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Grade 6 math review pack

30 mixed questions from every topic in Grade 6, with an answer key and explanations. Great for the start of the year, before a test, or over the holidays.

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Grade 6 Math Review Pack

Name: ____________________Date: ____________Score: ____ / 30
  1. Number Sense
    $6.99 \times 0.6$ = ?
    Answer: ______________________
  2. Between which two consecutive whole numbers is $\sqrt{61}$?
    A. 30 and 31B. 7 and 8C. 8 and 9D. 6 and 7
  3. $-\left[3^{2}-7 \times (5+8)\right]+5^{3}$ = ?
    Answer: ______________________
  4. Fractions
    Write $\dfrac{5}{6}$ as a decimal.
    A. $0.8\overline{3}$B. 0.83C. $0.\overline{714285}$D. $0.1\overline{6}$
  5. What is $\dfrac{2}{11}$ of 132?
    Answer: ______________________
  6. Integers
    $65 \div (-5) - (-11) \times (-5)$ = ?
    Answer: ______________________
  7. A bank account has 146 dollars. 6 withdrawals of 70 dollars are made, then 133 dollars is deposited. What is the balance in dollars? (A negative number means overdrawn.)
    Answer: ______________________
  8. Ratios, Rates and Percent
    A 25 dollar coat is 40% off, then 13% sales tax is added to the sale price. What is the final cost?
    A. $\$28.25$B. $\$16.95$C. $\$15.00$D. $\$18.25$
  9. A price goes up 10%, then down 40%, then down 20%. What is the overall percent change, to the nearest hundredth of a percent?
    A. +47.20%B. 48.70%C. −47.20%D. −50.00%
  10. Factors, Primes and Puzzles
    Use prime factorization to find the GCF of 117 and 126.
    Answer: ______________________
  11. What is the digit that can go in the box to make 4825□ divisible by 9?
    Answer: ______________________
  12. Algebra
    A rectangle's length is 7 cm more than its width. Its perimeter is 66 cm. What is its width?
    Answer: ______________________
  13. In the table x: 1, 2, 3, 4 → y: 1, −1, −3, −5, the pattern continues. For which x is y = −37?
    Answer: ______________________
  14. Triangles and Pythagoras
    What is the area of an equilateral triangle with sides of 5 cm, to one decimal place?
    A. 18.8 cm²B. 10.8 cm²C. 21.7 cm²D. 12.5 cm²
  15. A right triangle has a hypotenuse of 40 cm and one leg of 24 cm. What is its area? (cm²)
    Answer: ______________________
  16. Area of Polygons
    A heptagon has angles 153°, 116°, 141°, 132°, 93°, 152° and one unknown angle. Find the unknown angle. (degrees)
    Answer: ______________________
  17. What is the area of this trapezoid? (cm²)
    Answer: ______________________
  18. Volume and Surface Area
    A cube-shaped tank has inside edges of 170 cm. How many litres of water does it hold? (1 L = 1,000 cm³)
    Answer: ______________________
  19. A tent is a triangular prism. Its ends are right triangles with legs 9 dm and 12 dm (hypotenuse 15 dm), and it is 13 dm long. What is its total surface area? (dm²)
    Answer: ______________________
  20. Coordinate Geometry
    Find the midpoint of A(10, 11) and B(−9, 4). Write it like (−3, 5) or (1.5, −2).
    Answer: ______________________
  21. Find the distance between A(−1, 7) and B(7, 22).
    Answer: ______________________
  22. Coordinates and Transformations
    The point (−5, −6) is reflected in the y-axis. What is its image? Write it like (−3, 5).
    Answer: ______________________
  23. Which quadrant is the point (−2, −1) in?
    A. IB. IIC. IIID. IV
  24. Measurement
    A car uses 9 L of gas per 100 km. Gas costs $\$1.59$ per litre. What does a 300 km trip cost in gas?
    A. $\$47.70$B. $\$42.93$C. $\$14.31$D. $\$27.00$
  25. Contest Problems
    A square has sides of 24 cm. Joining the midpoints of its sides makes a smaller square. What is the area of the smaller square? (cm²)
    Answer: ______________________
  26. What is the remainder when $7^{44}$ is divided by 5?
    Answer: ______________________
  27. Data and Probability
    The average of 4 numbers is 55. When one more number is added, the average becomes 64. What number was added?
    Answer: ______________________
  28. The mean of 6 test scores is 33. A new score of 208 is added. What is the new mean? (one decimal place if needed)
    Answer: ______________________
  29. Financial Literacy
    1 Canadian dollar buys 61 Indian rupees. A souvenir costs 680 Indian rupees. About how many Canadian dollars is that? (to the nearest cent)
    A. 11.15B. 21.15C. 41,480D. 11.13
  30. 1,400 dollars earns 2% simple interest per year. What is the total amount after 4 years? (dollars)
    Answer: ______________________

Answer key

  1. 4.194 — Multiply without the points: 699 × 6 = 4194. Count decimal places: 2 + 1 = 3, so the answer is 4.194.
  2. B (7 and 8) — 7² = 49 < 61 < 64 = 8².
  3. 207 — Brackets first: 5 + 8 = 13. Next brackets: 3² − 7 × 13 = −82. Exponents: 5³ = 125. Now −(−82) + 125 = 207. So the answer is 207.
  4. A ($0.8\overline{3}$) — Long division: 5 ÷ 6. A remainder comes back, so the digits 3 repeat forever: 5/6 = 0.833… The bar goes over the repeating block. (0.83 is only an approximation.)
  5. 24 — 132 ÷ 11 = 12, × 2 = 24.
  6. -68 — 65 ÷ −5 = −13 and −11 × −5 = 55. Then −13 − (55) = −68.
  7. -141 — 146 − 6 × 70 + 133 = 146 − 420 + 133 = −141 dollars.
  8. B ($\$16.95$) — Sale price: 25 × 0.6 = 15.00. With tax: 15.00 × 1.13 = 16.95 dollars.
  9. C (−47.20%) — Start with 100. × 1.1, × 0.6, × 0.8 gives 52.8. So the overall change is 52.8 − 100 = −47.2%. (Not -50%: each percent applies to a new amount.)
  10. 9 — 117 = 3^{2} × 13 and 126 = 2 × 3^{2} × 7. Take each shared prime with the smaller exponent: GCF = 9.
  11. 8 — Rule for 9: digit sum divisible by 9. Trying the digits 0–9, 8 work.
  12. 13 — 2(w + w + 7) = 66. 4w + 14 = 66. 4w = 52, so w = 13 cm.
  13. 20 — The rule is y = −2x + 3. Solve −37 = −2x + 3: x = 20.
  14. B (10.8 cm²) — Area = (√3 ⁄ 4) × s² = 0.433 × 25 ≈ 10.8 cm². (Or ½ × base × height = ½ × 5 × 4.33.)
  15. 384 — First find the other leg: √(40² − 24²) = 32 cm. The legs are the base and height: ½ × 24 × 32 = 384 cm².
  16. 113 — Angle sum = (7 − 2) × 180 = 900°. Unknown = 900 − 787 = 113°.
  17. 154 — A = ½ × (a + b) × h = ½ × (18 + 26) × 7 = 154 cm².
  18. 4913 — Volume = 170³ = 4,913,000 cm³. ÷ 1,000 = 4,913 L.
  19. 576 — Two triangle ends: 2 × ½ × 9 × 12 = 108. Three rectangles: (9 + 12 + 15) × 13 = 468. Total: 576 dm².
  20. (0.5, 7.5) — M = ((x₁ + x₂) ÷ 2, (y₁ + y₂) ÷ 2) = ((10 + (−9)) ÷ 2, (11 + 4) ÷ 2) = (0.5, 7.5).
  21. 17 — d = √((x₂ − x₁)² + (y₂ − y₁)²). x₂ − x₁ = 7 − (−1) = 8; y₂ − y₁ = 22 − 7 = 15. d = √(64 + 225) = √289 = 17.
  22. (5, -6) — Rule: (x, y) → (−x, y). So (−5, −6) → (5, −6).
  23. C (III) — Quadrant I (+, +), II (−, +), III (−, −), IV (+, −). (−2, −1) is (−, −).
  24. B ($\$42.93$) — Litres: 9 × 300 ÷ 100 = 27 L. Cost: 27 × 1.59 = 42.93 dollars.
  25. 288 — The 4 corner triangles together make exactly half of the big square (fold each corner in and it covers the inner square). So the inner square is half: 24² ÷ 2 = 288 cm². (Check: its side is √(12² + 12²).)
  26. 1 — Powers of 7 leave remainders that repeat when divided by 5: 2, 4, 3, 1, 2, 4, … Following the cycle to the power 44 gives 1.
  27. 100 — Old total: 55 × 4 = 220. New total: 64 × 5 = 320. Added number: 320 − 220 = 100.
  28. 58 — Old total: 33 × 6 = 198. New total: 406. New mean: 406 ÷ 7 = 58. One outlier pulls the mean up a lot.
  29. A (11.15) — Divide: 680 ÷ 61 ≈ 11.15 Canadian dollars.
  30. 1512 — Interest: 1,400 × 0.02 × 4 = 112. Total: 1,400 + 112 = 1,512 dollars.

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