Practice Placement Test—Elementary Algebra

Math Sentences Part 1:
Solve the following linear equations:
  1. Write the following number in scientific notation: 23,500,000
    1. 23.5 x 106
    2. 2.35 x 106
    3. 23.5 x 107
    4. 2.35 x 107
    5. None of the above

  2. Evaluate the expression 5(-2t - 3) + 1 when t = -2.
    1. -34
    2. -14
    3. 6
    4. 9
    5. None of the above

  3. Evaluate the expression 2x2 - 3y + 7 when x = -3 , y = 4.
    1. -23
    2. 4
    3. 13
    4. 37
    5. None of the above

  4. Find the solution to the equation: 3(2x - 1) + 4 = 4x - 9
    1. x = -8
    2. x = -5
    3. x = 3/2
    4. x = 1
    5. None of the above

  5. Three consecutive odd numbers have a total of 57. What is the largest of these numbers?
    1. 17
    2. 19
    3. 21
    4. 23
    5. None of the above

  6. Perform the following operation on polynomials: (3a3 - 4a2 + 8) - (2a3 + 6a - 3)
    1. a3 - 10a2 + 11
    2. a3 - 4a2 + 6a + 5
    3. a3 - 4a2 + 6a + 11
    4. a3 - 4a2 - 6a + 11
    5. None of the above

  7. Perform the following operation on polynomials: (3a - 7b) * (4a + 5b)
    1. 12a2 - 13ab - 35b2
    2. 12a2 + 13ab - 35b2
    3. 12a2 - 43ab - 35b2
    4. 12a2 - 35b2
    5. None of the above

  8. Perform the following operation on polynomials: (6x - 2y)2
    1. 12x2 - 12xy + 4y2
    2. 12x2 + 24xy + 4y2
    3. 36x2 - 24xy + 4y2
    4. 36x2 + 12xy + 4y2
    5. None of the above

  9. Factor the following polynomial completely: 6x3 - 15x2 + 18x - 45
    1. 6(x2 - 3)(x - 5)
    2. 6(x2 - 3)(x - 5)
    3. 6(x2 - 3)(x - 5)
    4. 6(x2 - 3)(x - 5)
    5. None of the above

  10. Factor the following polynomial completely: 3b2 + 23b - 36
    1. (3b + 2)(b + 18)
    2. (3b - 4)(b + 9)
    3. (3b - 2)(b + 18)
    4. (3b + 4)(b - 9)
    5. None of the above

  11. Multiply the following polynomials: (3s - 2t + 8) * (-s + 5t)
    1. -3s2 + 13st + 10t2 - 8s + 40t
    2. -3s2 - 17st + 10t2 - 8s - 40t
    3. -3s2 - 13st - 10t2 - 8s - 40t
    4. -3s2 + 17st - 10t2 - 8s + 40t
    5. None of the above

  12. Solve the following: 3x + 5 < 8x - 35
    1. x > 8
    2. x < 8
    3. x > 6
    4. x < 6
    5. None of the above

  13. Solve the following: -3x + 25 Greater Than or Equal To 79
    1. x Greater Than or Equal To 51
    2. x Greater Than or Equal To 18
    3. x Greater Than or Equal To -18
    4. x Less Than or Equal To -34 1/3
    5. None of the above

  14. Solve the following: -4t - 2 < 6t + 5
    1. t > -0.7
    2. t > -0.3
    3. t < 0.3
    4. t < 0.7
    5. None of the above

  15. Simplify the following: cube root of fifty four A to the fifth power B to the seventh power
    1. 3a2b3 * cube root of six A B
    2. 3ab * cube root of six A squared B
    3. 3ab2 * cube root of two A B
    4. 3ab2 * cube root of two A squared B
    5. None of the above

  16. Multiply the following: (4 - Radical seven) * (3 + 2Radical seven)
    1. -16 + 11Radical seven
    2. -2 + 5Radical seven
    3. 2 + 2Radical seven
    4. 12 - 14Radical seven
    5. None of the above

  17. Multiply the following in the complex numbers: (4 - 3i) * (-5 + 2i)
    1. 20 + 23i - 6i2
    2. -26 + 7i
    3. -26 + 23i
    4. -14 + 7i
    5. None of the above

  18. Simplify the following complex numbers: i32
    1. 1
    2. i
    3. -1
    4. -i
    5. None of the above

  19. Solve the following equation: y = -3y2 + 14
    1. y = -2, 7/3
    2. y = 2, -7/3
    3. y = -7, 2/3
    4. y = -1, 14/3
    5. None of the above

  20. solve the following equation: 3x2 + 6x - 5 = 0
    1. x = -3 Plus or MinusRadical six / 3
    2. x = -1 Plus or Minus 4Radical six
    3. x = -2 Plus or Minus 2iRadical six
    4. x = 5 Plus or MinusRadical six / 6
    5. None of the above

  21. If the sum of two numbers is 16 and the product of the same two numbers in 48, what are the two numbers?
    1. 2 and 14
    2. 3 and 16
    3. 4 and 12
    4. 6 and 8
    5. None of the above

  22. A rectangular yard has an area of 2160 square feet. The length of the yard is three feet longer than its width. What is the perimeter of the yard?
    1. 45 feet
    2. 90 feet
    3. 93 feet
    4. 186 feet
    5. None of the above

  23. Solve the following system of equations: x + 2y = 3    -3x - 4y = -14
    1. (2, -3)
    2. (3, 1/2)
    3. (8, 2 1/2)
    4. All of the above
    5. None of the above

  24. Solve the following system of equations: 8x - 2y = 20   -2x + 1/2y = -5
    1. (3, 2)
    2. (2, -2)
    3. (4 1/4, 7)
    4. All of the above
    5. None of the above

  25. Divide the following expression and simplify: x squared minus four over two x plus four divided by three x squared minus twelve x plus twelve over x squared plus four x plus four
    1. 3(x + 2) / 2(x - 2)
    2. 3(x - 2)2 / 2(x + 2)
    3. (x + 2)2 / 6(x - 2)
    4. (x + 2)2 (x - 2) / 6
    5. None of the above

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