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Math 10C

Math 10C · Worksheets

Final exam challenge

Ten questions of mixed difficulty, covering Linear functions, Measurement, Numbers, roots and powers, Polynomials, Surface area and volume. Print it, or work through it on screen — the answer key starts on its own page.

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Final exam challenge

Math 10C · maddyhelps.com

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Circle the best answer for each question. Show your work in the space provided.

  1. To convert 3.5 m into centimetres you

    1. a) divide by 10, giving 0.35 cm
    2. b) divide by 100, giving 0.035 cm
    3. c) multiply by 100, giving 350 cm
    4. d) multiply by 10, giving 35 cm

  2. Simplified, (2x³y)⁴ is

    1. a) 16x¹²y⁴
    2. b) 16x⁷y
    3. c) 8x⁷y⁴
    4. d) 2x¹²y⁴

  3. Expanded, (2x − 3)(x + 4) is

    1. a) 2x² + 11x − 12
    2. b) 2x² + 5x − 12
    3. c) 2x² + 5x + 12
    4. d) 2x² − 12

  4. The value of 3⁻² is

    1. a) −6
    2. b) −9
    3. c) 9
    4. d) 1/9

  5. A measurement of 7.0 cm is stated to the nearest tenth. Its possible true values lie between

    1. a) 6.95 cm and 7.05 cm
    2. b) 6.0 cm and 8.0 cm
    3. c) 6.9 cm and 7.1 cm
    4. d) 7.00 cm and 7.05 cm

  6. A sphere has radius 6 cm. Its volume is about

    1. a) 905 cm³
    2. b) 226 cm³
    3. c) 144 cm³
    4. d) 452 cm³

  7. The solution to y = x + 4 and 2x + y = 10 is

    1. a) (3, 7)
    2. b) (6, 2)
    3. c) (2, 6)
    4. d) (4, 2)

  8. Expanded, (x + 2)(x² − 3x + 1) is

    1. a) x³ − x² − 5x + 2
    2. b) x³ − x² + 5x + 2
    3. c) x³ − 3x² + x + 2
    4. d) x³ + x² − 5x + 2

  9. The greatest common factor of 24 and 36 is

    1. a) 12
    2. b) 72
    3. c) 4
    4. d) 6

  10. The least common multiple of 8 and 12 is

    1. a) 48
    2. b) 4
    3. c) 96
    4. d) 24

Answer key · Final exam challenge

Math 10C · maddyhelps.com

  1. c) multiply by 100, giving 350 cm — A centimetre is smaller than a metre, so the same length needs <i>more</i> of them. Asking whether the number should get bigger or smaller before you calculate catches almost every conversion error.
  2. a) 16x¹²y⁴ — The outside exponent applies to every factor inside: 2⁴ = 16, (x³)⁴ = x¹², and y⁴. Forgetting to raise the coefficient is the most common error, and it gives 2x¹²y⁴.
  3. b) 2x² + 5x − 12 — 2x² + 8x − 3x − 12, which collects to 2x² + 5x − 12. Substituting x = 1 gives (−1)(5) = −5 on the left and 2 + 5 − 12 = −5 on the right ✓.
  4. d) 1/9 — A negative exponent means the reciprocal, not a negative answer: 3⁻² = 1/3² = 1/9. The sign of the exponent controls which side of the fraction line the power sits on.
  5. a) 6.95 cm and 7.05 cm — Rounding to the nearest tenth means anything within half a tenth either way was recorded as 7.0. That half-unit is the measurement's uncertainty, and every physical measurement has one.
  6. a) 905 cm³ — V = (4/3)πr³ = (4/3)π(216) ≈ 905 cm³. Cubing the radius is the step to be careful with: 6³ is 216, not 18.
  7. c) (2, 6) — Substitute the first into the second: 2x + (x + 4) = 10, so 3x = 6 and x = 2, giving y = 6. Always substitute back into the <i>other</i> equation to check: 2(2) + 6 = 10 ✓.
  8. a) x³ − x² − 5x + 2 — Multiply each of the two terms across all three: x³ − 3x² + x, then 2x² − 6x + 2. Collecting gives x³ − x² − 5x + 2. With more terms, a grid keeps track better than trying to hold it in your head.
  9. a) 12 — Compare prime factorizations: 24 = 2³ × 3 and 36 = 2² × 3², so the common part is 2² × 3 = 12. Taking the <i>lowest</i> power of each shared prime gives the GCF; the highest gives the LCM.
  10. d) 24 — 8 = 2³ and 12 = 2² × 3, so the LCM takes the highest power of each prime: 2³ × 3 = 24. Multiplying the two numbers gives 96, which is a common multiple but not the least one.