and appreciate the beauty He has placed in mathematics. We want to pursue the breadth and depth of mathematics in the fear of the LORD. Since mathematics is the language God used to create the universe, it is important to learn this ‘language’ and be able to articulate it to begin to understand our Creator and His creation. Mathematics is also a tool for man’s dominion and care of creation under God. We want our students to learn mathematical principles so that they will be prepared to organize, plan, calculate, and evaluate ideas and practices to better serve others and advance God’s kingdom on earth.

##### How Are Students Taught?

Teachers will use a variety of methodologies that are age and ability appropriate. These will include direct instruction, inquiry-based learning, demonstrations, and learning centers/independent work. The primary goal of the Math Program at CCS is to have students be able to communicate mathematical concepts well through written and spoken word.

**At each level of their mathematical career, students are expected to be able to:**

- Determine expressions and values based on mathematical procedures and rules.
- Use correct notation, language, and mathematical conventions to communicate results or solutions.
- Justify their mathematical reasoning and solutions.

(*Adapted from Mathematical Practices, AP Calculus Course and Exam Description.)

**Teacher behaviors:**

- Demonstrate the acceptance of students’ divergent ideas
- Influence learning by posing challenging and interesting questions
- Project a positive attitude about math and about students’ ability to “do” math
- Students are actively engaged in “doing” mathematics
- Interdisciplinary connections and examples are used to teach math
- Students are explaining how to apply principles and solve problems in small groups or with the entire class.
- Students use manipulatives when appropriate

##### Regular Assessments

As students work all year toward the cumulative final exam, it is critical to have regular assessments or tests. Formative assessments, or tests that check “chunks” of knowledge, can uncover deficiencies in learning that may prevent students from successfully completing summative, or cumulative, assessments. Oftentimes, formative assessments can be given in conjunction, or just after, lab work. If students are struggling with specific concepts, re-teaching is done before the summative exam is given. If students show mastery of each unit assessment, they will be better prepared for the final exam.

It is important to utilize more than just written assessments. Teachers regularly assess students’ understanding through Socratic dialogue and verbal presentations in addition to written tests and quizzes. This enables teachers to better understand the depth of a student’s understanding.

##### Homework

Students will be given homework every day they have class. Homework is a way to reinforce what they have learned that day. Homework lengths will vary, although they will be designed to fit into an overall plan of ten minutes times the grade level for all subjects in total.

In order to be successful in mathematics, students must practice the mechanics of each skill so they can later apply those skills to other novel situations. Routine practice and drilling should help students become quick and accurate in solving basic operations, thereby becoming procedurally fluent. Becoming procedurally fluent should help students free up their cognitive capacities to solve more complex tasks.

Practicing will help the students recognize the importance of trying, failing, learning, and repeating to demonstrate understanding of practiced concepts.

##### Balancing Breadth & Depth

It is necessary for our teachers to appropriately balance breadth with depth of content to cover the right amount of material in a limited amount of time. Teachers will focus on making sure that all students understand the key principles that are foundational to future courses. At the same time, teachers will use the remaining time to cover as many different scenarios as possible for each principle to equip the students to succeed in tackling novel situations and problems.

#### SEQUENCE OF CLASSES

(c) – core class

(e) – elective class

**6TH GRADE**

Math 6 (c) **All Things Algebra**

Math Tutoring (e)

Math Counts (e)

**7TH GRADE**

Accelerated Pre-Algebra (c) or

Pre-Algebra (c) **All Things Algebra**

Math Help (e)

Math Foundations (e)

Math Counts (e)

**8TH GRADE**

Accelerated Algebra (c) or

Algebra (c) **All Things Algebra**

Math Tutoring (e)

Math Foundations (e)

Math Counts (e)

**9TH GRADE**

H Geometry (c)** All Things Algebra**

Accelerated Geometry (c)

**10TH GRADE**

H Algebra II (c)** All Things Algebra/Teacher **

**11TH GRADE**

H Pre-Calculus (c, dc) or

H Trigonometry (c)

**12TH GRADE**

AP Statistics (c) or

AP Calculus AB (c, dc) or

College Algebra (c)

**For students looking to advance in math and take the most rigorous courses available:**

7th Grade – Accelerated Pre-Algebra

8th Grade – Accelerated Algebra

9th Grade – Accelerated Geometry

10th Grade – Accelerated Algebra II

* Notify administration and College Director your desire to skip a level at the beginning of 10^{th} grade. If you are a strong candidate, we will work a plan for you to self-study Pre-Calculus. During the 10^{th} grade school year we will get a current math teacher recommendation, use standardized test scores including the PSAT, examine current and past math grades and offer a Precalculus final assessments where the student must get an 85% or better to move forward.

11th Grade – AP Calculus

12th Grade – AP Statistics

#### 6TH GRADE MATH

##### Entrance & Exit Goals

**Before entering 6th grade math, students will be able to:**

- Write fractions in simplest form.
- Add, subtract, multiply, and divide fractions, mixed numbers, and decimals.
- Convert fractions/decimals/percents.
- Identify Prime numbers to 100.
- Find the prime factorization of a number.
- Use order of operations (PEMDAS)

**When exiting 6th grade math, students will be able to:**

- Write and evaluate variable expressions.
- Use the order of operations.
- Add, subtract, multiply and divide integers.
- Graph points on a coordinate plane.
- Identify and use properties of addition and multiplication and the Distributive Property.
- Simplify expressions.
- Solve one-step equations and inequalities.
- Add, subtract, multiply, and divide decimal numbers.
- Use divisibility tests.
- Find the prime factorization of a number.
- Find the greatest common factor and least common multiple using prime factorization.
- Write fractions in simplest form.
- Simplify expressions with integer exponents.
- Write fractions as decimals and write terminating and repeating decimals as fractions.
- Add, subtract, multiply, and divide fractions and mixed numbers.
- Solve proportions.
- Write percents as fractions and decimals and write decimals as fractions and percents.
- Find a part of a whole, a percent and a whole amount.
- Use the order of operations
- Add, subtract, multiply, and divide integers
- Write and simplify ratios.
- Find area and perimeter of geometric shapes.
- Find surface area of three-dimensional figures.

##### Learning Objectives

**1st Quarter:**

- Identify Place Value of Whole Numbers
- Write Whole Numbers in Standard and Expanded Form
- Round Whole Numbers and Compare Whole Numbers
- Add and Subtract Whole Numbers
- Multiply and Divide Whole Numbers
- Divisibility Rules (2,3, 4, 6, 9, and 10)
- Powers and Exponents
- Identify Perfect Square Numbers and Perfect Cubes
- Order of Operations (PEMDAS)
- Commutative, Associative, and Distributive Properties
- Prime/Composite Numbers
- Prime Factorization
- GCF and LCM using Prime Factorization
- Adding Integers Using counters and a number line
- Adding Integers

**2nd Quarter:**

- Subtracting Integers
- Multiplying Integers
- Dividing Integers
- Multiplying and Dividing Integers Applications
- Order of Operations with Integers
- Coordinate Plane and Graphing
- Mixed vs. Improper Forms, Simplifying Fractions
- Equivalent Fractions; Comparing & Ordering Fractions
- Adding & Subtracting Fractions (Like Denominators)
- Adding & Subtracting Fractions (Unlike Denominators)
- Multiplying Fractions
- Dividing Fractions
- All Fraction Operations
- Applications with Fraction Operations
- Decimals (Place Value, Comparing, Rounding)
- Adding & Subtracting Decimals
- Multiplying Decimals
- Dividing by Whole Numbers
- Dividing by Decimals
- All Decimal Operations
- Rational Numbers: Fractions & Decimals
- Negative Rational Numbers

**3rd Quarter:**

- Evaluating Expressions (positives only)
- Evaluating Expressions (positive and negative integers)
- Translating Expressions
- Translating & Evaluating Expressions (includes real world applications)
- Parts of an Expression; Combining Like Terms
- Distributive Property with Expressions
- Simplifying Expressions (Distribute & Combine)
- Equivalent Expressions; Factoring Expressions
- Dividing by Decimals
- All Decimal Operations
- Rational Numbers: Fractions & Decimals
- Negative Rational Numbers
- One-Step Equations (Addition & Subtraction)
- One-Step Equations (Multiplication & Division)
- One-Step Equations (Mixed Operations)
- Translating One-Step Equations
- One-Step Rational Equations
- Real World Applications with One-Step Equations
- Writing and Graphing Inequalities
- Solving One-Step Inequalities (Addition and Subtraction)
- Solving One-Step Inequalities (Multiplication and Division)
- One-Step Inequalities (Mixed Operations)
- Real World Applications using One-Step Inequalities

** 4th Quarter:**

- Writing & Simplifying Ratios
- Equivalent Ratios
- Ratio Tables & Graphs
- Rates and Unit Rates; Comparing Rates
- Proportional Relationships
- Finding Missing Values in Proportional Relationships (using unit rates)
- Percents; Percent and Fraction Conversions (using equivalent fractions over 100)
- Percents and Decimals
- Fraction and Percent Conversions
- Converting Fractions, Decimals, and Percents
- Comparing Fractions, Decimals, and Percents
- Percent of a Number
- Congruent Segments, Angles, and Polygons
- Perimeter of Plane Figures
- Area of Rectangles & Parallelograms
- Area of Triangles & Trapezoids
- Perimeter & Area Applications
- Polygons in the Coordinate Plane
- Area of Composite Figures
- Circles and Circumference
- Area of Circles
- Three-Dimensional Figures and Nets
- Surface Area of Rectangular Prisms
- Surface Area of Triangular Prisms
- Surface Area of Square and Triangular Pyramids
- Volume of Rectangular Prisms

#### 7TH GRADE: PREALGEBRA

##### Entrance & Exit Goals

**Before entering Pre-Algebra, students will be able to:**

- Write fractions in simplest form.
- Add, subtract, multiply, and divide fractions and mixed numbers.
- Convert fractions/decimals/percents.
- Add, subtract, multiply, and divide integers.
- Use the order of operations.

**When exiting Pre-Algebra, students will be able to:**

- Write and evaluate variable expressions.
- Use the order of operations.
- Add, subtract, multiply and divide integers.
- Graph points in the coordinate plane.
- Identify and use properties of addition and multiplication and the Distributive Property.
- Simplify expressions.
- Solve one-step equations and inequalities.
- Substitute into formulas.
- Use divisibility tests.
- Find the prime factorization of a number.
- Find the greatest common factor and least common multiple.
- Write fractions in simplest form.
- Simplify expressions with integer exponents.
- Write fractions as decimals and write terminating and repeating decimals as fractions.
- Add, subtract, multiply and divide fractions and mixed numbers.
- Solve proportions.
- Find probability and odds.
- Write percents as fractions and decimals and write decimals and fractions as percents.
- Find a part of a whole, a percent and a whole amount.
- Find mean, median and mode of a set of data.

##### Learning Objectives

**1st Quarter:**

Students will be able to:

- Add, subtract, multiply, and divide integers.
- Understand the real number system.
- Classify real numbers.
- Compare and order integers and rational numbers.
- Perform basic operations.
- Apply properties to evaluate and simplify expressions.
- Simplify factions using addition, subtraction, multiplication, and division.
- Write verbal expressions for algebraic expressions.
- Write algebraic expressions for verbal expressions
- Evaluate algebraic expressions by using order of operations.
- Use order of operations to simplify expressions.
- Use the distributive property to simplify and evaluate expressions.
- Perform operations on expressions with exponents.
- Simplify expressions containing negative and zero exponents.
- Simplify expressions involving monomials.
- Add, subtract, multiply, and divide monomials.
- Express numbers in scientific notation
- Find sum, difference, product, and quotient of numbers expressed in scientific notation.
- Add and subtract polynomials.

**2nd Quarter:**

Students will be able to:

- Write and evaluate variable expressions.
- Use mathematical properties to simplify variable expressions.
- Write and solve one-step equations.
- Write and solve one-step inequalities.
- Perform operations with positive and negative decimals.
- Write and solve multi-step equations.
- Write and solve multi-step inequalities.
- Write and compare ratios and rates.
- Identify equivalent fractions and write fractions in simplest form.
- Use rules of exponents and scientific notation
- Write fractions as decimals and decimals as fractions.
- Perform operations with fractions and mixed numbers.
- Solve equations and inequalities with rational numbers.
- Write and compare ratios and rates.
- Write and solve proportions.
- Find and use equivalent decimals, fractions, and percents.
- Use proportions and the percent equation to solve percent problems.
- Solve problems involving the percent of change.

**3rd Quarter:**

Students will be able to:

- Represent and interpret relations and functions.
- Find and interpret slopes of lines.
- Write and graph linear equations in two variables.
- Write and graph linear systems and linear inequalities.
- Use square roots and the Pythagorean theorem to solve problems.
- Identify rational numbers and irrational numbers.
- Use special right triangles and trigonometric ratios to solve problems.

**4th quarter:**

Students will be able to:

- Find angle measures and side lengths of triangles and quadrilaterals.
- Find the areas of parallelograms, trapezoids, and circles.
- Find the surface area and volumes of prisms, cylinders, pyramids, and cones.
- Identify special pairs of angles and find their measures.
- Find the measures of interior and exterior angles of polygons.
- Translate, reflect, rotate, and dilate geometric figures.
- Make and interpret data displays.
- Conduct surveys and analyze survey results.
- Calculate probabilities of events.

#### 8TH GRADE: ALGEBRA I

##### Entrance & Exit Goals

**Before entering Algebra 1, students will be able to: **

- Write and evaluate variable expressions
- Graph points in the coordinate plane.
- Identify and use properties of addition and multiplication and the Distributive Property.
- Simplify expressions.
- Solve one-step equations and inequalities.

**When exiting Algebra 1, students will be able to: **

- Solve multi-step equations and inequalities algebraically and graphically
- Use proper function notation
- Solve, graph, and analyze linear equations
- Solve absolute value equations and inequalities
- Solve and graph linear systems
- Simplify expressions with exponents
- Perform operations with polynomials
- Factor polynomial expressions
- Rewrite rational expressions (when dividing a polynomial with a monomial)
- Solve, graph, and analyze quadratic functions
- Simplify radical expressions and solve basic radical equations
- Use critical thinking skills to solve word problems and interpret results

##### Learning Objectives

**1st Quarter: **

Students will be able to:

- Understand the real number system.
- Classify real numbers.
- Compare and order integers and rational numbers.
- Perform basic operations.
- Apply properties to evaluate and simplify expressions.
- Use distributive property to write equivalent expressions.
- Solve one step, two-step, and multi-step equations and inequalities.
- Solve and graph inequalities.
- Evaluate and simplify algebraic expressions.
- Transform and solve equations.
- Solve multi-step equations.
- Solve problems involving grouping symbols.
- Solve equations with variables on each side.
- Compare ratios and solve proportions.
- Solve problems involving proportional change.
- Evaluate and solve absolute value equations.
- Solve and graph inequalities.
- Solve and graph inequalities involving
**absolute value.**

**2nd Quarter:**

Students will be able to:

- Represent relations.
- Interpret graphs as relations.
- Determine whether a relation is a function.
- Find function values.
- Use multiple representations for functions: verbal descriptions, rules, tables, and graphs.
- Specify locations using coordinate geometry.
- Use representations to communicate mathematical ideas.
- Recognize arithmetic sequences and relate them to linear functions.
- Write and graph linear functions in various forms.
- Find slope from a graph and by using the slope formula.
- Write linear equations in slope-intercept Form and in standard form.
- Graph linear equations by using the slope-intercept Form.
- Find and graph x- and y-intercepts.
- Graph vertical and horizontal lines.
- Solve and graph using the point-slope formula (given a point and a slope).
- Solve and graph using point-slope formula (given two points).
- Determine if lines are parallel, perpendicular, or neither from an ordered pair and an equation.
- Write equations with parallel and perpendicular lines.
- Do word problems involving linear equations.
- Graph scatter plots and a line of best fit and perform linear regression.

**3rd Quarter: **

Students will be able to:

- Identify direct variation.
- Write a direct variation equation.
- Identify and graph inverse variation.
- Solve systems of equations by graphing.
- Solve systems of equations by substitution.
- Solve systems of equations by elimination.
- Solve systems of equations using matrices.
- Solve and graph linear inequalities.
- Solve and graph systems of linear inequalities.
- Add, subtract, and multiply monomials.
- Raise monomials power to a power.
- Divide monomials.
- Simplify expressions using negative exponents.
- Add and subtract numbers in scientific notation.
- Multiply and divide numbers in scientific notation.
- Graph exponential functions.
- Solve word problems using exponential growth and decay.
- Identify a geometric sequence.
- Simplify radicals into reduced radical form.
- Apply the exponent rules to simplify a monomial expression, including expressions with negative.
- Add, subtract, multiply, and divide polynomial expressions.
- Simplify square roots.
- Simplify cube roots.
- Simplify square roots with monomial expressions.

**4th Quarter: **

Students will be able to:

- Factor a polynomial with a greatest common factor.
- Factor special polynomials including difference of squares and quadratic trinomials.
- Factor a polynomial completely requiring more than one step.
- Graph a quadratic equation written in standard form or vertex form.
- Identify the domain, range, axis of symmetry, vertex, x-intercept(s), and y-intercept of a quadratic equation.
- Recognize the transformations that took place from the parent function given a quadratic equation written in vertex form.
- Recognize that a quadratic equation can have one real solution, two real solutions, or no real solutions.
- Solve a quadratic equation using an appropriate method (factoring, square roots, completing the square, or the quadratic formula).

#### 9TH GRADE: GEOMETRY

##### Entrance & Exit Goals

**Before entering Honors Geometry, a student should be able to:**

- Read and graph data points.
- Write the equation of a straight line.
- Identify slope and y-intercept from a graph.
- Solve linear algebraic equations.
- Factor simple quadratic equations.
- Find area, volume, perimeter for basic shapes.

**When exiting Honors Geometry, a student should be able to:**

- Find the slope, length, midpoint, and endpoints of a line segment.
- Solve problems by recognizing, analyzing, and writing logical arguments.
- Apply the properties of angles, parallel, and perpendicular lines.
- Apply properties of circles.
- Apply properties of triangles, quadrilaterals, and regular polygons
- Work with geometric figures on the coordinate plane.
- Solve problems using properties of right triangles, including trigonometric ratios.
- Identify similar triangles and solve problems using ratios and proportions.
- Find measurements relating to geometric figures and geometric solids, including perimeters, areas, and volumes.
- Solve word problems using critical thinking skills.
- Solve multiple step applications of concepts.

##### Unit Objectives

**Unit 1 – The Basics of Geometry:**

Students will be able to:

- Use defined and undefined terms to understand the basics of geometry.
- Identify/draw/label points both collinear and noncollinear.
- Differentiate between equal and congruence.
- Use the Segment Addition Postulate to find the length of a segment and to solve problems.
- Find the distance between two points on a coordinate plane.
- Find the midpoint of a segment.
- Find the endpoint of a segment given one endpoint and the midpoint.
- Name and classify angles.
- Use a protractor to measure and draw angles.
- Define an angle bisector, perpendicular lines, and perpendicular bisector and analyze diagrams.
- Use the Angle Addition Postulate to solve problems.
- Determine complementary and supplementary angles.
- Analyze vertical and adjacent angle pairs.
- Use knowledge of angle pairs to determine missing information.

**Unit 2 – Logic and Proof:**

Students will be able to:

- Describe patterns and use inductive reasoning to predict the next element of a pattern.
- Identify and write conditional statements.
- Write the converse and inverse of a conditional statement.
- Write the contrapositive of a conditional statement.
- Identify and write biconditional statements.
- Write mathematical definitions as conditional or biconditional statements and identify whether these statements are true or false.
- Write proofs using the algebraic properties of equality.
- Use reflexive, symmetric, and transitive properties of equality to form conclusions.
- Write proofs using geometric theorems.
- Use reflexive, symmetric, and transitive properties of congruence of segments and angles to form conclusions.
- Write proofs using the Right-Angle Congruence Theorem, the Congruent Supplements Theorem, the Congruent Complements Theorem, the Linear Pair Postulate, and/or the Vertical Angles Congruence Theorem.

**Unit 3 – Parallel and Perpendicular Lines:**

Students will be able to:

- Identify lines as parallel, perpendicular, or skew.
- Identify corresponding, alternate interior, alternate exterior, and consecutive interior angle pairs.
- Use properties of parallel lines to determine angle relationships.
- Use properties of parallel lines to solve problems.
- Use angle relationships to prove that two lines cut by a transversal are parallel.
- Write proofs using the converses of theorems about parallel lines.
- Use properties of parallel lines to solve problems.
- Calculate the slope of a line given two points on the line, both in graphical form and in algebraic form.
- Graph equations of lines on the Cartesian coordinate plane using on the slope and the y-intercept.
- Use slope to distinguish between parallel and perpendicular lines.
- Write the equation of a line when given a point on the line and the slope of the line.
- Write the equation of a line when given two points on the line.
- Write the equation of a line when given a point on the line and a parallel line.
- Write the equation of a line when given a point on the line and a perpendicular line.

**Unit 4 – Congruent Triangles: **

Students will be able to:

- Classify triangles and find the measures of their angles.
- Use coordinate geometry to classify a triangle according to its side lengths.
- Use the Triangle Sum Theorem and the Exterior Angle Theorem to find missing information.
- Use theorems about isosceles and equilateral triangles to find missing information.
- Identify congruent triangles and their corresponding parts.
- Prove triangles are congruent using the Side-Side-Side Congruence Postulate.
- Prove triangles are congruent using the Side-Angle-Side Congruence Postulate.
- Prove triangles are congruent using the Hypotenuse-Leg Congruence Theorem.
- Prove triangles are congruent using the Angle-Side-Angle Congruence Theorem.
- Prove triangles are congruent using the Angle-Angle-Side Congruence Theorem.
- Use CPCTC (corresponding parts of congruent triangles are congruent) to solve problems.
- Write two column proofs using CPCTC.

**Unit 5 – Relationships within Triangles:**

Students will be able to:

- Use the perpendicular bisector of a segment to find missing information and solve problems.
- Use the bisector of an angle to find distance relationships and solve problems.
- Use properties of midsegments to find missing information.
- Use the Triangle Inequality Theorem to decide if a triangle exists.
- Use the Triangle Inequality Theorem to find the possible range of values for a third side of a triangle, given two sides.
- Use the perpendicular bisectors of a triangle to find missing information and solve problems.
- Identify the circumcenter of a triangle.
- Use the angle bisectors of a triangle to find missing information and solve problems.
- Identify the incenter of a triangle.
- Use the medians of a triangle to find missing information and solve problems.
- Identify the centroid of a triangle.
- Use the altitudes of a triangle to find missing information and solve problems.
- Identify the orthocenter of a triangle.

**Unit 6 – Similarity:**

Students will be able to:

- Write and simplify the ratio of two numbers.
- Solve proportions (including word problems).
- Identify the scale factor of similar figures.
- Use ratios and proportions to solve for sides and angles.
- Prove that two triangles are similar by using the definition of similar triangles and the Angle-Angle Similarity Postulate.
- Identify similar sides and angles of similar triangles.
- Prove that two triangles are similar by using the definition of similar triangles and the Side-Side-Side Similarity Theorem.
- Prove that two triangles are similar by using the definition of similar triangles and the Side-Angle-Side Similarity Theorem.
- Use proportions with parallel lines to find missing information.
- Use proportions with a triangle to find missing information.

**Unit 7 – Right Triangles and Trigonometry:**

Students will be able to:

- Simplify radicals, in preparation for the upcoming chapter.
- Use the Pythagorean Theorem to solve real-life problems.
- Use the Converse of the Pythagorean Theorem to prove that a triangle is a right triangle.
- Use side lengths to classify triangles by their angle measures.
- Apply properties of 45-45-90° triangles to find missing sides.
- Apply properties of 30-60-90° triangles to find missing sides.
- Find the sine, cosine, and tangent ratios of acute angles in right triangles.
- Use the sine, cosine, and tangent ratios to find missing information in right triangles.
- Find the measure of an acute angle in a right triangle if two sides of the triangle are known.
- Use the angle of elevation and angle of depression to model applied problems.

**Unit 8 – Quadrilaterals:**

Students will be able to:

- Calculate the sum of the measures of the interior angles of a convex polygon.
- Use the Polygon Interior Angles Theorem and the Polygon Exterior Angles Theorem to find missing information.
- Use the properties of parallelograms to find angle and side measures.
- Use properties of parallelograms to solve problems.
- Use the properties of rectangles, including properties of diagonals, to solve problems and find missing information.
- Use the properties of rhombi and squares, including properties of diagonals, to solve problems and find missing information.
- Use the properties of trapezoids to solve problems and find missing information.
- Use the properties of kites to solve problems and find missing information.
- When given four rectangular coordinates, determine which special type of quadrilateral these coordinates make.

**Unit 9 – Circles:**

Students will be able to:

- Identify segments and lines related to circles.
- Find the circumferences and areas of circles.
- Use central angle measures to find arc measures of circles.
- Use relationships of arcs and chords in a circle to solve problems and find missing information.
- Write equations of circles in the coordinate plane.
- Graph circles in the coordinate plane.
- Use properties of inscribed angles and inscribed polygons of circles to solve problems and find missing information.
- Use the properties of tangent lines of circles to solve problems and find missing information.
- Use the properties of interior intersections and “on the circle” intersections to find arc measures and interior angle measures.
- Use the properties of exterior intersections to find arc measures and exterior angle measures.
- Use the properties of intersecting chords or secants inside a circle to find segment lengths.
- Use the properties of intersecting secants outside a circle to find segment lengths.
- Use the properties of an intersecting secant and tangent outside a circle to find segment lengths.

**Unit 10 – Measuring Lengths and Areas:**

Students will be able to:

- Find the areas of triangles, rectangles, parallelograms, squares, trapezoids, and circles.
- Find the area and perimeter of composite figures.
- Find the area of regular polygons.
- Calculate the length of arcs located on a circle.
- Calculate the area of a sector within a circle.

**Unit 11 – Surface Area and Volume of Solids:**

Students will be able to:

- Find the surface area of right pyramids and right cones.
- Find the volume of right pyramids and right cones.
- Find the surface area of right prisms and right cylinders.
- Find the volume of right prisms and right cylinders.
- Find the surface area and the volume of spheres.

#### 10TH GRADE: ALGEBRA II

##### Entrance & Exit Goals

**Before entering Honors Algebra 2, a student should be able to:**

- Simplify expressions, calculate rational numbers, and use order of operations.
- Solve multi-step equations and inequalities.
- Graph linear equations and inequalities.
- Demonstrate understanding of coordinate geometry.
- Translate word sentences into equations.

**When exiting Honors Algebra 2, a student should be able to:**

- Perform arithmetic, composition, and inverse operations on functions.
- Transform any function using rigid transformations, dilations, and reflections.
- Solve systems with 2 variables algebraically and graphically.
- Solve systems with 3 variables algebraically and with technology.
- Use matrices to solve systems of equations and model real-world situations.
- Factor polynomials completely
- Simplify radicals into reduced radical form without a calculator.
- Solve quadratic, rational, radical, exponential, and logarithmic equations.
- Divide polynomials, including simplifying complex rational expressions.
- Graph quadratic, exponential, logarithmic, and rational functions.
- Determine the domain, range, and end behavior (if applicable) of any function.
- Develop critical thinking skills by solving various word problems that model real-world situations linearly, quadratically, exponentially, and rationally.

##### Unit Objectives

**Unit 1 – Relations, Function Basics, and Linear Functions:**

Students will be able to:

- Determine whether relations are functions by looking at ordered pairs, mappings, and graphs.
- Determine the domain and range of relations by looking at ordered pairs and mappings.
- Determine the domain and range of relations by looking at graphs.
- Evaluate functions for given values of x.
- Perform operations on functions, including arithmetic operations and compositions.
- Calculate the slope of a line, given two points on the line.
- Plot the graph of a linear equation by using the slope and the y-intercept.
- Plot the graph of a linear equation by using the x- and y- intercepts.
- Write the particular equation of a linear function given information about its graph.

**Unit 2 – Linear Modeling:**

Students will be able to:

- Given a situation in which two real world variables are related by a straight-line graph, be able to sketch the graph, find the particular equation, use the equation to predict values of either variable, and figure out what the slope and intercepts tell you about the real world.

**Unit 3 – Systems of Equations and Inequalities:**

Students will be able to:

- Solve a system of linear equations by graphing them on the Cartesian coordinate plane.
- Solve a system of linear equations in two variables by using the substitution method and the elimination method.
- Write a system of equations in two variables from a word problem and then solve the system to answer the question.
- Find the single ordered triple that satisfies a system of three linear equations with three variables using technology.
- Write a system of equations in three variables from a word problem and then solve the system using technology to answer the question.

**Unit 4 – Matrices:**

Students will be able to:

- Add and subtract matrices.
- Multiply matrices with a scalar and with other matrices.
- Calculate the determinant of a second order and third order matrix.
- Determine the inverse of a second order matrix.
- Use Cramer’s Rule to solve a system of two equations.
- Use inverses to solve a system of two equations.

**Mini-Unit 1 – Stuff We Probably Forgot from Algebra 1:**

Students will be able to:

- Solve linear inequalities.
- Solve compound inequalities.
- Solve an absolute value equation.
- Solve an absolute value “less than” inequality.
- Solve an absolute value “greater than” inequality.

**Mini-Unit 2 – Descriptive Statistics:**

Students will be able to:

- Calculate measures of center (mean, median) for a distribution of quantitative data.
- Calculate and interpret measures of variability (range, standard deviation, IQR) for a distribution of quantitative data.
- Make and interpret boxplots of quantitative data.

**Mini-Unit 3 – All About Factoring:**

Students will be able to:

- Factor polynomials by factoring out the greatest common factor.
- Factor binomial expressions using the difference of two squares, the sum of cubes, or the difference of cubes.
- Factor quadratic trinomials.
- Use grouping to factor polynomials with four terms.

**Unit 5 – Quadratics – Solving and Graphing:**

Students will be able to:

- Convert quadratic equations in standard form to vertex form.
- Graph quadratic functions by converting the equations to vertex form and plotting the vertex, axis of symmetry, y-intercept, and a symmetry point.
- Solve quadratic equations by factoring and then by using the Zero Product property.
- Solve quadratic equations by taking the square root of each side.
- Solve quadratic equations by using the Quadratic Formula.
- Graph quadratic functions by finding the x-intercepts, y-intercepts, vertex, and axis of symmetry.
- Use the discriminant to classify the solutions of a quadratic equation.
- When given the equation of a quadratic function, calculate the value of y for a known value of x, and the values of x for a known value of y.
- When given a quadratic equation whose solutions are complex numbers, write the solutions in terms of i.

**Unit 6 – Quadratic Modeling:**

Students will be able to:

- When given three points on the graph of a quadratic function, or the vertex and one other point, find the particular equation of the function using technology.
- Use a quadratic function as a mathematical model, given a real-world situation.
- Examine the path of a projectile and explain the motion using a quadratic function.

**Unit 7 – Parent Functions and Transformations:**

Students will be able to:

- Determine the main characteristics (such as domain, range, end behavior, continuity, and maximum number of roots) of the parent functions for linear, absolute value, quadratic, square root, and exponential functions.
- Investigate the effects of horizontal shifts, vertical shifts, and reflections about the x and y axes on functions.
- When given the sketch of a function f(x), perform horizontal shifts, vertical shifts, and reflections about the x and y axes.
- When given the equation of a function, describe the transformations that have occurred between the original function and the transformed function.
- When given an ordered pair that lies on the original function, find the corresponding ordered pair on the transformed function when given the equation of the transformed function.

**Unit 8 – Radicals:**

Students will be able to:

- Evaluate radicals where the radicand is an integer and the index is either 2, 3, or 4.
- Evaluate radicals where the radicand contains variables and the index is a 2, 3, or 4.
- Multiply radicals (monomials only).
- Add and subtract radical expressions.
- Divide radical expressions, both monomial and binomial.
- Solve radical equations.

**Unit 9 – Exponents and Exponential Functions:**

Students will be able to:

- Derive the product rule for exponents, the quotient rule for exponents, the power rule for exponents, the negative exponent rule, and the zero-exponent rule.
- Demonstrate the definitions of exponentiation for rational exponents by evaluating powers and by simplifying expressions involving rational exponents.
- When given an expression containing radicals or fractional exponents, evaluate it quickly without a calculator.
- Convert numbers in standard form to scientific notation, and vice versa.
- Multiply and divide numbers in scientific notation.
- Solve exponential equations with the same base.

**Unit 10 – Logarithms:**

Students will be able to:

- Convert equations in exponential form to logarithmic form and vice versa.
- Simplify logarithms by changing the logarithmic equation to exponential form and then solving by converting the bases to be the same number.
- Simplify logarithms by using the Change of Base formula.
- Expand and condense logarithms by using the Product Property of Logarithms, the Quotient Property of Logarithms, and the Power Property of Logarithms.
- Solve logarithmic equations in the form of “log = log”.
- Solve logarithmic equations in the form of “log = number”.
- Solve exponential equations by taking the common logarithm of both sides of the equation.

**Unit 11 – Exponential Modeling:**

Students will be able to:

- Use the add-multiply property of exponential functions to calculate many values quickly and to tell whether or not an exponential function is a suitable model for a given set of data.
- When given a real-world situation relating two variables, use an exponential function as a mathematical model.
- Solve exponential growth and decay problems.
- Solve compound interest problems.

**Unit 12 – Rational Expressions, Equations, and Functions:**

Students will be able to:

- Simplify rational expressions where the numerators and denominators are monomials, binomials, and/or trinomials.
- Multiply and divide rational expressions, while simplifying the result.
- Divide a polynomial by a binomial using long division.
- Add and subtract rational expressions.
- Simplify complex rational expressions.
- Solve rational equations.
- Graph rational functions by hand after calculating the x-intercepts, the vertical and horizontal asymptotes, the holes, and a few key points.
- Determine the domain and range for rational functions.

**Unit 13 – Variation Modeling:**

Students will be able to:

- When given a real-world situation, determine which kind of variation function is a reasonable mathematical model, find the particular equation of the function, and predict x or y.
- When given a real-world situation in which one variable is proportional to a non-integer power of another variable, determine the proportionality constant, and use the resulting variation function as a mathematical model.
- When given a real-world situation involving more than two variables, find general and particular equations relating the variables, and use these as mathematical models.

#### 11TH GRADE: HONORS TRIGONOMETRY

##### Entrance & Exit Goals

**Before entering Honors Trigonometry, a student should be able to:**

- Solve and graph linear equations and inequalities and systems of linear equations or inequalities.
- Solve and graph quadratic equations.
- Simplify expressions containing radicals, exponents, and logarithms.
- Factor expressions.

**When exiting Honors Trigonometry, a student should be able to:**

- Graph trigonometric functions and their inverses.
- Know the degrees, radians, and coordinates of the unit circle.
- Use the unit circle and trigonometric identities to find values of trigonometric functions and to simplify trigonometric expressions.
- Solve trigonometric equations in linear form.
- Solve acute, right, and obtuse triangles.
- Use properties of vectors to solve real world problems.
- Convert ordered pairs between polar form and rectangular form.
- Graph conic sections.
- Use Venn and tree diagrams to help organize data and solve probability problems.
- Use basic counting principles, including permutations and combinations.
- Solve compound event problems involving union, intersection, and complement.

##### Learning Objectives

**Unit 1 – Right Triangles:**

Students will be able to:

- Use the Pythagorean Theorem to find side lengths in right triangles.
- Apply properties of 45-45-90
^{o}triangles to find missing sides. - Apply properties of 30-60-90
^{o}triangles to find missing sides. - Find the sine, cosine, tangent, secant, cosecant, and cotangent ratios of acute angles in right triangles.
- Given a basic trigonometric equation, solve for the variable.
- Use trigonometric ratios, the Triangle Sum Theorem, and the Pythagorean Theorem to solve right triangles.
- Draw pictures presented by the information in word problems so that you can solve the problems later or when you are asked for some answer.
- Apply trig functions to “real world” problems using angles of elevation and depression.

**Unit 2 – Angles and Their Measures:**

Students will be able to:

- Convert decimal degree measures to degrees, minutes, and seconds, and vice versa.
- Find the number of degrees in a given number of rotations.
- Identify angles that are coterminal with a given angle.
- Find the measure of the reference angle for any given angle.
- Change from radian measure to degree measure, and vice versa.
- Change from radian measure or degree measure to revolutions.
- Find the length of an arc given the measure of the central angle.
- Find the linear and angular velocity.
- Using special triangles, derive the ordered pairs on the unit circle for all four quadrants.
- Find the values of the six trigonometric functions using the unit circle.
- Find the values of the six trigonometric functions of an angle in standard position given a point on its terminal side.
- Find the value of a trigonometric function for an angle given the location of its terminal side and the value of another trigonometric function.

**Unit 3 – Graphing Sine, Cosine, and Tangent:**

Students will be able to:

- Use the coordinates of the unit circle to plot the graph of y=sin(x) from -2pi to 2pi.
- Find the domain, range, minimum value, maximum value, amplitude, and period of the function y=sin(x).
- Use the coordinates of the unit circle to plot the graph of y=cos(x) from -2pi to 2pi.
- Find the domain, range, minimum value, maximum value, amplitude, and period of the function y=cos(x).
- Given the equation of a transformed sine or cosine function, describe how the transformed function differs from the original.
- Find the amplitude and period for transformed sine and cosine functions.
- Find the equation of the sine or cosine function given the period, phase shift, and vertical shift.
- Use the coordinates on the unit circle to plot the graph of y=tan(x) from -2pi to 2pi.
- Find the domain, range, minimum value, maximum value, and period of the function y=tan(x).
- Given the equation of a transformed tangent function, describe how the transformed function differs from the original.

**Unit 4 – Trigonometric Identities:**

Students will be able to:

- Identify and use reciprocal identities, quotient identities, and Pythagorean identities to find the value of the trigonometric functions.
- Use the sum and difference identities for the sine and cosine functions.
- Use the double angle identities for the sine and cosine functions.
- Use the half angle identities for the sine and cosine functions.

**Unit 5 – Vectors:**

Students will be able to:

- Find the magnitude of a vector given its endpoints.
- Determine if vectors are equivalent, parallel, or opposite.
- When given a vector in component form, find the magnitude and direction (as a positive vector angle).
- Write a vector in component form given its endpoints.
- Add, subtract, and perform scalar multiplication on vectors given in component form.
- Write a vector as a unit vector.
- Write a vector in trigonometric form.
- Resolve a vector, given its magnitude and direction, into its horizontal and vertical components.
- When given the magnitude and direction of two or more vectors, add the vectors, and calculate the magnitude and direction of the resultant.

**Unit 6 – Simplifying Trigonometric Identities, Solving Trigonometric Equations, and Inverse Trigonometric Functions:**

Students will be able to:

- Find the principal values of inverse trigonometric functions using the unit circle.
- Find the principal values of inverse trigonometric functions using right triangles.
- Solve trigonometric equations in linear form.
- Simplify trigonometric expressions using basic trigonometric identities.

**Unit 7 – Oblique Triangle Laws:**

Students will be able to:

- Solve oblique triangles, given AAS or ASA, by using the Law of Sines.
- Solve oblique triangles, given SSA, by using the Law of Sines.
- Use the Law of Cosines to solve oblique triangles given SSS or SAS.
- Derive the formula for area of an oblique triangle using the sine function.
- Find the area of a triangle if the measures of two sides and the included angle are given.
- Find the area of triangles if the measures of the three sides are given.

**Unit 8 – Polar Coordinates and Complex Numbers:**

Students will be able to:

- Add and subtract complex numbers.
- Multiply and divide complex numbers.
- Simplify expressions with i raised to any power.
- Graph an ordered pair on a polar graph.
- Convert between polar and rectangular coordinates.

**Unit 9 – Conic Sections:**

Students will be able to:

- Write the equation of a circle and sketch its graph.
- Write the equation of an ellipse and sketch its graph.
- Write the equation of a hyperbola and sketch its graph using asymptotes.
- Write the equation of a parabola and sketch its graph.
- Classify a conic section from its equation.

**Unit 10 – Probability and Combinatorics:**

Students will be able to:

- Use and understand set notation.
- Understand basic concepts of sets, such as elements, subsets, intersections, unions, and complements.
- Draw and interpret Venn Diagrams
- Calculate the probability of an event and its complement.
- Calculate probability of, and work with combined events, mutually exclusive events, independent events, Venn Diagrams, and tables.
- Solve problems with and without replacement.
- Work with conditional probability using the formula and other methods.
- Distinguish between situations involving permutations and combinations.

#### 11TH GRADE: HONORS PRECALCULUS

##### Entrance & Exit Goals

**Before entering Honors Precalculus, a student should be able to:**

- Simplify, graph, and solve linear and quadratic functions.
- Simplify, graph, and solve exponential and logarithmic functions.
- Understand and use correctly the language describing the properties and behavior of functions.
- Use geometric formulas to find areas and volumes.
- Define the sine, cosine, and tangent functions using a right triangle.
- Use coordinate geometry to solve problems.

**When exiting Honors Precalculus, a student should be able to:**

- Identify quadratic relations of two variables and classify them as circles, ellipses, parabolas, and hyperbolas, solving for the key features of each shape.
- Solve third degree and higher equations of one variable completely, including any complex solutions.
- Completely factor a third degree or higher equation.
- Articulate the difference between a sequence and a series.
- Understand the differences between arithmetic and geometric sequences and series.
- Simplify and evaluate expressions which include factorials.
- Expand a binomial series into its individual terms.
- Calculate basic probabilities that include permutations and combinations.
- Calculate the Mathematical expectation of a random variable.
- Utilize and convert between measuring angles in degrees and radians.
- Define and utilize all six basic trigonometric functions and their inverses.
- Understand and use trigonometric identities to simplify complex trigonometric expressions.
- Understand the difference between vector and scalar quantities.
- Perform vector addition and subtraction and resolve vectors into their components.

##### Unit Objectives

**Unit 1 – Quadratic Relations and Systems:**

Students will be able to:

- Define a quadratic relation.
- Given the equation or inequality of a circle or circular region, be able to draw the graph.
- Express the distance between two points in a Cartesian coordinate system in terms of the coordinates of the two points.
- Given the equation of an ellipse, sketch the graph and calculate the focal radius and plot the foci.
- Given the equation of a parabola, find the vertex and intercepts, and be able to sketch the graph quickly.
- Given the equation of a hyperbola, find the vertices and asymptotes, and be able to sketch the graph quickly.
- Given a quadratic relation, tell whether the graph is a circle, ellipse, hyperbola, or parabola.
- Calculate the solution set of a system of two equations in two variables, where at least one equation is quadratic, and none are of higher degree.
- Be able to demonstrate their answer to the system of equations graphically.

**Unit 2 – Higher Degree Functions and Complex Numbers:**

Students will be able to:

- Discover what the graph of a cubic equation looks like by pointwise plotting.
- Add, subtract, multiply, and divide complex numbers.
- Given two numbers, write a quadratic equation having these numbers as its solutions.
- Given a quadratic trinomial, factor it over the set of complex numbers.
- Given two numbers, write a quadratic equation having these numbers as its solutions.
- Given a quadratic trinomial, factor it over the set of complex numbers.
- Plot the graph of a given higher degree function by using synthetic substitution to calculate data for plotting.
- Plot the graph of a given higher degree function by using a graphing calculator to calculate data for plotting.
- Find all values of x that makes a polynomial.
- Understand and apply Descartes’ Rule of Signs to find the possible number of zeros for a polynomial of degree 3 or higher.
- Understand and apply the Upper Bound Theorem to determine the upper bound for real zeros for a higher degree polynomial.
- Given a real-world situation in which one variable depends on another by a cubic or higher degree function, find the particular equation and use it as a mathematical model.

**Unit 3 – Sequences and Series:**

Students will be able to:

- Discover a pattern.
- Write a few more terms of the sequence.
- Get a formula for the nth term.
- Use the formula to calculate other terms’ values.
- Draw a graph of the sequence.
- Determine whether the sequence is arithmetic, geometric, or neither.
- Given a value of
*n*for a specified arithmetic or geometric sequence, find the value of the*n*^{th}. - Given the value of the
*n*^{th }term of a specified arithmetic or geometric sequence, find the value of*n*. - Given a partial sum in sigma notation, evaluate it by writing all the terms and then adding them.
- Given the first few terms of a series, write S
_{n}using sigma notation. - Given an arithmetic or geometric series, be able to calculate S
_{n}, the*n*^{th}partial sum quickly. - Given S
_{n}, the*n*^{th}partial sum of an arithmetic or geometric series, and other information. - about the series (such as the first term, and/or the common difference or common ratio), be able to identify the missing information describing the series.
- Given a geometric series, tell whether or not it converges, and if it does converge, find the limit to which it converges.
- Given a repeating decimal, write it as a convergent geometric series and find a rational number equal to the decimal.
- Given a situation from the real world in which the dependent variable changes stepwise, use an arithmetic or geometric sequence or series as a mathematical model.
- Use the definition of factorials to simplify expressions containing factorials.
- Express in factorial form expressions containing products of consecutive integers.
- Discover patterns followed by the signs, exponents, and coefficients in a binomial series.
- Given a binomial power, expand it as a binomial series in one step.
- Given a binomial power of the form, find the term number k, or find the term which contains where
*k*and*r*are integers from 0 to*n*.

**Unit 4 – Probability, Data Analysis, and Functions of a Random Variable:**

Students will be able to:

- Distinguish among the various words used to describe probability.
- Determine the number of outcomes in an event or sample space without listing or counting them.
- Be able to calculate the number of permutations containing
*r*elements that can be made from a set that has*n.* - Find the probability of getting a desired permutation if an arrangement is selected at random.
- Be able to calculate the number of combinations containing
*r*elements that can be made from a set that has*n.* - Find the probability of getting a desired combination if an arrangement is selected at random.
- Given the probabilities of Events A and B, P(A) and P(B), be able to calculate P(A and then B), P(A or B), and P( not A) and P(not B).
- Given a random experiment, be able to calculate the probability distribution of the random.
- variable that is counting how many times a certain outcome occurs out of
*n.* - Calculate the mathematical expectation of a given random experiment.
- Calculate the mean and standard deviation for a given set of data.
- Graph the Frequency Distribution of a given set of data.

**Unit 5 – Trigonometric Functions:**

Students will be able to:

- Tell whether or not a situation from the real world involving two variables represents a periodic function or not.
- Sketch a reasonable graph showing how two real world variables are related.
- Given the measure of an angle in degrees or radians, sketch the position of point P on the Unit Circle.
- Be able to convert an angle measurement between degrees and radians.
- Find the EXACT values of the six trigonometric functions if the angle is any multiple of 30° or 45°.
- Know the definitions of the six trigonometric functions in terms of the sides of a right triangle.
- Use a calculator to evaluate any of the 6 trigonometric functions at any angle.
- Use a calculator to evaluate the measure of any angle in degrees and radians, given the ratio of one of the six trigonometric functions.
- Draw graphs of the six trigonometric functions accurately by pointwise plotting.
- Draw graphs of the six trigonometric functions quickly by finding critical points.
- Sketch the graph of a particular sinusoid quickly when given the equation of the sinusoid.
- Given the graph of a sinusoidal function, write the particular equation.
- Given information about a sinusoidal function, write the particular equation.
- Derive an equation that describes a situation in the real world where something varies sinusoidally.
- Use a sinusoidal equation model to make predictions about behavior in the real world.
- Reach conclusions about the real world using a sinusoidal equation model.
- Draw the graphs of the inverse trigonometric functions and relations.
- Simplify expressions containing inverse trigonometric functions and relations.
- Given an equation in the form of, find the values of
*x*for a given value of. - Derive the particular equation for a situation from the real world in which y varies sinusoidally with x and use it to find x for a given y.
- Derive the particular equation for a situation from the real world in which y varies sinusoidally with x and use it to find x for a given y.

**Unit 6 – Properties of Trigonometric Functions:**

Students will be able to:

- Use Reciprocal Properties, Quotient Properties, and Pythagorean Properties to transform a given expression to a specified, equivalent form, possibly simplifying the expression.
- Given a trigonometric equation, prove it is an identity.
- Express functions of
*-x*in terms of functions of*x*. - Express cos(A ±B) and sin(A ± B) in terms of sin(A) , cos(A) , sin(B) , and cos(B).
- Express tan(A ±B) in terms of tan(A) and tan(B).
- Express cos(2A) and sin(2A) in terms of sin(A) and cos(A).
- Express tan(2A) in terms of tan(A).
- Express , , and in terms of sin(x) and cos(x)
- Given a trigonometric equation and a domain of the variable, find all solutions of the given equation in the domain.

**Unit 7 – Triangle Problems and Vectors:**

Students will be able to:

- Given two sides or a side and an angle of a right triangle, find measures of the other sides and angles.
- Use the Law of Cosines to find the length of the third side of a triangle when given two sides and the included angle.
- Use the Law of Cosines to find any angle of a triangle when given all three sides of a triangle.
- Use the Law of Sines to find the measure of an angle or the length of a side in a triangle.
- Given SSA, determine whether or not there are possible triangles, and if so, find the other side length and angle measures.
- Given 3 sides of a triangle, find the area of a triangle using Heron’s formula.
- Given SAS, find the area of a triangle.
- Convert a vector from polar form to rectangular form.
- Convert a vector from rectangular form to polar form.
- Given two vectors, be able to add them or subtract them.
- Convert a vector from rectangular form to polar form.

#### 12TH GRADE: COLLEGE ALGEBRA

##### Entrance & Exit Goals

**Before entering Honors College Algebra, a student should be able to:**

- Graph a line.
- Solve multistep equations in one and two variables.
- Solve quadratic equations.
- Factor polynomials completely.

**When exiting Honors College Algebra, a student should be able to:**

- Use basic counting principles, including permutations and combinations.
- Solve compound event problems involving union, intersection, and complement.
- Display categorical and quantitative data in various and appropriate graphs.
- Quantify data using measures of central tendency and spread.
- Perform operations with matrices and use them to solve systems of equations.
- Perform operations with functions, such as arithmetic operations, composition, transformations, stretches, and compressions.
- Fit linear models to data.
- Solve quadratic equations and quadratic inequalities, including complex numbers.
- Find the zeros of polynomial functions by approximation and using simple algebraic methods.
- Given its zeros and their multiplicities, construct a polynomial function and sketch its graph.
- Use matrices to solve systems of equations and model real-world situations.
- Solve rational, radical, exponential, and logarithmic equations.
- Graph rational, radical, exponential, and logarithmic equations
- Work with simple and compound interest.
- Work with mortgages and amortization schedules.

##### Learning Objectives

**Unit 1 – Probability and Combinatorics:**

Students will be able to:

- Use and understand set notation.
- Understand basic concepts of sets, such as elements, subsets, intersections, unions, and complements.
- Draw and interpret Venn Diagrams.
- Calculate the probability of an event and its complement.
- Calculate probability of, and work with combined events, mutually exclusive events, independent events, Venn Diagrams, and tables.
- Solve problems with and without replacement.
- Work with conditional probability using the formula and other methods.
- Distinguish between situations involving permutations and combinations.

**Unit 2 – Descriptive Statistics:**

Students will be able to:

- Calculate measures of center (mean, median) for a distribution of quantitative data.
- Calculate and interpret measures of variability (range, standard deviation, IQR) for a distribution of quantitative data.
- Make and interpret boxplots of quantitative data.
- Identify outliers using the 1.5×IQR rule.
- Use the Empirical Rule to estimate the proportion of values in a specified interval for a Normal distribution.
- Find the proportion of values in a specified interval in a Normal distribution using technology.

**Unit 3 – Equations and Inequalities:**

Students will be able to:

- Recognize linear equations.
- Solve linear equations with integer coefficients.
- Solve linear equations involving fractions.
- Solve linear equations involving decimals.
- Recognize rational equations.
- Solve rational equations that lead to linear equations.
- Solve quadratic equations by factoring and the zero-product property.
- Solve quadratic equations using the square root property.
- Solve quadratic equations using the quadratic formula.
- Solve higher-order polynomial equations by factoring.
- Solve equations that are quadratic in form.
- Solve equations involving single radicals.
- Solve linear inequalities.
- Solve three-part inequalities.
- Solve quadratic inequalities.
- Solve an absolute value equation.
- Solve an absolute value “less than” inequality.
- Solve an absolute value “greater than” inequality.

**Unit 4 – Graphs:**

Students will be able to:

- Plot ordered pairs.
- Find intercepts of a graph given an equation.
- Find the midpoint of a line segment using the midpoint formula.
- Find the distance between two points using the distance formula.
- Write the standard form of an equation of a circle.
- Sketch the graph of a circle.
- Convert the general form of a circle into standard form.
- Determine the slope of a line.
- Sketch a line given a point and the slope.
- Find the equation of a line using the point-slope form.
- Find the equation of a line using the slope-intercept form.
- Write the equation of a line in standard form.
- Find the slope and the y-intercept of a line in standard form.
- Sketch lines by plotting intercepts.
- Find the equation of a horizontal line and a vertical line.
- Determine whether two lines are parallel, perpendicular, or neither.
- Find the equations of parallel and perpendicular lines.

**Unit 5 – Functions and Their Graphs:**

Students will be able to:

- Compare and contrast the definitions of relations and functions.
- Determine whether equations represent functions.
- Use function notation to evaluate functions.
- Use the vertical line test.
- Determine the domain of a function given the equation.
- Determine the intercepts of a function.
- Determine the domain and range of a function from its graph.
- Determine whether a function is increasing, decreasing, or constant.
- Determine relative maximum and relative minimum values of a function.
- Determine whether a function is even, odd, or neither.
- Determine information about a function from a graph.
- Sketch the graphs of the basic functions.
- Sketch the graphs of basic functions with restricted domains.
- Analyze piecewise-defined functions.
- Use vertical shifts to graph functions.
- Use horizontal shifts to graph functions.
- Use reflections to graph functions.
- Use vertical stretches and compressions to graph functions.
- Use combinations of transformations to graph functions.
- Form and evaluate composite functions.

**Unit 6 – Linear, Quadratic, and Polynomial Functions:**

Students will be able to:

- Summarize the definition of a quadratic function and its graph.
- Graph quadratic functions written in vertex form.
- Graph quadratic functions using the vertex formula.
- Determine the equation of a quadratic function given its graph.
- Maximize projectile motion functions.
- Maximize functions in economics.
- Summarize the definition of a polynomial function.
- Sketch the graphs of power functions.
- Determine the end behavior of polynomial functions.
- Determine the intercepts of a polynomial function.
- Determine the real zeros of polynomial functions and their multiplicities.
- Sketch the graph of a polynomial function.
- Determine a possible equation of a polynomial function given its graph.
- Find the domain and intercepts of rational functions.
- Identify vertical asymptotes.
- Identify horizontal asymptotes.
- Use transformations to sketch the graphs of rational functions.
- Find removable discontinuities, intercepts, asymptotes and sketch graphs of rational functions.

**Unit 7 – Exponential and Logarithmic Functions:**

Students will be able to:

- Summarize the characteristics of exponential functions.
- Sketch the graphs of exponential functions using transformations.
- Solve exponential equations by relating the bases.
- Solve problems involving applications of exponential functions.
- Demonstrate the definition of a logarithmic function.
- Evaluate logarithmic expressions.
- Solve problems using the common and natural logarithms.
- Summarize the characteristics of logarithmic functions.
- Sketch the graphs of logarithmic functions using transformations.
- Find the domain of logarithmic functions.
- Use the product rule, quotient rule, and power rule for logarithms.
- Expand and condense logarithmic expressions.
- Solve logarithmic equations using both the logarithm property of equality and by converting logarithmic form to exponential form.
- Evaluate logarithms using the change of base formula.
- Solve exponential equations by taking the logarithm of both sides.
- Solve problems involving compound interest applications.
- Solve problems involving exponential growth and decay applications.

**Unit 8 – Systems of Equations and Matrices:**

Students will be able to:

- Solve a system of linear equations in two variables by using the substitution method and the elimination method.
- Add and subtract matrices.
- Multiply matrices with a scalar and with other matrices.
- Calculate the determinant of a second-order matrix.
- Use Cramer’s Rule to solve a system of two equations.

**Unit 9 – Financial Literacy:**

Students will be able to:

- Find the simple interest using the simple interest formula.
- Find the maturity value of a loan.
- Convert months to a fractional or decimal part of a year.
- Find the principal, rate, or time using the simple interest formula.
- Find the exact time.
- Find the due date.
- Find the ordinary interest and the exact interest.
- Find the bank discount and proceeds for a simple discount note.
- Distinguish between simple interest notes and simple discount notes.
- Find the maturity value necessary to provide a needed amount of proceeds.
- Determine the allocation of a partial payment to interest and principal and find the amount due at maturity.
- Use the formula, calculate the compound interest and future value.
- Calculate the effective interest rate.
- Find the present value of a sum of money that is accruing compound interest.
- Given the cost of a down payment, calculate the amount of money borrowed from the bank and the amount of interest accrued.
- Understand points and calculate the corresponding dollar amount.
- Find the fixed monthly mortgage payment.
- Construct a loan repayment schedule.
- Explain the purpose, requirements, and responsibilities of a loan.
- Describe types of loans: automobile, personal, home equity, home mortgage; student – secured (collateral) and unsecured (non-collateral).
- Examine a variety of loan sources.
- Compare interest rates available for loans.
- Complete a loan application.
- Evaluate factors that affect creditworthiness.
- Explain the purpose and components of credit reports (including the credit report score) and laws affecting credit.
- Evaluate the terms and conditions of consumer loans, including length of time to pay off loans.
- Compare annual fees.
- Compare late payment penalties.
- Compare allowable maximum balances.
- Analyze the benefits and cost of consumer credit.
- Compare sources of consumer credit.
- Evaluate the terms and conditions of credit cards.
- Compare annual percentage rates (APR).

#### 12TH GRADE: AP STATISTICS

##### Entrance & Exit Goals

**Before entering AP Statistics, a student should be able to:**

- Solve basic linear, quadratic, and logarithmic equations
- work independently, or in small groups, on multiple-step problems
- clearly express thoughts, both verbally and written, using complete sentences.

**When exiting AP Statistics, a student should be able to:**

- interpret data represented in graphs and tables
- create appropriate graphs with data
- present data with an appropriate model and make valid predictions from the model
- find basic probabilities
- identify and/or avoid bias in data collection
- design a valid experiment
- calculate a confidence interval and interpret it within the context of the situation
- perform a hypothesis test and interpret it within the context of the problem
- interpret statistical software output and use a graphing calculator to perform appropriate calculations
- critically assess a real-world problem and choose an appropriate method to attack the problem
- take and pass the national AP Statistics exam

##### Learning Objectives

**Unit 1 – Collecting Data:**

Students will be able to:

- Identify the population and sample in a statistical study.
- Identify voluntary response sampling and convenience sampling and explain how these sampling methods can lead to bias.
- Describe how to select a simple random sample with technology or a table of random digits.
- Describe how to select a sample using stratified random sampling and cluster sampling, distinguish stratified random sampling from cluster sampling, and give an advantage of each method.
- Explain how undercoverage, nonresponse, question wording, and other aspects of a sample survey can lead to bias.
- Explain the concept of confounding and how it limits the ability to make cause-and-effect conclusions.
- Distinguish between an observational study and an experiment and identify the explanatory and response variables in each type of study.
- Identify the experimental units and treatments in an experiment.
- Describe the placebo effect and the purpose of blinding in an experiment.
- Describe how to randomly assign treatments in an experiment using slips of paper, technology, or a table of random digits.
- Explain the purpose of comparison, random assignment, control, and replication in an experiment.
- Describe a completely randomized design for an experiment.
- Describe a randomized block design and a matched pairs design for an experiment and explain the purpose of blocking in an experiment.
- Explain the concept of sampling variability when making an inference about a population and how sample size affects sampling variability.
- Explain the meaning of statistically significant in the context of an experiment and use simulation to determine if the results of an experiment are statistically significant.
- Identify when it is appropriate to make an inference about a population and when it is appropriate to make an inference about cause and effect.
- Evaluate if a statistical study has been carried out in an ethical manner.

**Unit 2 – Data Analysis:**

Students will be able to:

- Identify the individuals and variables in a set of data.
- Classify variables as categorical or quantitative.
- Make and interpret bar graphs for categorical data.
- Identify what makes some graphs of categorical data misleading.
- Calculate marginal and joint relative frequencies from a two-way table.
- Calculate conditional relative frequencies from a two-way table.
- Use bar graphs to compare distributions of categorical data.
- Describe the nature of the association between two categorical variables.
- Make and interpret dotplots, stemplots, and histograms of quantitative data.
- Identify the shape of a distribution from a graph.
- Describe the overall pattern (shape, center, and variability) of a distribution and identify any major departures from the pattern (outliers).
- Compare distributions of quantitative data using dotplots, stemplots, and histograms.
- Calculate measures of center (mean, median) for a distribution of quantitative data.
- Calculate and interpret measures of variability (range, standard deviation, IQR) for a distribution of quantitative data.
- Explain how outliers and skewness affect measures of center and variability.
- Identify outliers using the 1.5×IQR rule.
- Make and interpret boxplots of quantitative data.
- Use boxplots and numerical summaries to compare distributions of quantitative data.

**Unit 3 – Modeling Distributions of Data:**

Students will be able to:

- Find and interpret the percentile of an individual value within a distribution of data.
- Estimate percentiles and individual values using a cumulative relative frequency graph.
- Find and interpret the standardized score (z-score) of an individual value within a distribution of data.
- Describe the effect of adding, subtracting, multiplying by, or dividing by a constant on the shape, center, and variability of a distribution of data.
- Use a density curve to model distributions of quantitative data.
- Identify the relative locations of the mean and median of a distribution from a density curve.
- Use the 68–95–99.7 rule to estimate (i) the proportion of values in a specified interval, or (ii) the value that corresponds to a given percentile in a Normal distribution.
- Find the proportion of values in a specified interval in a Normal distribution using Table A or technology.
- Find the value that corresponds to a given percentile in a Normal distribution using Table A or technology.
- Determine whether a distribution of data is approximately Normal from graphical and numerical evidence.

**Unit 4 – Probability – What Are the Chances?**

Students will be able to:

- Interpret probability as a long-run relative frequency.
- Use simulation to model chance behavior.
- Give a probability model for a chance process with equally likely outcomes and use it to find the probability of an event.
- Use basic probability rules, including the complement rule and the addition rule for mutually exclusive events.
- Use a two-way table or Venn diagram to model a chance process and calculate probabilities involving two events.
- Apply the general addition rule to calculate probabilities.
- Calculate and interpret conditional probabilities.
- Determine whether two events are independent.
- Use the general multiplication rule to calculate probabilities.
- Use a tree diagram to model a chance process involving a sequence of outcomes and to find probabilities.
- When appropriate, use the multiplication rule for independent events to calculate probabilities.

**Unit 5 – Random Variables:**

Students will be able to:

- Use the probability distribution of a discrete random variable to calculate the probability of an event.
- Make a histogram to display the probability distribution of a discrete random variable and describe its shape.
- Calculate and interpret the mean (expected value) of a discrete random variable.
- Calculate and interpret the standard deviation of a discrete random variable.
- Use the probability distribution of a continuous random variable (uniform or Normal) to calculate the probability of an event.
- Describe the effect of adding or subtracting a constant or multiplying or dividing by a constant on the probability distribution of a random variable.
- Calculate the mean and standard deviation of the sum or difference of random variables.
- Find probabilities involving the sum or difference of independent Normal random variables.
- Determine whether the conditions for a binomial setting are met.
- Calculate and interpret probabilities involving binomial distributions.
- Calculate the mean and standard deviation of a binomial random variable. Interpret these values in context.
- When appropriate, use the Normal approximation to the binomial distribution to calculate probabilities.
- Find probabilities involving geometric random variables.

**Unit 6 – Sampling Distributions:**

Students will be able to:

- Distinguish between a parameter and a statistic.
- Create a sampling distribution using all possible samples from a small population.
- Use the sampling distribution of a statistic to evaluate a claim about a parameter.
- Distinguish among the distribution of a population, the distribution of a sample, and the sampling distribution of a statistic.
- Determine if a statistic is an unbiased estimator of a population parameter.
- Describe the relationship between sample size and the variability of a statistic.
- Calculate the mean and standard deviation of the sampling distribution of a sample proportion and interpret the standard deviation.
- Determine if the sampling distribution of is approximately Normal.
- If appropriate, use a Normal distribution to calculate probabilities involving .
- Explain how the shape of the sampling distribution of is affected by the shape of the population distribution and the sample size.
- Calculate the mean and standard deviation of the sampling distribution of a sample mean and interpret the standard deviation.
- If appropriate, use a Normal distribution to calculate probabilities involving .
- Explain how the shape of the sampling distribution of is affected by the shape of the population distribution and the sample size.

**Unit 7 – Estimating with Confidence:**

Students will be able to:

- Identify an appropriate point estimator and calculate the value of a point estimate.
- Interpret a confidence interval in context.
- Determine the point estimate and margin of error from a confidence interval.
- Use a confidence interval to make a decision about the value of a parameter.
- Interpret a confidence level in context.
- Describe how the sample size and confidence level affect the margin of error.
- Explain how practical issues like nonresponse, undercoverage, and response bias can affect the interpretation of a confidence interval.
- State and check the Random, 10%, and Large Counts conditions for constructing a confidence interval for a population proportion.
- Determine the critical value for calculating a C% confidence interval for a population proportion using a table or technology.
- Construct and interpret a confidence interval for a population proportion.
- Determine the sample size required to obtain a C% confidence interval for a population proportion with a specified margin of error.
- Determine the critical value for calculating a C% confidence interval for a population mean using a table or technology.
- State and check the Random, 10%, and Normal/Large Sample conditions for constructing a confidence interval for a population mean.
- Construct and interpret a confidence interval for a population mean.
- Determine the sample size required to obtain a C% confidence interval for a population mean with a specified margin of error.

**Unit 8 – Testing a Claim:**

Students will be able to:

- State appropriate hypotheses for a significance test about a population parameter.
- Interpret a P-value in context.
- Make an appropriate conclusion for a significance test.
- Interpret a Type I and a Type II error in context. Give a consequence of each error in a given setting.
- State and check the Random, 10%, and Large Counts conditions for performing a significance test about a population proportion.
- Calculate the standardized test statistic and P-value for a test about a population proportion.
- Perform a significance test about a population proportion.
- State and check the Random, 10%, and Normal/Large Sample conditions for performing a significance test about a population mean.
- Calculate the standardized test statistic and P-value for a test about a population mean.
- Perform a significance test about a population mean.

**Unit 9 – Comparing Two Populations or Treatments:**

Students will be able to:

- Use a confidence interval to make a conclusion for a two-sided test about a population parameter.
- Interpret the power of a significance test and describe what factors affect the power of a test.
- Describe the shape, center, and variability of the sampling distribution of
- Determine whether the conditions are met for doing about a difference between two proportions.
- Construct and interpret a confidence interval for a difference between two proportions.
- Calculate the standardized test statistic and P-value for a test about a difference between two proportions.
- Perform a significance test about a difference between two proportions.
- Describe the shape, center, and variability of the sampling distribution of
- Determine whether the conditions are met for doing inference about a difference between two means.
- Construct and interpret a confidence interval for a difference between two means.
- Calculate the standardized test statistic and P-value for a test about a difference between two means.
- Perform a significance test for the difference between two means.
- Analyze the distribution of differences in a paired data set using graphs and summary statistics.
- Construct and interpret a confidence interval for a mean difference.
- Perform a significance test about a mean difference.
- Determine when it is appropriate to use paired t procedures versus two-sample t procedures.

**Unit 10 – Inference for Distributions of Categorical Data:**

Students will be able to:

- State appropriate hypotheses and compute the expected counts and chi-square statistic for a chi-square test for goodness of fit.
- Calculate the chi-square statistic, degrees of freedom, and P-value for a chi-square test for goodness of fit.
- State and check the Random, 10%, and Large Counts conditions for performing a chi-square test for goodness of fit.
- Perform a chi-square test for goodness of fit.
- Conduct a follow-up analysis when the results of a chi-square test are statistically significant.
- State appropriate hypotheses and compute the expected counts and chi-square test statistic for a chi-square test based on data in a two-way table.
- State and check the Random, 10%, and Large Counts conditions for a chi-square test based on data in a two-way table.
- Calculate the degrees of freedom and P-value for a chi-square test based on data in a two-way table.
- Perform a chi-square test for homogeneity.
- Perform a chi-square test for independence.
- Choose the appropriate chi-square test in a given setting.

**Unit 11 – Describing Relationship:**

Students will be able to:

- Distinguish between explanatory and response variables for quantitative data.
- Make a scatterplot to display the relationship between two quantitative variables.
- Describe the direction, form, and strength of a relationship displayed in a scatterplot and identify unusual features.
- Interpret the correlation.
- Understand the basic properties of correlation, including how the correlation is influenced by outliers.
- Distinguish correlation from causation.
- Make predictions using regression lines, keeping in mind the dangers of extrapolation.
- Calculate and interpret a residual.
- Interpret the slope and y intercept of a least-squares regression line.
- Determine the equation of a least-squares regression line using technology or computer output.
- Construct and interpret residual plots to assess whether a regression model is appropriate.
- Interpret the standard deviation of the residuals and use these values to assess how well the least-squares regression line models the relationship between two variables.
- Describe how the slope, y intercept, standard deviation of the residuals, and are influenced by outliers.
- Find the slope and y intercept of the least-squares regression line from the means and standard deviations of x and y and their correlation.
- Check the conditions for performing inference about the slope of the population (true) regression line.
- Interpret the values of , , s, and in context, and determine these values from computer output.
- Construct and interpret a confidence interval for the slope of the population (true) regression line.
- Perform a significance test about the slope of the population (true) regression line.
- Use transformations involving powers and roots to find a power model that describes the relationship between two variables and use the model to make predictions.
- Use transformations involving logarithms to find a power model that describes the relationship between two quantitative variables and use the model to make predictions.
- Use transformations involving logarithms to find an exponential model that describes the relationship between two quantitative variables and use the model to make predictions.
- Determine which of several transformations does a better job of producing a linear relationship.

#### 12TH GRADE: AP CALCULUS AB

##### Entrance & Exit Goals

**Before entering AP Calculus AB, a student should be able to:**

- Simplify, graph, and solve algebraic and trigonometric functions.
- Simplify, graph, and solve exponential and logarithmic functions.
- Understand the properties and behavior of functions.
- Use geometric formulas to find areas and volumes.
- Use coordinate geometry to solve problems.

When exiting AP Calculus AB, a student should be able to:

- Evaluate limits from tables, graphs, and analytically including determining when a limit does not exist.
- Understand and communicate information regarding the continuity of a function, including applying the Intermediate Value Theorem and the Extreme Value Theorem.
- Understand the relationship between rates of change and derivatives.
- Find the derivative of a function using multiple rules and methods of differentiation.
- Analyze a function using derivatives to determine increasing and decreasing behavior, Extreme values, can concavity.
- Apply the Mean Value Theorem.
- Find antiderivatives and evaluate indefinite integrals.
- Approximate the area under a curve using the rectangle approximation method and Riemann sums.
- Understand the relationship between definite integrals and the area under a curve.
- Understand and apply the Fundamental Theorem of Calculus and the Second Fundamental Theorem of Calculus.
- Determine the average value of a function on an interval.
- Solve differential equations using separation of variables.
- Apply integral calculus to solve real world problems involving exponential growth and decay, particle motion, the area between two curves, and volumes of special solids.
- Determine the reasonableness of solutions, including sign, size, relative accuracy, and units of measurement.
- Take and pass the national AP Calculus AB exam.

##### Learning Objectives

**Unit 1 – Limits and Continuity:**

Students will be able to:

- Study and use a formal definition of a limit.
- Evaluate a limit using properties of limits.
- Develop and use a strategy for finding limits.
- Evaluate a limit using dividing out and rationalizing techniques.
- Evaluate a limit using the Squeeze Theorem.
- Determine continuity at a point and on an open interval.
- Determine one-sided limits and continuity on a closed interval.
- Understand and use the Intermediate Value Theorem.
- Determine infinite limits from the left and from the right.
- Find and sketch the vertical asymptotes of the graph of a function.
- Determine limits at infinity and negative infinity.
- Find and sketch the horizontal asymptotes of the graph of a function.

**Unit 2 – Differentiation – Definition and Fundamental Properties:**

Students will be able to:

- Find the slope of the tangent line to a curve at a point.
- Use the limit definition to find the derivative of a function.
- Understand the relationship between differentiability and continuity.
- Find the derivative of a function using the Constant Rule.
- Find the derivative of a function using the Power Rule.
- Find the derivative of a function using the Constant Multiple Rule.
- Find the derivative of a function using the Sum and Difference Rules.
- Find the derivative of sine, cosine and exponential functions.
- Use derivatives to find rates of change.
- Find the derivative of a function using the Product Rule and the Quotient Rule.
- Find the derivative of a trigonometric function.

**Unit 3 – Differentiation – Composite, Implicit, and Inverse Functions:**

Students will be able to:

- Find the derivative of a composite function using the Chain Rule.
- Find the derivative of a function using the General Power Rule.
- Simplify the derivative of a function using algebra.
- Find the derivative of a function involving the natural log function.
- Define and differentiate exponential functions that have bases other than e
- Distinguish between functions written in implicit and explicit forms.
- Use implicit differentiation to find the derivative of a function.
- Find derivatives of a function using logarithmic differentiation.
- Find the derivative of an inverse function.

**Unit 4 – Contextual Application of Differentiation:**

Students will be able to:

- Differentiate an inverse trigonometric function.
- Identify an appropriate mathematical rule or procedure based on the relationship between concepts or processes to solve problems.
- Apply appropriate mathematical rules to solve straight-line motion problems connecting position, velocity, and acceleration.
- Identify common underlying structures in problems involving rates of change in contexts other than motion.
- Find related rates and use them to solve real-world problems.
- Approximate values of a function using local linearity and explain how an approximated value relates to the actual value.
- Determine limits of indeterminate forms using L’Hospital’s Rule.
- Understand and use Rolle’s Theorem and the Mean Value Theorem.

**Unit 5 – Analytical Applications of Differentiation:**

Students will be able to:

- Determine intervals on which a function is increasing or decreasing.
- Apply the First Derivative Test to find relative extrema of a function.
- Determine intervals on which a function is concave upward or concave downward.
- Find any points of inflection of the graph of a function.
- Apply the Second Derivative Test to find relative extrema of a function.
- Determine finite limits at Infinity.
- Determine horizontal asymptotes, if any, of a function.
- Determine infinite limits at Infinity.
- Analyze and sketch the graph of a function.
- Solve applied maximum and minimum problems – optimum solutions to real world problems.
- Understand the concept of the tangent line approximation.
- Compare the value of the differential, dy, with the actual change in y, ∆y.
- Find the differential of a function using differentiation formulas.
- Write the general solution of a differential equation.

**Unit 6 – Integration and Accumulation of Change:**

Students will be able to:

- Use indefinite integral notation for antiderivatives.
- Use basic integration rules to find antiderivatives.
- Find a particular solution of a differential equation.
- Use sigma notation to write and evaluate a sum.
- Understand the concept of area under a curve.
- Approximate the area of a plane region.
- Find the area of a plane region using limits.
- Understand and apply the definition of a Riemann Sum.
- Evaluate a definite integral using limits.
- Evaluate a definite integral using properties of definite integrals.
- Understand the difference between a right sum, a left sum, a midpoint sum, and a trapezoidal S sum.
- Evaluate a definite integral using The Fundamental Theorem of Calculus.
- Understand and use the Mean Value Theorem for Integrals.
- Find the average value of a function over a closed interval.
- Understand and use the Second Fundamental Theorem of Calculus.
- Use pattern recognition to evaluate an indefinite integral.
- Use a change of variables to evaluate an indefinite integral.
- Use the General Power Rule for Integration to evaluate an indefinite integral.
- Use a change of variables to evaluate a definite integral.
- Evaluate a definite integral involving an even or odd function.
- Use the Log Rule for Integration to integrate a rational function.
- Integrate trigonometric functions.
- Integrate functions whose antiderivatives involve inverse trigonometric functions.
- Use the method of completing the square to integrate a function.

**Unit 7 – Differential Equations:**

Students will be able to:

- Use separation of variables to solve a simple differential equation.
- Use exponential functions to model growth and decay of real-world phenomena.
- Use initial conditions to find particular solutions of differential equations.
- Use a slope field to sketch solutions of a differential equation.

**Unit 8 – Applications of Integration:**

Students will be able to:

- Find the area of a region between two curves using integration.
- Find the area of a region between intersecting curves using integration.
- Describe integration as an accumulation process.
- Find the volume of a solid of revolution using the disk method.
- Find the volume of a solid of revolution using the washer method.
- Find the volume of a solid with known cross sections.
- Find the volume of a solid of revolution using the shell method.
- Compare the uses of the washer method and the shell method.