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College Algebra

Practice Test

College AlgebraPractice Test
  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 Systems of Equations and Inequalities
    1. Introduction to Systems of Equations and Inequalities
    2. 7.1 Systems of Linear Equations: Two Variables
    3. 7.2 Systems of Linear Equations: Three Variables
    4. 7.3 Systems of Nonlinear Equations and Inequalities: Two Variables
    5. 7.4 Partial Fractions
    6. 7.5 Matrices and Matrix Operations
    7. 7.6 Solving Systems with Gaussian Elimination
    8. 7.7 Solving Systems with Inverses
    9. 7.8 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
  9. 8 Analytic Geometry
    1. Introduction to Analytic Geometry
    2. 8.1 The Ellipse
    3. 8.2 The Hyperbola
    4. 8.3 The Parabola
    5. 8.4 Rotation of Axes
    6. 8.5 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
  10. 9 Sequences, Probability, and Counting Theory
    1. Introduction to Sequences, Probability and Counting Theory
    2. 9.1 Sequences and Their Notations
    3. 9.2 Arithmetic Sequences
    4. 9.3 Geometric Sequences
    5. 9.4 Series and Their Notations
    6. 9.5 Counting Principles
    7. 9.6 Binomial Theorem
    8. 9.7 Probability
    9. Chapter Review
      1. Key Terms
      2. Key Equations
      3. Key Concepts
    10. Exercises
      1. Review Exercises
      2. Practice Test
  11. 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
  12. Index

Practice Test

1.

The population of a pod of bottlenose dolphins is modeled by the function A(t)=8 (1.17) t , A(t)=8 (1.17) t , where t t is given in years. To the nearest whole number, what will the pod population be after 3 3 years?

2.

Find an exponential equation that passes through the points (0, 4) (0, 4) and (2, 9). (2, 9).

3.

Drew wants to save $2,500 to go to the next World Cup. To the nearest dollar, how much will he need to invest in an account now with 6.25% 6.25% APR, compounding daily, in order to reach his goal in 4 4 years?

4.

An investment account was opened with an initial deposit of $9,600 and earns 7.4% 7.4% interest, compounded continuously. How much will the account be worth after 15 15 years?

5.

Graph the function f(x)=5 ( 0.5 ) x f(x)=5 ( 0.5 ) x and its reflection across the y-axis on the same axes, and give the y-intercept.

6.

The graph shows transformations of the graph of f(x)= ( 1 2 ) x . f(x)= ( 1 2 ) x . What is the equation for the transformation?

Graph of f(x)= (1/2)^x.
7.

Rewrite log 8.5 ( 614.125 )=a log 8.5 ( 614.125 )=a as an equivalent exponential equation.

8.

Rewrite e 1 2 =m e 1 2 =m as an equivalent logarithmic equation.

9.

Solve for x x by converting the logarithmic equation lo g 1 7 (x)=2 lo g 1 7 (x)=2 to exponential form.

10.

Evaluate log(10,000,000) log(10,000,000) without using a calculator.

11.

Evaluate ln( 0.716 ) ln( 0.716 ) using a calculator. Round to the nearest thousandth.

12.

Graph the function g(x)=log( 126x )+3. g(x)=log( 126x )+3.

13.

State the domain, vertical asymptote, and end behavior of the function f(x)= log 5 ( 3913x )+7. f(x)= log 5 ( 3913x )+7.

14.

Rewrite log( 17a2b ) log( 17a2b ) as a sum.

15.

Rewrite log t ( 96 ) log t ( 8 ) log t ( 96 ) log t ( 8 ) in compact form.

16.

Rewrite log 8 ( a 1 b ) log 8 ( a 1 b ) as a product.

17.

Use properties of logarithm to expand ln( y 3 z 2 x4 3 ). ln( y 3 z 2 x4 3 ).

18.

Condense the expression 4ln( c )+ln( d )+ ln( a ) 3 + ln( b+3 ) 3 4ln( c )+ln( d )+ ln( a ) 3 + ln( b+3 ) 3 to a single logarithm.

19.

Rewrite 16 3x5 =1000 16 3x5 =1000 as a logarithm. Then apply the change of base formula to solve for x x using the natural log. Round to the nearest thousandth.

20.

Solve ( 1 81 ) x 1 243 = ( 1 9 ) 3x1 ( 1 81 ) x 1 243 = ( 1 9 ) 3x1 by rewriting each side with a common base.

21.

Use logarithms to find the exact solution for 9 e 10a8 5=41 9 e 10a8 5=41 . If there is no solution, write no solution.

22.

Find the exact solution for 10 e 4x+2 +5=56. 10 e 4x+2 +5=56. If there is no solution, write no solution.

23.

Find the exact solution for 5 e 4x1 4=64. 5 e 4x1 4=64. If there is no solution, write no solution.

24.

Find the exact solution for 2 x3 = 6 2x1 . 2 x3 = 6 2x1 . If there is no solution, write no solution.

25.

Find the exact solution for e 2x e x 72=0. e 2x e x 72=0. If there is no solution, write no solution.

26.

Use the definition of a logarithm to find the exact solution for 4log( 2n )7=11 4log( 2n )7=11

27.

Use the one-to-one property of logarithms to find an exact solution for log( 4 x 2 10 )+log( 3 )=log( 51 ) log( 4 x 2 10 )+log( 3 )=log( 51 ) If there is no solution, write no solution.

28.

The formula for measuring sound intensity in decibels D D is defined by the equation D=10log( I I 0 ), D=10log( I I 0 ), where I I is the intensity of the sound in watts per square meter and I 0 = 10 12 I 0 = 10 12 is the lowest level of sound that the average person can hear. How many decibels are emitted from a rock concert with a sound intensity of 4.7 10 1 4.7 10 1 watts per square meter?

29.

A radiation safety officer is working with 112 112 grams of a radioactive substance. After 17 17 days, the sample has decayed to 80 80 grams. Rounding to five significant digits, write an exponential equation representing this situation. To the nearest day, what is the half-life of this substance?

30.

Write the formula found in the previous exercise as an equivalent equation with base e. e. Express the exponent to five significant digits.

31.

A bottle of soda with a temperature of 71° 71° Fahrenheit was taken off a shelf and placed in a refrigerator with an internal temperature of 35° F. 35° F. After ten minutes, the internal temperature of the soda was 63° F. 63° F. Use Newton’s Law of Cooling to write a formula that models this situation. To the nearest degree, what will the temperature of the soda be after one hour?

32.

The population of a wildlife habitat is modeled by the equation P( t )= 360 1+6.2 e 0.35t , P( t )= 360 1+6.2 e 0.35t , where t t is given in years. How many animals were originally transported to the habitat? How many years will it take before the habitat reaches half its capacity?

33.

Enter the data from Table 1 into a graphing calculator and graph the resulting scatter plot. Determine whether the data from the table would likely represent a function that is linear, exponential, or logarithmic.

xf(x)
13
28.55
311.79
414.09
515.88
617.33
718.57
819.64
920.58
1021.42
Table 1
34.

The population of a lake of fish is modeled by the logistic equation P(t)= 16,120 1+25 e 0.75t , P(t)= 16,120 1+25 e 0.75t , where t t is time in years. To the nearest hundredth, how many years will it take the lake to reach 80% 80% of its carrying capacity?

For the following exercises, use a graphing utility to create a scatter diagram of the data given in the table. Observe the shape of the scatter diagram to determine whether the data is best described by an exponential, logarithmic, or logistic model. Then use the appropriate regression feature to find an equation that models the data. When necessary, round values to five decimal places.

35.
xf(x)
120
221.6
329.2
436.4
546.6
655.7
772.6
887.1
9107.2
10138.1
36.
xf(x)
313.98
417.84
520.01
622.7
724.1
826.15
927.37
1028.38
1129.97
1231.07
1331.43
37.
xf(x)
02.2
0.52.9
13.9
1.54.8
26.4
39.3
412.3
515
616.2
717.3
817.9
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