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Math 10C

Math 10C · Worksheets

Cumulative review

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

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Cumulative review

Math 10C · maddyhelps.com

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

  1. Expanded, (x + 3)² is

    1. a) x² + 6x + 9
    2. b) x² + 9
    3. c) x² + 3x + 9
    4. d) x² + 6x + 3

  2. If f(x) = 2x + 5, then f(x + 1) is

    1. a) 3x + 5
    2. b) 2x + 5 + 1
    3. c) 2x + 6
    4. d) 2x + 7

  3. The system y = 2x + 1 and y = 2x − 3 has

    1. a) a solution at the origin
    2. b) one solution
    3. c) infinitely many solutions
    4. d) no solution, because the lines are parallel

  4. A ladder 6 m long leans against a wall and reaches 5 m up it. The angle it makes with the ground is about

    1. a) 40°
    2. b) 56°
    3. c) 34°
    4. d) 50°

  5. The SI base unit of length is the

    1. a) kilometre
    2. b) metre
    3. c) inch
    4. d) centimetre

  6. A recipe needs 2 cups of liquid and 1 cup is 250 mL. In litres that is

    1. a) 500 L
    2. b) 0.25 L
    3. c) 0.5 L
    4. d) 2.5 L

  7. To convert 3.5 m into centimetres you

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

  8. A solid is a cylinder of radius 2 cm and height 8 cm with a hemisphere of the same radius on top. Its volume is about

    1. a) 117 cm³
    2. b) 84 cm³
    3. c) 134 cm³
    4. d) 101 cm³

  9. In a right triangle, cos θ = 0.6. The angle θ is about

    1. a) 31°
    2. b) 0.6°
    3. c) 53°
    4. d) 37°

  10. The greatest common factor of 6x² and 9x is

    1. a) 54x²
    2. b) 3
    3. c) 3x
    4. d) 3x²

Answer key · Cumulative review

Math 10C · maddyhelps.com

  1. a) x² + 6x + 9 — A square means the bracket times itself, so the middle term is twice the product: x² + 3x + 3x + 9. Writing x² + 9 is the single most common algebra error at this level.
  2. d) 2x + 7 — Replace every x with (x + 1): 2(x + 1) + 5 = 2x + 2 + 5 = 2x + 7. The bracket matters — the 2 multiplies the whole input, not just the x.
  3. d) no solution, because the lines are parallel — Same slope, different intercepts, so the lines never meet. Equal slopes <i>and</i> equal intercepts would be the same line and give infinitely many solutions.
  4. b) 56° — The height is opposite the angle and the ladder is the hypotenuse, so sin θ = 5/6 and θ = sin⁻¹(0.833) ≈ 56°. Drawing the triangle and labelling the sides before choosing the ratio is the whole method.
  5. b) metre — SI builds every other length from the metre using prefixes: a kilometre is a thousand metres, a centimetre is a hundredth. The inch belongs to the imperial system, which is not built on powers of ten at all.
  6. c) 0.5 L — 2 × 250 = 500 mL, and 1000 mL make a litre, so 0.5 L. Two conversions in a row: first to the unit you were given a factor for, then to the one asked for.
  7. 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.
  8. a) 117 cm³ — Add the parts: cylinder π(4)(8) ≈ 100.5, hemisphere ½ × (4/3)π(8) ≈ 16.8, total ≈ 117 cm³. For a composite <i>volume</i> you always add; for a composite <i>surface area</i> you also have to remove the faces that are now joined.
  9. c) 53° — θ = cos⁻¹(0.6) ≈ 53.1°. Make sure the calculator is in degree mode — in radians the same keystrokes give 0.93, which looks like a plausible answer and is not.
  10. c) 3x — Take the largest number dividing both coefficients (3) and the lowest power of x present in both (x). So 6x² + 9x factors to 3x(2x + 3).