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Algebra and Trigonometry

Practice Test

Algebra and TrigonometryPractice Test
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Table of contents
  1. Preface
  2. 1 Prerequisites
    1. Introduction to Prerequisites
    2. 1.1 Real Numbers: Algebra Essentials
    3. 1.2 Exponents and Scientific Notation
    4. 1.3 Radicals and Rational Exponents
    5. 1.4 Polynomials
    6. 1.5 Factoring Polynomials
    7. 1.6 Rational Expressions
    8. Chapter Review
      1. Key Terms
      2. Key Equations
      3. Key Concepts
    9. Exercises
      1. Review Exercises
      2. Practice Test
  3. 2 Equations and Inequalities
    1. Introduction to Equations and Inequalities
    2. 2.1 The Rectangular Coordinate Systems and Graphs
    3. 2.2 Linear Equations in One Variable
    4. 2.3 Models and Applications
    5. 2.4 Complex Numbers
    6. 2.5 Quadratic Equations
    7. 2.6 Other Types of Equations
    8. 2.7 Linear Inequalities and Absolute Value Inequalities
    9. Chapter Review
      1. Key Terms
      2. Key Equations
      3. Key Concepts
    10. Exercises
      1. Review Exercises
      2. Practice Test
  4. 3 Functions
    1. Introduction to Functions
    2. 3.1 Functions and Function Notation
    3. 3.2 Domain and Range
    4. 3.3 Rates of Change and Behavior of Graphs
    5. 3.4 Composition of Functions
    6. 3.5 Transformation of Functions
    7. 3.6 Absolute Value Functions
    8. 3.7 Inverse Functions
    9. Chapter Review
      1. Key Terms
      2. Key Equations
      3. Key Concepts
    10. Exercises
      1. Review Exercises
      2. Practice Test
  5. 4 Linear Functions
    1. Introduction to Linear Functions
    2. 4.1 Linear Functions
    3. 4.2 Modeling with Linear Functions
    4. 4.3 Fitting Linear Models to Data
    5. Chapter Review
      1. Key Terms
      2. Key Concepts
    6. Exercises
      1. Review Exercises
      2. Practice Test
  6. 5 Polynomial and Rational Functions
    1. Introduction to Polynomial and Rational Functions
    2. 5.1 Quadratic Functions
    3. 5.2 Power Functions and Polynomial Functions
    4. 5.3 Graphs of Polynomial Functions
    5. 5.4 Dividing Polynomials
    6. 5.5 Zeros of Polynomial Functions
    7. 5.6 Rational Functions
    8. 5.7 Inverses and Radical Functions
    9. 5.8 Modeling Using Variation
    10. Chapter Review
      1. Key Terms
      2. Key Equations
      3. Key Concepts
    11. Exercises
      1. Review Exercises
      2. Practice Test
  7. 6 Exponential and Logarithmic Functions
    1. Introduction to Exponential and Logarithmic Functions
    2. 6.1 Exponential Functions
    3. 6.2 Graphs of Exponential Functions
    4. 6.3 Logarithmic Functions
    5. 6.4 Graphs of Logarithmic Functions
    6. 6.5 Logarithmic Properties
    7. 6.6 Exponential and Logarithmic Equations
    8. 6.7 Exponential and Logarithmic Models
    9. 6.8 Fitting Exponential Models to Data
    10. Chapter Review
      1. Key Terms
      2. Key Equations
      3. Key Concepts
    11. Exercises
      1. Review Exercises
      2. Practice Test
  8. 7 The Unit Circle: Sine and Cosine Functions
    1. Introduction to The Unit Circle: Sine and Cosine Functions
    2. 7.1 Angles
    3. 7.2 Right Triangle Trigonometry
    4. 7.3 Unit Circle
    5. 7.4 The Other Trigonometric Functions
    6. Chapter Review
      1. Key Terms
      2. Key Equations
      3. Key Concepts
    7. Exercises
      1. Review Exercises
      2. Practice Test
  9. 8 Periodic Functions
    1. Introduction to Periodic Functions
    2. 8.1 Graphs of the Sine and Cosine Functions
    3. 8.2 Graphs of the Other Trigonometric Functions
    4. 8.3 Inverse Trigonometric Functions
    5. Chapter Review
      1. Key Terms
      2. Key Equations
      3. Key Concepts
    6. Exercises
      1. Review Exercises
      2. Practice Test
  10. 9 Trigonometric Identities and Equations
    1. Introduction to Trigonometric Identities and Equations
    2. 9.1 Verifying Trigonometric Identities and Using Trigonometric Identities to Simplify Trigonometric Expressions
    3. 9.2 Sum and Difference Identities
    4. 9.3 Double-Angle, Half-Angle, and Reduction Formulas
    5. 9.4 Sum-to-Product and Product-to-Sum Formulas
    6. 9.5 Solving Trigonometric Equations
    7. Chapter Review
      1. Key Terms
      2. Key Equations
      3. Key Concepts
    8. Exercises
      1. Review Exercises
      2. Practice Test
  11. 10 Further Applications of Trigonometry
    1. Introduction to Further Applications of Trigonometry
    2. 10.1 Non-right Triangles: Law of Sines
    3. 10.2 Non-right Triangles: Law of Cosines
    4. 10.3 Polar Coordinates
    5. 10.4 Polar Coordinates: Graphs
    6. 10.5 Polar Form of Complex Numbers
    7. 10.6 Parametric Equations
    8. 10.7 Parametric Equations: Graphs
    9. 10.8 Vectors
    10. Chapter Review
      1. Key Terms
      2. Key Equations
      3. Key Concepts
    11. Exercises
      1. Review Exercises
      2. Practice Test
  12. 11 Systems of Equations and Inequalities
    1. Introduction to Systems of Equations and Inequalities
    2. 11.1 Systems of Linear Equations: Two Variables
    3. 11.2 Systems of Linear Equations: Three Variables
    4. 11.3 Systems of Nonlinear Equations and Inequalities: Two Variables
    5. 11.4 Partial Fractions
    6. 11.5 Matrices and Matrix Operations
    7. 11.6 Solving Systems with Gaussian Elimination
    8. 11.7 Solving Systems with Inverses
    9. 11.8 Solving Systems with Cramer's Rule
    10. Chapter Review
      1. Key Terms
      2. Key Equations
      3. Key Concepts
    11. Exercises
      1. Review Exercises
      2. Practice Test
  13. 12 Analytic Geometry
    1. Introduction to Analytic Geometry
    2. 12.1 The Ellipse
    3. 12.2 The Hyperbola
    4. 12.3 The Parabola
    5. 12.4 Rotation of Axes
    6. 12.5 Conic Sections in Polar Coordinates
    7. Chapter Review
      1. Key Terms
      2. Key Equations
      3. Key Concepts
    8. Exercises
      1. Review Exercises
      2. Practice Test
  14. 13 Sequences, Probability, and Counting Theory
    1. Introduction to Sequences, Probability and Counting Theory
    2. 13.1 Sequences and Their Notations
    3. 13.2 Arithmetic Sequences
    4. 13.3 Geometric Sequences
    5. 13.4 Series and Their Notations
    6. 13.5 Counting Principles
    7. 13.6 Binomial Theorem
    8. 13.7 Probability
    9. Chapter Review
      1. Key Terms
      2. Key Equations
      3. Key Concepts
    10. Exercises
      1. Review Exercises
      2. Practice Test
  15. A | Proofs, Identities, and Toolkit Functions
  16. Answer Key
    1. Chapter 1
    2. Chapter 2
    3. Chapter 3
    4. Chapter 4
    5. Chapter 5
    6. Chapter 6
    7. Chapter 7
    8. Chapter 8
    9. Chapter 9
    10. Chapter 10
    11. Chapter 11
    12. Chapter 12
    13. Chapter 13
  17. Index

Practice Test

1.

Assume α α is opposite side a,β a,β is opposite side b, b, and γ γ is opposite side c. c. Solve the triangle, if possible, and round each answer to the nearest tenth, given β=68°,b=21,c=16. β=68°,b=21,c=16.

2.

Find the area of the triangle in Figure 1. Round each answer to the nearest tenth.

A triangle. One angle is 60 degrees with opposite side 6.25. The other two sides are 5 and 7.
Figure 1
3.

A pilot flies in a straight path for 2 hours. He then makes a course correction, heading 15° to the right of his original course, and flies 1 hour in the new direction. If he maintains a constant speed of 575 miles per hour, how far is he from his starting position?

4.

Convert ( 2,2 ) ( 2,2 ) to polar coordinates, and then plot the point.

5.

Convert ( 2, π 3 ) ( 2, π 3 ) to rectangular coordinates.

6.

Convert the polar equation to a Cartesian equation: x 2 + y 2 =5y. x 2 + y 2 =5y.

7.

Convert to rectangular form and graph: r=−3cscθ. r=−3cscθ.

8.

Test the equation for symmetry: r=−4sin( 2θ ). r=−4sin( 2θ ).

9.

Graph r=3+3cosθ. r=3+3cosθ.

10.

Graph r=3−5sinθ. r=3−5sinθ.

11.

Find the absolute value of the complex number 5−9i. 5−9i.

12.

Write the complex number in polar form: 4+i. 4+i.

13.

Convert the complex number from polar to rectangular form: z=5cis( 2π 3 ). z=5cis( 2π 3 ).

Given z 1 =8cis( 36° ) z 1 =8cis( 36° ) and z 2 =2cis( 15° ), z 2 =2cis( 15° ), evaluate each expression.

14.

z 1 z 2 z 1 z 2

15.

z 1 z 2 z 1 z 2

16.

( z 2 ) 3 ( z 2 ) 3

17.

z 1 z 1

18.

Plot the complex number −5−i −5−i in the complex plane.

19.

Eliminate the parameter t t to rewrite the following parametric equations as a Cartesian equation: { x(t)=t+1 y(t)=2 t 2 . { x(t)=t+1 y(t)=2 t 2 .

20.

Parameterize (write a parametric equation for) the following Cartesian equation by using x( t )=acost x( t )=acost and y(t)=bsint: y(t)=bsint: x 2 36 + y 2 100 =1. x 2 36 + y 2 100 =1.

21.

Graph the set of parametric equations and find the Cartesian equation: { x(t)=−2sint y(t)=5cost . { x(t)=−2sint y(t)=5cost .

22.

A ball is launched with an initial velocity of 95 feet per second at an angle of 52° to the horizontal. The ball is released at a height of 3.5 feet above the ground.

  1. ⓐFind the parametric equations to model the path of the ball.
  2. ⓑWhere is the ball after 2 seconds?
  3. ⓒHow long is the ball in the air?

For the following exercises, use the vectors u = i − 3j and v = 2i + 3j.

23.

Find 2u − 3v.

24.

Calculate u⋅v. u⋅v.

25.

Find a unit vector in the same direction as v. v.

26.

Given vector v v has an initial point P 1 =( 2,2 ) P 1 =( 2,2 ) and terminal point P 2 =( −1,0 ), P 2 =( −1,0 ), write the vector v v in terms of i i and j. j. On the graph, draw v, v, and −v. −v.

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