Semester 1 Review Answers

Unit 1 (Chapter 1 Test)
unit 1 review answers

Unit 2 (Chapter 2 Test)
unit 2 review answers

Unit 3 (Chapter 7 Test)
unit 3 review answers

Unit 4 (Chapter 3 Test)
Unit 4 (Chapter 3 Test) answers

Unit 4 Review answers

Unit 4 review answers

4.4: Exponential and Logarithmic Equations

Objectives:

• Solve exponential equations.
• Solve logarithmic equations.

Example 1

Student Example 1

Example 2

Student Example 2

Problem Set 4.4:

# 4-20 even, 26, 30, 76, 78, 108

4.3: Properties of Logarithms

Objectives:

• Evaluate logarithmic expressions using the "Change of Base" formula.
• Rewrite logarithmic expressions using properties of logarithms.

Example 1 & Student Example 1

Example 2 & Student Example 2

Example 3 & Student Example 3

Problem Set 4.3:

#1, 3, 9-12, 23-27,  44-48, 67-72

4.2: Logarithmic Functions

Objectives:

• Use properties of logarithmic functions to evaluate logarithmic expressions.
• Graph logarithmic functions.

Example 1 & Student Example 1

Example 2 & Student Example 2

Example 3

Student Example 3

Example 4

Problem Set 4.2:

#2-14 even, 18, 20, 29, 30, 39-44,62,64,70

4.1: Exponential Functions and their Graphs

Objectives:

• Evaluate exponential functions.
• Graph exponential functions.

Example 1

Student Example 1

Example 2

Student Example 2

Example 3

Student Example 3

Problem Set 4.1

#5-10, 18, 20, 45-48, 62, 68

Unit 3 Review Answers

3.4: Systems of Inequalities

Objectives:

• Sketch graphs of inequalities in two variables.
• Solve systems of inequalities.

Example 1

Student Example 1

Example 2

Student Example 2

Problem Set 3.4:

#10, 12, 28, 36, 46, 71

3.3b: Multivariable Linear Systems

Objectives:

• Solve systems that are inconsistent or have infinitely many solutions.
• Solve non-square systems.

Example 1

Student Example 1

Example 2

Student Example 2

Example 3

Problem Set 3.3b:

#20, 22, 26, 28, 51

3.3a: Multivariable Linear Systems

Objectives:

• Solve systems using back substitution.
• Solve systems using Gaussian Elimination.

Gaussian Elimination Dot Diagram

Example 1

3.3a problem set:

#2, 4, 6, 13, 16, 18

3.2: Two Variable Linear Systems

Objectives:

• Solve linear systems by elimination.
• Classify linear systems.

Example 1

Student Example 1

Example 2

Student Example 2

Example 3
*Error: row speed = 5mph, current speed = 3 
(I made a mistake in solving the system)

Student Example 3

Problem set 3.2

#12, 18, 19, 20, 43, 49, 51, 53

3.1b: Linear and Non-linear Systems of Equations

Objectives:

• Given a word problem, set up and solve a linear or non-linear system of equations.

Example 1

Example 2

Student Example 1

Problem set 3.1b:

64, 65, 67, 68

3.1a: Systems of Equations

Objectives:

• Solve systems by graphing.
• Solve systems algebraically.

Example 1

Example 2

Student Example 1

Problem Set 3.1a:

#2, 6, 8, 16, 26, 44, 48

2.5: Zeros of Polynomials

Objectives:

• Define the "Fundamental Theorem of Algebra".
• Apply the Rational Roots test in finding zeros of polynomials.
• Apply conjugate pairs in finding zeros of polynomials.

Example 1

Student example 1

Example 2

Student example 2

Example 3

Student example 3

Problem set 2.5

# 6, 10, 18, 26, 38, 40, 42, 48, 51, 74

2.4: Complex Numbers

Objectives

• Write complex numbers in standard form.
• Solve quadratic equations with complex roots.

 Example 1

Student Example 1

Example 2

Student Example 2

Example 3

Student Example 3

Example 4

Student Example 4

Problem set 2.4:

# 6, 8, 14, 50, 60, 62, 66, 68, 76, 84

2.3b: Polynomial Synthetic Division

Objectives:

• Divide polynomials using synthetic division.
• Apply the Remainder and Factor Theorems in solving problems.

Example 1

Student Example 1

Example 2

Student Example 2

Example 3 and Student Example 3

Problem set 2.3b

 # 24, 25, 36, 46, 50, 58

2.3a: Polynomial Long Division

Objectives:

• Divide polynomials using long division.

Example 1


Student Example 1


Example 2


Student Example 2


Problem set 2.3a
#1, 5, 7, 8, 14, 15, 16

2.2: Higher Order Polynomials

Objectives:

• Sketch polynomials using:
• Degree
• Leading coefficient test
• Zeros
• Use the Intermediate Value Theorem to locate zeros of a function

Example 1 & Student Example 1

 Example 2

Student Example 2

Example 3

Student Example 3

Problem Set 2.2 (in class):

1-8 (matching)

17, 20, 52, 70, 71, 88

2.1: Quadratic Functions and Models

Objectives:  

• Write quadratic functions in standard form .
• Graph quadratic equations in standard form.  
• Solve applied problems using quadratic equations.

Example 1

Student Example 1

Example 2

Student Example 2

Example 3

Student Example 3

Problem set 2.1 (in class):

#1-8, 19,22, 38, 44,78

1.10: Mathematical Modeling with Variation

Objectives

• Write mathematical models for direct, inverse, and joint variation.

Example 1


Example 2


Example 3


Example 4


Problem Set 1.10
#25-29, 55-58

1.9: Inverse Functions

Objectives:

• Find inverse functions algebraically.
• Find inverse functions graphically.

Example 1


Student Example 1


Example 2


Student Example 2

 
1.9 Problem Set (in class):
# 2-6 even, 19 - 27, 39, 42

1.8: Combinations of Functions

Objectives:

• Combine functions arithmetically.
• Find the composition of two functions.

Example 1

Student example 1

Example 2

Example 3

Example 4

problem set 1.8 (in class)

# 6-12 even, 13-23 odd, 32,33,36,37,45,46,58

1.6/1.7: A Library of Functions & Transformations

Objectives:

• Define and create a library of "parent functions".
• Sketch functions using
• vertical and horizontal shifts
• reflections
• non-rigid transformations (stretches/compressions)

Example 1 & student example 1


Example 2


student example 2


Example 3 & student example 3


Example 4 & student example 4


Example 5 & student example 5



Example 6


Example7


problem sets 1.6/1.7 (in class)

1.6 # 29, 30, 43, 44, 53-60

1.7 # 6, 10, 12, 19-22, 44-46, 51, 52, 54

1.4: Functions

Objectives:

• Use function notation.
• Evaluate functions.
• Find the domain of functions.

Example 1

Example 2

Student Example 1

Example 3

Student Example 2

Example 4 + Student Example 3

Example 5

problem set 1.4 (in class Thursday)

#2-10 even, 16-24 even, 29, 32, 34, 37, 57-63 odd

1.3: Linear Equations in Two Variables

Objectives:

•  Write linear equations in two variables.
• Use equations in two variables to graph linear equations.

Example 1


Student Example 1


Example 2


Student Example 2


problem set 1.3 (in class)
# 9-19 odd, 41, 43, 61, 69, 71 

1.2: Graphs of Equations

Objectives:

• Sketch the graph of an equation.
• Find equations and sketch graphs of circles.

Example 1


Student Example 1


Example 2


Student Example 2


problem set 1.2 (in class Monday)
#1-7 odd, 18, 19, 59-69 odd

ATTENTION

I have decided to wait on posting the 1.2 notes as we did not finish the introduction today during 4th period. This means tonight your homework is to:

• Finish problem set 1.1 (distance and midpoint formulas)
• Come prepared with any questions you have about the distance and midpoint formulas.
• I will elaborate on the intro to 1.2 tomorrow and you will take 1.2 notes over the weekend.

-Tolar

1.1 Rectangular Coordinates

Objectives:

• Plot points in the Cartesian coordinate plane.
• Apply the midpoint and distance formulas.

Example 1


Student Example 1


Example 2


Student Example 2


Example 3


Student Example 3


In Class:
problem set 1.1

Hello world!

Welcome! This is the website where you will come to take notes and watch examples for your Precalculus course. Please bookmark it.


Please watch the video and send an email to tolar@goasa.com with the information referenced in the video. If you have any issue viewing the video, send an email detailing the problem.

I'm looking forward to a great year!

-Mr. Tolar