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Math 9

Math 9 · Worksheets

Cumulative review

Ten questions of mixed difficulty, covering Circle geometry, Equations and inequalities, Polynomials, Powers, Similarity, Square roots. Print it, or work through it on screen — the answer key starts on its own page.

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Cumulative review

Math 9 · maddyhelps.com

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

  1. A cube with 10 cm edges sits in the centre of the top of a rectangular prism that is 20 cm long, 20 cm wide and 5 cm high. What is the surface area of the object?

    1. a) 1700 cm²
    2. b) 1600 cm²
    3. c) 1300 cm²
    4. d) 1800 cm²

  2. In the polynomial 6x² − x + 9, the coefficient of x is

    1. a) 1
    2. b) 6
    3. c) −1
    4. d) 0

  3. √40 lies between which two whole numbers?

    1. a) 20 and 21
    2. b) 7 and 8
    3. c) 6 and 7
    4. d) 5 and 6

  4. Triangle ABC is similar to triangle DEF, with AB = 6 cm, BC = 8 cm and DE = 9 cm. How long is EF?

    1. a) 12 cm
    2. b) 13.5 cm
    3. c) 5.3 cm
    4. d) 11 cm

  5. A drawing of a phone is made with a scale factor of 3. The real phone is 14 cm long. How long is the phone in the drawing?

    1. a) 17 cm
    2. b) 11 cm
    3. c) 42 cm
    4. d) 4.7 cm

  6. The value of −2⁴ is

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

  7. Two tangents from point P touch a circle with centre O at A and B. Angle APB = 50°. What is angle AOB?

    1. a) 100°
    2. b) 130°
    3. c) 50°
    4. d) 40°

  8. Solve 12/x = −3.

    1. a) x = −36
    2. b) x = −1/4
    3. c) x = −4
    4. d) x = 4

  9. Two cube-shaped boxes, each with 30 cm edges, are taped together face to face. What is the surface area of the pair as one object?

    1. a) 10 800 cm²
    2. b) 9000 cm²
    3. c) 5400 cm²
    4. d) 9900 cm²

  10. The value of (−2 × 3)² − 2 × 3² is

    1. a) 0
    2. b) 18
    3. c) −54
    4. d) −36

Answer key · Cumulative review

Math 9 · maddyhelps.com

  1. b) 1600 cm² — Cube 6 × 100 = 600 cm², prism 2(400 + 100 + 100) = 1200 cm², and the 100 cm² where they meet is hidden on both: 1800 − 200 = 1600 cm². Only the part of the prism's top under the cube is hidden — removing the whole 400 cm² top gives 1300.
  2. c) −1 — −x means −1 × x, so the coefficient is −1: the sign in front belongs to the term. A variable with no number written in front has a coefficient of 1 or −1, never 0.
  3. c) 6 and 7 — Find the perfect squares on either side: 36 < 40 < 49, so √40 is between √36 = 6 and √49 = 7. Halving 40 to get 20 is the most common way to get this wrong.
  4. a) 12 cm — Corresponding sides are in the same ratio: DE/AB = 9/6 = 1.5, so EF = 1.5 × 8 = 12 cm. DE is 3 cm longer than AB, but adding 3 to 8 gives 11 — similar figures multiply, they do not add.
  5. c) 42 cm — A scale factor of 3 means every length in the drawing is 3 times the real length: 3 × 14 = 42 cm. Dividing gives 4.7 cm, which would be a reduction, and adding 3 gives 17 cm — scale factors multiply.
  6. c) −16 — With no brackets, the exponent applies only to the 2, and the negative is applied afterwards: −2⁴ = −(2 × 2 × 2 × 2) = −16. Reading it as (−2)⁴ gives 16, the single most common error with powers.
  7. b) 130° — OA ⟂ PA and OB ⟂ PB, so quadrilateral OAPB has two right angles. Its angles add to 360°, so angle AOB = 360° − 90° − 90° − 50° = 130°. Assuming the angle at O equals the angle at P gives 50°.
  8. c) x = −4 — Multiply both sides by x: 12 = −3x, so x = 12 ÷ (−3) = −4. Check: 12 ÷ (−4) = −3 ✓. Multiplying 12 by −3 gives −36, which treats x as if it were on top of the fraction.
  9. b) 9000 cm² — Each face is 30 × 30 = 900 cm², and two cubes have 12 faces: 10 800 cm². Taping them hides one face on each box, so subtract 2 × 900 to get 9000 cm². Subtracting only one face gives 9900.
  10. b) 18 — The bracket is squared as a whole: (−6)² = 36. In 2 × 3² only the 3 is squared: 2 × 9 = 18, so 36 − 18 = 18. Squaring 2 × 3 together in the second term gives 36 − 36 = 0; without brackets, the power belongs to the 3 alone.