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Math 30-1 · Worksheets

Cumulative review 1

Ten questions of mixed difficulty, covering Counting, 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 1

Math 30-1 · maddyhelps.com

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

  1. How many terms are in the expansion of (2x − 3y)⁸?

    1. a) 16
    2. b) 8
    3. c) 7
    4. d) 9

  2. A team of 4 is chosen from 7 girls and 5 boys. How many teams have exactly 2 girls and 2 boys?

    1. a) 495
    2. b) 70
    3. c) 210
    4. d) 420

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

  4. How many different arrangements can be made using all the letters of the word MISSISSIPPI?

    1. a) 69 300
    2. b) 138 600
    3. c) 34 650
    4. d) 39 916 800

  5. What is 3π/4 in degrees?

    1. a) 270°
    2. b) 120°
    3. c) 150°
    4. d) 135°

  6. A sinusoidal graph has a maximum of 9 and a minimum of 1. What is the equation of its midline?

    1. a) y = 0
    2. b) y = 4
    3. c) y = 5
    4. d) y = 8

  7. Solve for n: ₙP₂ = 42

    1. a) 8
    2. b) 21
    3. c) 7
    4. d) 6

  8. If f(x) = √x and g(x) = x − 5, what is the domain of f(g(x))?

    1. a) x ≥ 5
    2. b) all real numbers
    3. c) x ≥ 0
    4. d) x ≥ −5

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

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

  10. What is the degree of y = 3x⁴ − 2x + 7?

    1. a) 1
    2. b) 7
    3. c) 4
    4. d) 3

Answer key · Cumulative review 1

Math 30-1 · maddyhelps.com

  1. d) 9 — The number of terms is n + 1 = 9. The coefficients 2 and −3 change the numbers in front but never the number of terms.
  2. c) 210 — Choose each group separately, then multiply: ₇C₂ × ₅C₂ = 21 × 10 = 210. Adding instead of multiplying is the usual slip here.
  3. a) 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.
  4. c) 34 650 — 11 letters with I ×4, S ×4, P ×2: 11! ÷ (4! × 4! × 2!) = 39 916 800 ÷ 1152 = 34 650. Every repeated letter needs its own factorial on the bottom.
  5. d) 135° — Replace π with 180°: 3 × 180° ÷ 4 = 135°.
  6. c) y = 5 — The midline sits halfway between the extremes: (9 + 1) ÷ 2 = 5.
  7. c) 7 — ₙP₂ = n(n − 1), so n(n − 1) = 42. Two consecutive numbers multiplying to 42 are 7 and 6, so n = 7.
  8. a) x ≥ 5 — f(g(x)) = √(x − 5), and the expression under the root cannot be negative: x − 5 ≥ 0, so x ≥ 5.
  9. d) 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. c) 4 — The degree is the highest power of x, which is 4. The 3 is the leading coefficient and the 7 is the constant term.