MCC College Algebra Study Guide

MCC MATHEMATICS DEPARTMENT

College Algebra (and trigonometry) Review Questions

(for testing out of MAT 150/151 and into MAT 220/221)

The college algebra placement test requires familiarity with mathematical terminology as well as specific algebra skills. This exam also tests elementary knowledge of trigonometry.

The following are sample college algebra questions that cover material that should be reviewed prior to taking the math placement test. It does not merely target information that is on the placement test but will highlight areas in which proficiency is expected from a student testing out of college algebra. Additional tutorial material is available in the Information Commons to currently enrolled MCC students.

NOTE: While completion of this review material will be helpful in preparing for the math placement test, the MCC math department is unable to guarantee desired placement.

As you prepare to take the college algebra asset test, keep the following points in mind:

  1. At the present time, calculators are NOT allowed when taking the Asset test.
  2. Since the placement test is a timed multiple choice test, study this material with a mind toward speed and accuracy as well as content.
  3. The problems are not graduated in difficulty, therefore if you get stuck on one, go on to another problem.
  4. There are a number of different forms of each placement test, therefore this study guide will contain information that may not appear on your particular version of the test.
  5. The intent of this review material is not to simply get you through the math placement test, but to enable you to review many of the key topics covered in the college algebra (and trig) course that are needed to be successful on the placement test as well as in calculus.

Review Questions
  1. Use the laws of exponents to simplify the following expressions. Write your final answers without negative exponents.
    2. Answers
    a. d.
    b. e.
    c. f.
  2. Factor out the greatest common factor. Write your answers without negative exponents.
    3. Answers
  3. Perform the function operations given the following functions:
    4. Answers

    F(x) = and g(x) =

    a. f(x+h)d. f(g(x))
    b. e.
    c. f(g(4))
  4. Solve the following inequalities:
    5. Answers

  5. State the domain of the following functions:
    6. Answers
    a. g(x) = d. h(t) =
    b. f(t) = ln (t+1)e. h(x) =
    c. f(x) =

  6. Use the properties of logarithms to perform the indicated operations.
    7. Answers

    1. Write each of the following as the sum and difference of simplest logarithms.
      2. i. ii.
    2. Write the following as a single logarithm.
      3. i. ii.
    3. Simplify:
      4. i. ii. iii.
  7. Solve the following equations:
    8. Answers
    a. d.
    b. e.
    c. f.
  8. Solve the following equations:
    9. Answers
    a. d. ln x + 5 = ln (x + 1)
    b. e. ln (x2 - 9) = 2
    c.
  9. Solve word problems of the following types. Ratio, Proportion, Motion, Mixture, Geometry, work, I=PRT, money and numerical.

    1. (Numerical) Three less than twice the third of three consecutive integers equals the sum of the three integers. Find the integers.
      2. Answers

    2. (Ratio-Geometry) The lengths of the sides of a triangle are in the ratio 2:3:4. The perimeter is 63 cm. Find the length of each side.
      3. Answers

    3. (Variation) Y varies jointly as x and the square of z, and inversely as the principal square root of w. If Y = 270 when x = 5, z = 6, and w = 4, what is Y when x = 3, z = 6, and w = 9?
      4. Answers

    4. (Motion) Steve traveled 340 miles. For most of the trip he drove 60 mph, but for one period of time he was slowed to 20 mph due to construction. If Steve's total travel time was 7 hours, how many miles did he drive at the reduced speed?
      5. Answers

    5. (Mixtures) The radiator in an automobile holds 14 quarts. How much pure anti-freeze should be mixed with a 20% anti-freeze solution to obtain a 40% mixture that will fill the tank?
      6. Answers

    6. (Investment, I=PRT) Greg has $17,000 invested in bonds that pay 13% annually. He also has money invested in a certificate of deposit at 17% annually. The total amount of interest he earns from both investments is the same as if all the money was invested in a single account at 14%. How much does he have invested in the certificate of deposit? Round your answer to the nearest dollar.
      7. Answers

    7. (Money-Coins) A collection of dimes and nickels is worth $3.75. If there are 55 coins in the collection, how many of each type of coin are there?
      8. Answers

    8. (Work) An inlet pipe can fill a barrel of wine in 6 hours, and an outlet pipe can empty it in 8 hours. Through an error both pipes are left on. How long will it take for the barrel to fill?
      9. Answers

    9. (Geometry) A rancher's pasture is rectangular and has an area of 84 square miles. The length is 5 miles more than the width. How much will it cost to enclose the pasture with a fence if fencing materials cost an average of #1.80 per linear foot? (5280 ft = 1 mile)
      10. Answers

  10. Find the equation of the line that passes through the points (-2,3) and (5,1).
    11. Answers

  11. Find the equation of the line that is perpendicular to the line in #10 and goes through (-2,3).
    12. Answers

  12. Find the equation of the line that is parallel to the line in #10 and goes through the origin.
    13. Answers

  13. Find the values of a & b so that f(x) = and f(2) = 3 and f(-1) = 4.
    14. Answers

  14. For the imaginary number simplify the following and express your answer in the form of a + bi where a & b are real numbers.
    15. Answers
    a. b. c. d.
  15. Graph the solutions to the following systems of inequalities.
    16. Answers
    a. c.
    b. d.
  16. Given the quadratic equation y =
    17. Answers

    1. Complete the square on x

    2. State the vertex of the parabola

    3. State the interval on which y is increasing

    4. d. Graph the parabola

  17. Solve the following systems of equations.
    18. Answers
    a. b. c.

    Trigonometric Identities: You are expected to have memorized and be able to use the trigonometric identities most commonly encountered in calculus. They are included here for you review.

    Pythagorean Identities:

    Addition and Subtraction Identities:
    sin (x+y) = sin x cos y + cos x sin ycos (x+y) = cos x cos y - sin x sin y
    sin (x-y) = sin x cos y - cos x sin ycos (x-y) = cos x cos y + sin x sin y

    Double Angle Identities:
    Sin 2x = 2 sin x cos x

    Half Angle Identities:
    OR



  18. Which trigonometric functions are increasing for the domain
    19. Answers

  19. If and find
    20. Answers

  20. If cos x = and csc x < 0 find sin x.
    21. Answers

  21. If and then find and
    22. Answers

  22. If and (where and terminate in the first quadrant)
    23. Answers

    Find , and

  23. Find the exact value of cos
    24. Answers

  24. Solve for x in the interval [ 0, ):
    25. Answers

    1. a. sin 2x = cos x

    2. b.

    3. c. 2 + cos 2x = 3 cos x