Pre-Algebra Placement Test Practice

Multiple choice pre-algebra questions to assess your skills in: order of operations, integers, decimals, fractions, divisibility, factors, prime numbers, GCF, LCM, scientific notation, exponents, square roots, ratios, proportions, percentages, basic statistics (mean, median, mode), slope of a line, and applications. Questions include answers and detailed step-by-step solutions.

Pre-Algebra Multiple Choice Questions

  1. Evaluate:

    \[72 - 9 \div 3 \cdot 2 + 2 =\]

    A) 21
    B) 23
    C) 44
    D) 68
    E) 74

    Detailed Solution.

  2. In scientific notation:

    \[3.0 \times 10^{-5} + 0.0000022 =\]

    A) \(3.5 \times 10^{-5}\)
    B) \(3.22 \times 10^{-5}\)
    C) \(5.2 \times 10^{-6}\)
    D) \(3.5 \times 10^{-6}\)
    E) \(5.2 \times 10^{-11}\)

    Detailed Solution.

  3. If \(\frac{2}{3} \div \frac{4}{5} \times \frac{6}{7}\) is calculated and the fraction reduced to simplest form, what is the numerator?

    Fraction division and multiplication

    A) 12
    B) 8
    C) 7
    D) 6
    E) 3

    Detailed Solution.

  4. Calculate: \(\frac{3}{4} + \frac{2}{5} - \frac{1}{8}\)

    Fraction addition and subtraction

    A) \(\frac{59}{80}\)
    B) \(\frac{17}{20}\)
    C) \(\frac{6}{7}\)
    D) \(\frac{16}{15}\)
    E) \(\frac{17}{15}\)

    Detailed Solution.

  5. A shop owner increased a shirt's price from \( \$20 \) to \( \$26 \). What percentage increase is this?

    A) 6
    B) 26
    C) 30
    D) 46
    E) 60

    Detailed Solution.

  6. Evaluate:

    \[\frac{3}{4} + 0.85 + 20\% =\]

    A) 27.85
    B) 1.8
    C) 23.85
    D) 2.85
    E) 21.6

    Detailed Solution.

  7. Tom worked 6 hours at \( \$5.50 \) per hour. He bought two magazines at \( \$9.50 \) each and a pen at $8.25. How much money does he have left?

    A) $60.25
    B) $15.25
    C) $33
    D) $27.25
    E) $5.75

    Detailed Solution.

  8. Bill bought \(1\frac{3}{4}\) pounds of Cheddar, 3.75 pounds of blue cheese, and \(4\frac{1}{2}\) pounds of goat cheese. Total pounds of cheese?

    A) 8
    B) 7.75
    C) 9.25
    D) 10
    E) 7

    Detailed Solution.

  9. In a school, 40% of students are 8 years old or younger. The remaining students number 120. How many students are 8 or younger?

    A) 80
    B) 160
    C) 480
    D) 320
    E) 740

    Detailed Solution.

  10. One-fifth of students have no siblings. Of the rest, 40% have one sibling. What percentage of all students have more than one sibling?

    A) 60
    B) 80
    C) 48
    D) 20
    E) 45

    Detailed Solution.

  11. A car hire company offers Plan A: \( \$20/day \) plus 5¢/km, and Plan B: \( \$15/day \) plus 7¢/km. For how many kilometers do both plans cost the same?

    A) 1000
    B) 800
    C) 242
    D) 400
    E) 250

    Detailed Solution.

  12. Joe worked \(x\) hours and earned \(y\) dollars. How much does he earn for \(z\) hours?

    A) \(\frac{yz}{x}\)
    B) \(\frac{z}{xy}\)
    C) \(xyz\)
    D) \(\frac{zx}{y}\)
    E) \(\frac{xy}{z}\)

    Detailed Solution.

  13. In a science test, a class of 30 students averaged 80. The 20 girls averaged 85. What is the average of the 10 boys?

    A) 60
    B) 70
    C) 80
    D) 85
    E) 90

    Detailed Solution.

  14. Find \(y\) if \(\frac{y}{5} = \frac{10}{25}\).

    A) 80
    B) 25
    C) 2
    D) 8
    E) 1

    Detailed Solution.

  15. Evaluate:

    \[\sqrt{3^2 + 4^2} =\]

    A) 7
    B) 25
    C) 50
    D) 12
    E) 5

    Detailed Solution.

  16. A club has 24 members (15 females, rest males). What is the ratio of males to total members?

    A) 15:24
    B) 24:9
    C) 9:24
    D) 9:39
    E) 9:15

    Detailed Solution.

  17. Write 2.05 as a mixed number.

    A) \(20\frac{1}{2}\)
    B) \(2\frac{1}{2}\)
    C) \(2\frac{1}{5}\)
    D) \(2\frac{1}{20}\)
    E) \(2\frac{2}{5}\)

    Detailed Solution.

  18. Which number is divisible by 3?

    A) 101267
    B) 22345
    C) 934567
    D) 934566
    E) 11177811

    Detailed Solution.

  19. Which is NOT a prime number?

    A) 27
    B) 29
    C) 17
    D) 37
    E) 23

    Detailed Solution.

  20. What is the slope of a line parallel to the line through points \((2,0)\) and \((-1,3)\)?

    A) -3
    B) 1
    C) 0
    D) 3
    E) -1

    Detailed Solution.

  21. What is the GCF of 32 and 48?

    A) 32
    B) 16
    C) 8
    D) 4
    E) 2

    Detailed Solution.

  22. Which pair has an LCM of 24?

    A) 6 and 8
    B) 6 and 12
    C) 4 and 6
    D) 4 and 3
    E) 4 and 8

    Detailed Solution.

Answers

  1. D
  2. B
  3. C
  4. A
  5. C
  6. B
  7. E
  8. D
  9. A
  10. C
  11. E
  12. A
  13. B
  14. C
  15. E
  16. C
  17. D
  18. D
  19. A
  20. E
  21. B
  22. A

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Middle School Math

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