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Math 9

Math 9 · Worksheets

Mixed review · Relations, polynomials and equations

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

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Mixed review · Relations, polynomials and equations

Math 9 · maddyhelps.com

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

  1. Solve 3x + 7 = −8.

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

  2. (10x² + 15x) ÷ 5x simplifies to

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

  3. Maddy has $45 saved and adds $12 a week. Which equation finds the number of weeks, w, until she has $153?

    1. a) 45 + 12w = 153
    2. b) 57w = 153
    3. c) 12 + 45w = 153
    4. d) 12w = 153

  4. A gym charges a $40 sign-up fee plus $15 a month. Which equation gives the total cost, C, in dollars, after m months?

    1. a) C = 55m
    2. b) C = 15(m + 40)
    3. c) C = 15m + 40
    4. d) C = 40m + 15

  5. A candle is 30 cm tall and burns down 2 cm each hour, so its height after t hours is h = 30 − 2t. After how many hours will it be 12 cm tall?

    1. a) 9 h
    2. b) 15 h
    3. c) 21 h
    4. d) 6 h

  6. Solve 5 − 2x ≤ 11.

    1. a) x ≤ −3
    2. b) x ≤ −8
    3. c) x ≥ 3
    4. d) x ≥ −3

  7. A table of values has x = −1, 0, 1, 2 and y = 7, 4, 1, −2. Which equation describes the relation?

    1. a) y = 4x − 3
    2. b) y = −3x + 4
    3. c) y = 3x + 4
    4. d) y = −3x + 7

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

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

  9. Solve −3x > 12.

    1. a) x < −36
    2. b) x < −4
    3. c) x > −4
    4. d) x > 4

  10. (2x² − 4x + 1) − (5x² + x − 6) simplifies to

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

Answer key · Mixed review · Relations, polynomials and equations

Math 9 · maddyhelps.com

  1. c) 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.
  2. b) 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 ✓.
  3. a) 45 + 12w = 153 — The $12 is added every week, so it multiplies w, and the $45 is there once, at the start. 57w = 153 counts the $45 again every week. Solving the right equation gives 12w = 108, so w = 9 weeks.
  4. c) C = 15m + 40 — The $15 is paid every month, so it multiplies m; the $40 is paid once, so it is the constant. Swapping them gives C = 40m + 15, and C = 55m charges the sign-up fee every month.
  5. a) 9 h — Set 30 − 2t = 12. Then 2t = 18 and t = 9 hours; check: 30 − 2(9) = 12 ✓. 15 h is when the candle burns out completely, and 6 h is 12 ÷ 2, which ignores the starting height.
  6. d) x ≥ −3 — Subtract 5: −2x ≤ 6. Divide by −2 and reverse the sign: x ≥ −3. Test x = 0: 5 − 0 = 5 ≤ 11 ✓, and 0 is in x ≥ −3; not reversing gives x ≤ −3, which leaves out 0 even though 0 works.
  7. b) y = −3x + 4 — y goes down 3 each time x goes up 1, so the equation has −3x. The constant is the y-value when x = 0, which is 4 — not the first y in the table, which belongs to x = −1. Using 7 gives y = −3x + 7.
  8. d) −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.
  9. b) x < −4 — Dividing both sides by −3 gives −4, and dividing by a negative reverses the inequality: x < −4. Test x = −5: −3(−5) = 15 > 12 ✓. Forgetting to reverse gives x > −4, but x = 0 is in that set and −3(0) = 0 is not greater than 12.
  10. b) −3x² − 5x + 7 — Subtracting means adding the opposite of every term in the second bracket: 2x² − 4x + 1 − 5x² − x + 6 = −3x² − 5x + 7. Changing the sign of only the first term, 5x², gives −3x² − 3x − 5 — the most common subtraction error.