maddyhelps

Math 9

Math 9 · Worksheets

Year-end challenge

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

All worksheets

Year-end challenge

Math 9 · maddyhelps.com

Name
Date
Score
/ 10

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

  1. Without a calculator, the best estimate of √27 is

    1. a) 5.2
    2. b) 5.7
    3. c) 13.5
    4. d) 4.8

  2. (3x² + 2x − 1) + (x² − 5x + 4) simplifies to

    1. a) 4x² − 3x + 3
    2. b) 4x² + 7x + 3
    3. c) 4x⁴ − 3x² + 3
    4. d) 4x² − 3x − 5

  3. A vertical line passes through the point (−2, 5). What is its equation?

    1. a) x = −2
    2. b) x = 5
    3. c) y = 5
    4. d) y = −2

  4. A survey on whether city buses are too crowded is done at 11 a.m. on a Sunday. What is the main problem?

    1. a) cultural sensitivity: the question may offend some riders
    2. b) cost: surveying riders on buses is too expensive to do
    3. c) privacy: riders' names could be linked to their answers
    4. d) timing: buses are quiet then, so crowding will be understated

  5. Solve 3x + 7 = −8.

    1. a) x = −5
    2. b) x = −1/3
    3. c) x = 5
    4. d) x = −45

  6. Which number has a square root between 0.7 and 0.8?

    1. a) 0.6
    2. b) 6.4
    3. c) 0.75
    4. d) 0.06

  7. (10x² + 15x) ÷ 5x simplifies to

    1. a) 2x + 15x
    2. b) 2x + 3x
    3. c) 2x + 3
    4. d) 2x² + 3x

  8. For which of these numbers is the square root greater than the number itself?

    1. a) 1.44
    2. b) 1
    3. c) 0.49
    4. d) 49

  9. A floor plan is drawn with a scale factor of 1/50. On the plan, a room is 8 cm by 6 cm. What is the real floor area of the room?

    1. a) 1200 m²
    2. b) 0.24 m²
    3. c) 7 m²
    4. d) 12 m²

  10. A cylinder with radius 2 cm and height 5 cm stands on top of a rectangular prism that is 8 cm by 8 cm by 3 cm. To the nearest square centimetre, what is the surface area of the object?

    1. a) 299 cm²
    2. b) 287 cm²
    3. c) 312 cm²
    4. d) 350 cm²

Answer key · Year-end challenge

Math 9 · maddyhelps.com

  1. a) 5.2 — 27 is 2 more than 25 but 9 less than 36, so √27 is only a little more than 5 — about 5.2. Guessing near the halfway point ignores how much closer 27 is to 25, and 4.8 is on the wrong side of 5.
  2. a) 4x² − 3x + 3 — Add like terms only: 3x² + x² = 4x², 2x + (−5x) = −3x, and −1 + 4 = 3. The exponents do not change when you add — x² + x² is 2x², not x⁴ — because you are counting x²-tiles, not multiplying them.
  3. a) x = −2 — Every point on a vertical line has the same x-coordinate, so the line is x = −2. The equation y = 5 is the horizontal line through the same point; mixing up which letter goes with which direction is the usual slip.
  4. d) timing: buses are quiet then, so crowding will be understated — When a survey is done can decide its answer. Sunday morning is one of the quietest times on a bus, so riders then have not seen the rush-hour crowding the question is about; nothing in the survey asks for names, and the question itself is not offensive.
  5. a) x = −5 — Subtract 7 from both sides: 3x = −15. Then divide by 3: x = −5, and check: 3(−5) + 7 = −8 ✓. Adding 7 instead of subtracting it gives 3x = −1 and x = −1/3.
  6. a) 0.6 — Square the ends: 0.7² = 0.49 and 0.8² = 0.64, so the number is between 0.49 and 0.64, and 0.6 is (√0.6 ≈ 0.77). Choosing 0.75 forgets to square — its root is about 0.87 — and 6.4 comes from writing 0.8² as 6.4 instead of 0.64.
  7. c) 2x + 3 — Divide each term by 5x: 10x² ÷ 5x = 2x and 15x ÷ 5x = 3. Dividing only the numbers gives 2x² + 3x, and dividing only the first term leaves 15x behind. Check by multiplying back: 5x(2x + 3) = 10x² + 15x ✓.
  8. c) 0.49 — √0.49 = 0.7, which is greater than 0.49: for a number between 0 and 1, multiplying it by itself makes it smaller, so its root is larger. √1.44 = 1.2 and √49 = 7 are smaller than their numbers, and √1 = 1 is equal, not greater.
  9. d) 12 m² — Scale each length first: 8 × 50 = 400 cm = 4 m and 6 × 50 = 300 cm = 3 m, so the area is 4 × 3 = 12 m². Multiplying the plan's area, 48 cm², by 50 gives 0.24 m² — an area grows by the scale factor twice, once for each dimension.
  10. b) 287 cm² — Prism 2(64 + 24 + 24) = 224 cm²; cylinder 2πr² + 2πrh = 8π + 20π ≈ 88 cm². The circle where they touch is hidden on the cylinder's base and on the prism's top, so subtract 2 × 4π ≈ 25 cm²: 224 + 88 − 25 ≈ 287 cm². Ignoring the overlap gives 312, and subtracting the circle once gives 299.