Honors Pre-Calculus at HHS

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HW Solutions Folder
Chapter 4 HW Solutions

Unit 1 - Sequences and Series

Day 1   13-1 Arithmetic and Geometric Sequences
Assignment: pg. 476, #’s 1, 5, 13, 17, 21, 25, 29, 33, 37, 47, 49, 53, 55, 59, 61

Day 2   13-2 Recursive Definitions
Assignment: pg. 481, #’s 1, 5, 9-21 odd, 22

Day 3   13-3 Arithmetic and Geometric Series and Their Sums
Assignment: pg. 482, #’s 25, 28, 31, 33 and
     pg. 489, #’s 1, 3, 7, 9, 11, 13, 17, 27, 29, 31

Day 4   13-4 Limits of Infinite Sequences
Assignment: pg. 490, #’s 33, 37, 40, 42, 43 and
     pg. 496 #’s 1-33 odd (SKIP #'s 7, 17, 23, 25, 27)

Day 5   13-5 Sums of Infinite Series
Assignment: pg. 502, #’s 3, 9, 11, 17, 21, 29, 33, and 35

Day 6   13-6 Sigma Notation
Assignment: pg. 508, #’s 1 – 37 odd (SKIP #'s 15, 19, 21)

Day 7   13-7 Mathematical Induction
Assignment: pg. 513, #’s 1-11 odd

Day 8   More Mathematical Induction
Assignment: pg. 513, #’s 16, 19, 21, & 25

Day 9   Review

Day 10 Test Chapter 13 (800-point assessment)
(Chapter 13 HW Assignments are due)

Unit 2 - Linear and Quadratic Functions

Day 11 1-1 Points and Lines
   Assignment: pg. 5, #'s 10, 11, 17, 20, 21, 25, 27
     1-2 Slopes of Lines
     Assignment: pg. 11, #'s 13 – 27 odd

Day 12 1-3 Find Equations of Lines
     Assignment: pg. 16, #'s 1 – 19 odd, 21 – 23
     (#24 extra credit due day of the test)
     1-4 Linear Functions and Models (linear regressions)
     Assignment: pg. 22, #'s 1 – 23 odd

Day 13 1-5 The Complex Numbers
     Assignment: pg. 28, #'s 1-45 odd

Day 14 1-6 Solving Quadratic Equations
     Assignment: pg. 35, #'s 17 – 45 every other odd
     1-7 Quadratic Functions and Their Graphs
     Assignment: pg. 41, #'s 3 – 33 multiples of 3, 35, 39

Day 15 1-8 Quadratic Models
     Assignment: pg. 45, #'s 1 – 17 odd

Day 16 Review

Day 17 Test Chapter 1 (500 point assessment)
(Chapter 1 HW Assignments are due)

Unit 3 - Polynomial Functions

Day 18 2-1 Polynomials
   Assignment: pg. 56, #'s 1-31 odd, 34, 35

Day 19 2-2 Synthetic Division, The Remainder and Factor Theorems
Assignment: pg. 61, #'s 1-25 odd

Day 20 2-3 Graphing Polynomial Functions
   Assignment: pg. 66, #'s 1-39 every 3rd

Day 21 2-4 Finding Maximums and Minimums of Polynomial Functions
   Assignment: pg. 71, #'s 1-13 odd; and
     pg. 72, #'s 1-9 odd

Day 22 2-5 Using Technology to Approximate Roots of Polynomial Equations
   Intermediate Value Theorem
   Assignment: pg. 78, #'s 1-17 odd

Day 23 2-6 Solving Polynomial Equations by Factoring
   Assignment: pg. 83, #'s 1-21 odd, 29, 33, 35, 39

Day 24 2-7 General Results for Polynomial Equations
  Assignment: pg. 89, #'s 1, 5, 9, 13, 17, 21- 29 odd

Day 25 Review

Day 26 Test Chapter 2 (700 point assessment)
   (Chapter 2 HW Assignments are due)

Unit 4 - Inequalities, Properties of Functions

Day 27 3-1 Linear & Absolute Value Inequalities
   Assignment: pg. 98, #'s 1, 4, 7, 10, 13, 16, 19, 22, 25, 28, 33, 34
   3-2 Polynomial Inequalities in One Variable
   Assignment: pg. 103, #'s 1 – 43 odd

Day 28 4-1 Functions
   Assignment: pg. 122, #'s 1 – 17 odd, 22

Day 29 4-2 Operations on Functions
   Assignment: pg. 128, #'s 1 – 33 odd

Day 30 4-3 Reflecting Graphs; Symmetry
   Assignment: pg. 136, #'s 1 – 41 odd

Day 31 4-4 Periodic Functions; Stretching and Translating Graphs
   Assignment: pg. 143, #'s 1 - 8

Day 32 4-5 Inverse Functions
   Assignment: pg. 149, #'s 1 – 19 odd, and
   Assignment: pg. 144/, #'s 9 - 19

Day 33 4-6 Functions in Two Variables
     Assignment: pg. 155, #'s 1 – 9 odd, 13 – 19 odd, and
     Assignment: pg. 150, #'s 21 – 31

Day 34 4-7 Forming Functions from Verbal Descriptions
     Assignment: pg. 161, #'s 1 – 31 odd

Day 35 Come up for Air

Day 36 Review

Day 37 Test Chapter 3 sections 1 & 2, Chapter 4 (800 point assessment)
(Chapter 3 and 4 HW assignments are due)

Unit 5 - Exponents and Logarithms

Day 38 5-1 Growth & Decay: Integral Exponents
Assignment: pg. 173, #'s 1 – 45 odd, 46 – 49

Day 39 5-2 Growth & Decay: Rational Exponents
     Assignment: pg. 178, #'s 1 – 57 odd

Day 40 5-3 Exponential Functions
Assignment: pg. 183, #'s 1 – 15

Day 41 5-4 The Number e and the Function
Assignment: pg. 189, #'s 1 – 5

Day 42 Wake up and smell what’s cooking
Assignment: pg. 184, #'s 17 – 29, and
Assignment: pg. 189, #'s 7 – 23 odd, 22

Day 43 5-5 Logarithmic Functions
   Assignment: pg. 194, #'s 1 – 51 odd

Day 44 5-6 Laws of Logarithms
   Assignment: pg. 200, #'s 1 – 39 odd
   5-7 Exponential Functions; Changing Bases
   Assignment: pg. 205, #'s 1 –23 odd

Day 45 Whew!
     Assignment: pg. 202, #'s 41 – 51 odd, and
     Assignment: pg. 206, #'s 25 – 45 odd, 44

Day 46 Review

Day 47 Test Chapter 5 (800 point assessment)
   (Chapter 5 HW assignments are due)

Unit 6 - Analytic Geometry

Day 48 6-1 Coordinate Proofs
   Assignment: pg. 218, #'s 1 – 13 odd

Day 49 6-2 Equations of Circles
     Assignment: pg. 219, #'s 14-18, and
   Assignment: pg. 222, #'s 1-35 odd

Day 50 6-3 Ellipses
   Assignment: pg. 223, #'s 37-59 odd 48, and
   Assignment: pg. 228, #'s 1-23 odd

Day 51 6-4 Hyperbolas
   Assignment: pg. 229, #'s 25-37 odd, 38-42, and
   Assignment: pg. 235, #'s 1-23 odd, 24

Day 52 6-5 Parabolas
   Assignment: pg. 236, #'s 25-45 odd, 26

Day 53 6-6 Systems of Second-Degree Equations
   Assignment: pg. 241, #'s 17-31 odd, 20, and
   Assignment: pg. 244, #'s 1-23 odd

Day 54 6-7 A New Look at Conic Sections
   Assignment: pg. 245, #'s 25-31 odd, and
   Assignment: pg. 250, #'s 1-21 odd

Day 55 Review

Day 56 Test Chapter 6 (700 point assessment)
   (Chapter 6 HW problems are due)

Unit 7 - Trigonometric Functions Part 1 of 4

Day 57 7-1 Measurement of Angles
Assignment: pg. 261, #'s 1-33 odd
7-2 Sectors of Circles
Assignment: pg. 264, #'s 1, 5, 9, 13, 15 – 17, 21, 23, 25

Day 58 7-3 The Sine and Cosine Functions
Assignment: pg. 273, #'s 1 – 23 odd

Day 59 7-4 Evaluation and Graphing Sine and Cosine
Assignment: pg. 279, #'s 1 – 19 odd, and
Assignment: pg. 273, #'s 29 - 43

Day 60 7-5 The Other Trigonometric Functions
Assignment: pg. 285, #'s 3, 6, 11, 15, 17, 20, 21 – 27 odd, and
Assignment: pg. 279, #'s 21 – 33 odd, 34

Day 61 7-6 The Inverse Trigonometric Functions
Assignment: pg.289, #'s 1 – 21 odd, 22 - 30

Day 62 Review for Test

Day 63 Test Chapter 7 (600 point assessment)
(Chapter 7 HW assignments are now due)

Unit 7 - Trigonometric Functions Part 2 of 4

Day 64 8-1 Simple Trigonometric Equations
Assignment: pg. 299, #'s 1 – 29 odd

Day 65 8-2 Sine and Cosine Curves
Assignment: pg. 305, #'s 1, 5, 9, 11, 15, 17, 19, 23, and
Assignment: pg. 300, #'s 31 – 36, 45

Day 66 8-3 Modeling Periodic Behavior
Assignment: pg. 313, #'s 1 – 15 odd, and
Assignment: pg. 306, #'s 25, 27, 29 - 36

Day 67 8-4 Relationships Among the Functions
Assignment: pg. 321, #'s 1 – 23 odd, and
Assignment: pg. 314, #'s 17, 19, 21, 24 - 26

Day 68 8-5 Solving More Difficult Trigonometric Equations
Assignment: pg. 326, #'s 1 – 33 odd, and
Assignment: pg. 321, #'s 28 – 39, 42

Day 69 Review

Day 70 Test Chapter 8 (500 point assessment)
(Chapter 8 HW assignments now due)

Unit 7 - Trigonometric Functions Part 3 of 4

Day 71 9-1 Solving Right Triangles
Assignment: pp 334/1, 7, 13 – 25 odd
9-2 The Area of a Triangle
Assignment: pp 342/1, 7, 9, 15, 19, 31, 33. 35

Day 72 9-3 The Law of Sines
Assignment: pp 347/3, 7, 11, 15, 19, 21 – 25, and
Assignment: pp 337/31, 33, 35, 37, 40

Day 73 9-3 The Law of Cosines
Assignment: pp 352/1, 7, 9, 13, 15, 17, 18, 21, 23

Day 74 More Applications
Assignment: pp 355/1 – 29 odd, 33, 35

Day 75 9-5 Applications of Trigonometry to Navigation and Surveying
Assignment: pp 362/1 – 9, 11 – 18

Day 76 Review

Day 77 Test Chapter 9 (500 point assessment)
(Chapter 9 HW assignments are due now)

Unit 7 - Trigonometric Functions Part 4 of 4

Day 78 10-1 Formulas for sum and difference of sine and cosine
Assignment: pp 373/1 – 27 odd
10-2 Formulas for Tangent
Assignment: pp 377/1, 5 – 19 odd, 23, 29

Day 79 10-3 Double-Angle and Half-Angle Formulas
Assignment: pp 383-1 – 25 odd, and
Assignment: pp 373/29 – 43 odd

Day 80 10-4 Solving Trigonometric Equations
Assignment: pp 389/1 – 43 odd

Day 81 Review

Day 82 Test Chapter 10 (300 point assessment)
(Chapter 10 HW assignments are due now)

Unit 8 - Polar Coordinates and Complex Numbers

Day 83 11-1 Polar Coordinates and Graphs
Assignment: pg. 400, #'s 1, 5, 9, 11, 13, 17, 19, 21, 25, 29 – 34

Day 84 11-2 Polar form of a complex number
Assignment: pg. 406, #'s 7, 11, 15, 17, 21, 23, 26, 28, 30, 31

Day 85 11-3 Powers of Complex Numbers
Assignment: pg. 410, #'s 1, 3, 5, 6, 8, 9, 13, 14, 17, 18

Day 86 11-4 Roots of Complex Numbers
Assignment: pg. 413, #'s 1, 7, 11-16

Day 87 Review for Final

Day 88 Review for Final

Day 89 Review for Final

Day 90 Final Exam (Comprehensive 2000 point assessment)
(Chapter 11 HW assignments are due now)

Unit 1 Objectives: By the completion of this unit, students will be able to

Identify an arithmetic or geometric sequence and find a formula for its nth term.
Use sequences defined recursively to solve problems.
Find the sum of the first n terms of arithmetic or geometric series.
Find or estimate the limit of an infinite sequence or to determine that the limit does not exist.
Find the sum of an infinite geometric series.
Represent series using sigma notation.
Use mathematical induction to prove that a statement is true.

Rubric for Unit 1 Test: Here

Unit 2 Objectives: By the completion of this unit, students will be able to

Find the intersection of two lines and to find the length and the coordinates of the midpoint of a segment.
Find the slope of a line and to determine whether two lines are parallel, perpendicular, or neither.
Find the equation of a line given certain geometric properties of the line.
Model real-world situations by means of linear functions.
Add, Subtract, Multiply, and Divide complex numbers.
Solve quadratic equations using different methods.
Define and graph quadratic functions.
Model real-world situations using quadratic functions.

Rubric for unit 2 test: Here

Unit 3 Objectives: By the completion of this unit, students will be able to

Identify a polynomial function, to evaluate it using synthetic substitution, and to determine its zeros.
Use synthetic division and to apply the remainder and factor theorems.
Graph a polynomial function and to determine an equation for a polynomial graph.
Write a polynomial function for a given situation and to find the maximum or minimum value of the function.
Use technology to approximate the real roots of a polynomial equation.
Solve polynomial equations by various methods of factoring including the use of the rational root theorem.
Apply general theorems about polynomial equations.

Rubric for unit 3 test: here

Unit 4 Objectives: By the completion of this unit, students will be able to

Solve and graph linear inequalities in one variable.
Solve and graph polynomial inequalities in one variable.
Identify a function, to determine the domain, range, and zeros of a function, and to graph a function.
Perform operations on functions and to determine the domains of the resulting functions.
Reflect graphs and to use symmetry to sketch graphs.
Determine periodicity and amplitude from graphs, to stretch and shrink graphs both vertically and horizontally, and to translate graphs.
Find the inverse of a function, if the inverse exists.
Graph functions of two variables in a two-dimensional coordinate system and to read such graphs.
Form a function of one variable from a verbal description and, when appropriate, to determine the minimum or maximum value of the function.

Rubric for unit 4 test: here

Unit 5 Objectives: By the completion of this unit, students will be able to

Define and apply integral exponents.
Define and apply rational exponents.
Define and use exponential functions.
Define and apply the natural exponential function.
Define and apply logarithms.
Prove and apply laws of logarithms.
Solve exponential equations and to change logarithms from one base to another.

Rubric for unit 5 test: here

Unit 6 Objectives: By the completion of this unit, students will be able to

Prove theorems from geometry by using coordinates
Find equations of circles and to find the coordinates of any points where circles and lines meet.
Find the equations of ellipses and to graph them.
Find equations of hyperbolas and to graph them.
Find equations of parabolas and to graph them.
Solve systems of 2nd degree equations.
Define conic sections in terms of eccentricity and to classify the graph of a 2nd degree equation by examining the coefficients in the equation.

Rubric for unit 6 test: here

Unit 7 Objectives: By the completion of this unit, students will be able to

Find the measure of n angle in either degrees or radians and to find co-terminal angles.
Find the arc length and area of a sector of a circle and to solve problems involving apparent size.
Use the definition of sine and cosine to find values of these functions and to solve simple trigonometric equations.
Use reference angles, calculators or tables, and special angles to find values of the sine and cosine functions and to sketch the graphs of these functions.
Find the values of the tangent, secant, co-secant and co-tangent functions and to sketch the functions' graphs.
Find the values of the inverse trigonometric functions.

Rubric for unit 7 Part 1 test: here

Unit 7 Objectives continued: By the completion of this unit, students will be able to

Solve simple trigonometric equations and to apply them.
Find equations of different sine and cosine curves and to apply these equations.
Use trigonometric functions to model periodic behavior.
Simplify trigonometric expressions and to prove trigonometric identities.
Use trigonometric identities or technology to solve more difficult trigonometric equations.

Rubric for unit 7 Part 2 test: here

Unit 7 Objectives continued: By the completion of this unit, students will be able to

Use trigonometry to find unknown sides or angles of a right triangle.
Find the area of a triangle given the lengths of two sides and the measure of the included angle.
Use the law of sines to find unknown part of a triangle.
Use the law of cosines to find unknown parts of a triangle.
Use trigonometry to solve navigation and surveying problems.

Rubric for unit 7 Part 3 test: here

Unit 7 Objectives continued: By the completion of this unit, students will be able to

Derive and apply formulas for sum and difference of angles for sine and cosine.
Derive and apply formulas for sum and difference of angles for tangent.
Derive and apply double angle and half angle formulas.
Use identities to solve trigonometric equations.

Rubric for unit 7 Part 4 test: here

Unit 8 Objectives: By the completion of this unit, students will be able to

Graph Polar equations
Write complex numbers in polar form and to find products in polar form.
Use De Moivre's theorem to find powers of complex numbers.
Find roots of complex numbers

Rubric for final exam: here

HonorsPre-Calculus

Honors
Pre-Calculus