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Math 30-1 · Worksheets

Cumulative review 2

Ten questions of mixed difficulty, covering Counting, Exponents and logs, Polynomial, radical, rational, Sinusoidal models, Transformations, Trigonometry. Print it, or work through it on screen — the answer key starts on its own page.

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Cumulative review 2

Math 30-1 · maddyhelps.com

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

  1. Which describes the end behaviour of y = x³?

    1. a) up on both ends
    2. b) down on both ends
    3. c) down to the left, up to the right
    4. d) up to the left, down to the right

  2. A rider's height is h(t) = −10 cos(πt/20) + 12, in metres after t seconds. How high is the rider at t = 0?

    1. a) 22 m
    2. b) 2 m
    3. c) −10 m
    4. d) 12 m

  3. A sinusoidal graph has a maximum at (2, 7) and the next minimum at (8, 1). What is its period?

    1. a) 3
    2. b) 8
    3. c) 12
    4. d) 6

  4. What is the remainder when P(x) = x² + 3x − 1 is divided by x − 2?

    1. a) 9
    2. b) −11
    3. c) 1
    4. d) 3

  5. Solve for n: ₙC₂ = 28

    1. a) 28
    2. b) 7
    3. c) 14
    4. d) 8

  6. Solve 3ˣ = 20, to the nearest hundredth.

    1. a) 2.73
    2. b) 6.67
    3. c) 1.82
    4. d) 0.37

  7. Daylight in a city varies sinusoidally over a year, from a maximum of 17 hours to a minimum of 7 hours. What are the amplitude and period?

    1. a) 5 hours and 182.5 days
    2. b) 5 hours and 365 days
    3. c) 12 hours and 365 days
    4. d) 10 hours and 365 days

  8. The graph of the inverse of a function is a reflection of the original graph in:

    1. a) the line y = x
    2. b) the line y = −x
    3. c) the y-axis
    4. d) the x-axis

  9. What is the amplitude of y = 3 sin x?

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

  10. If f(x) = x + 1 and g(x) = 2x, what is f(g(3))?

    1. a) 6
    2. b) 7
    3. c) 9
    4. d) 8

Answer key · Cumulative review 2

Math 30-1 · maddyhelps.com

  1. c) down to the left, up to the right — Odd degree means the ends go opposite ways; a positive leading coefficient means it rises to the right. So it starts low and ends high.
  2. b) 2 m — cos 0 = 1, so h(0) = −10 + 12 = 2 m. The negative cosine starts at its minimum — the rider boards at the bottom.
  3. c) 12 — From a maximum to the next minimum is half a cycle: 8 − 2 = 6. A full period is twice that, 12.
  4. a) 9 — The remainder theorem says the remainder is P(2): 4 + 6 − 1 = 9. No long division needed.
  5. d) 8 — ₙC₂ = n(n − 1) ÷ 2, so n(n − 1) = 56. Consecutive numbers multiplying to 56 are 8 and 7, so n = 8.
  6. a) 2.73 — No common base, so take logs: x log 3 = log 20, giving x = log 20 ÷ log 3 ≈ 2.73. Check: 3² = 9 and 3³ = 27, so it must be between 2 and 3.
  7. b) 5 hours and 365 days — Amplitude = (17 − 7) ÷ 2 = 5 hours, and the pattern repeats once a year. 12 hours is the midline, not the amplitude.
  8. a) the line y = x — An inverse swaps every x and y, and swapping coordinates is exactly a reflection in the line y = x.
  9. a) 3 — The amplitude is |a|, the distance from the midline to a peak: 3. The full height from trough to peak would be 6.
  10. b) 7 — Work from the inside out: g(3) = 6, then f(6) = 7. Doing f first gives g(f(3)) = 8, which is a different composition.