Grade 8 Math: 10 Free Practice Questions

Answer: 24
The solution is x = 24. Move the x-terms together and the constants together: x/4 - x/8 = 3. With the common denominator 32, the left side is 4x/32, so 4x = 96 and x = 24. If you chose 8, you added the two fractions instead of subtracting. If you chose 104, you added 5 to 8 when it needed to be subtracted. Check: 24/4 + 5 = 11 and 24/8 + 8 = 11.

Answer: −3
8 = 2^3 and 1/2 = 2^-1, so (1/2)^n = 2^(-n). Set −n = 3, so n = −3. Check: (1/2)^-3 = 2^3 = 8. If you chose 3 you ignored that 1/2 is 2^-1, and 8 and −8 compare the base with the result directly. A fraction base with a positive exponent gives a fraction, so the exponent must be negative to reach 8.

Answer: 3 × 10⁵
Divide the foil thickness by the film thickness. (3.6 × 10⁻³) ÷ (1.2 × 10⁻⁸): divide 3.6 ÷ 1.2 = 3 and subtract the exponents −3 − (−8) = 5, giving 3 × 10⁵. The foil is 300,000 times as thick. Common mistake: computing −3 − 8 = −11 instead of −3 − (−8) = 5.

Answer: 30 inches
The diagonal is 30 inches. The diagonal cuts the rectangle into two right triangles whose legs are the height and the width, so d² = 18² + 24² = 324 + 576 = 900 and d = 30. If you chose 42, you added the two sides, which is the distance along the edges, not across. If you chose 900, you forgot the square root. Check: the diagonal must be shorter than the sum of the sides.

Answer: 7
The vertical leg is 7. Triangles under the same line are similar, so rise ÷ run is the same for both. The first gives 14 ÷ 4 = 3.5. Applying that to the smaller horizontal leg gives 3.5 × 2 = 7. Subtracting 2 from 14 treats the change in the legs as equal, which is only right if the slope is 1. Check: 7 ÷ 2 = 3.5.

Answer: 27
Step 1: what would remain if the extra 8 seashells were set aside first (84 − 8) = 76 Step 2: equal share for each of the 4 people from what's left (76 ÷ 4) = 19 Step 3: what the one person with the extra amount actually receives (19 + 8) = 27 So the answer is 27 — that person's total.

Answer: 7x - 1 = 34
The equation 7x - 1 = 34 is the one that works. To test a value, substitute it for x and see whether both sides match. With x = 5, the left side of 7x - 1 = 34 comes out equal to the right side. Each of the other three equations gives a left side that is off from its right side when x = 5, so 5 is not their solution. If you picked one of them, you probably checked only part of the calculation. Always finish the arithmetic on both sides before comparing.

Answer: 54
The answer is 54. The students who sleep under 8 hours are counted in the Total column of that row, which adds the two cells 13 + 41 = 54. If you chose 13 or 41, you read only one cell. If you chose 78, you read the grand total, which counts everyone. A total on the edge of the table is a marginal frequency, and it sums a whole row or column.

Answer: 0.01001000100001…
The answer is 0.01001000100001…, because the zeros before each 1 keep growing, so no block repeats and the decimal never ends. The others are rational: 0.010101… = 1/99 repeats, √144 = 12 because 12 × 12 = 144, and −17/6 is a ratio of integers. If you chose 0.010101…, you saw a pattern and assumed it was irrational, but a block that repeats exactly is rational. Ask whether the same block returns every time.

Answer: 5
Step 1: amount taken off the $50 price at 25% off (50 × 25 ÷ 100) = 12 Step 2: the sale price after the discount (50 − 12) = 38 Step 3: money left from the $43 budget after buying it (43 − 38) = 5 So the answer is 5 — money left over after the sale.