Grade 8 Math: 10 Free Practice Questions

Answer: 18
Step 1: what would remain if the extra 6 baseball cards were set aside first (66 − 6) = 60 Step 2: equal share for each of the 5 people from what's left (60 ÷ 5) = 12 Step 3: what the one person with the extra amount actually receives (12 + 6) = 18 So the answer is 18 — that person's total.

Answer: The triangles are similar, so rise over run stays the same
Triangles drawn between points on the line are similar, so rise over run never changes. Pick any two points and draw a right triangle with the line as its slanted side. A different pair gives a bigger or smaller triangle with the same angles, so the legs stay in the same ratio. Points on a line do not share a y-coordinate, and rise equals run only when the slope is 1. Check with (1, 2), (2, 4) and (4, 8): the ratio is 2 every time.

Answer: (5, 2)
M' is (5, 2). A 90 degree clockwise rotation about the origin follows the rule (x, y) becomes (y, -x), so (-2, 5) becomes (5, 2). If you chose (-5, -2) you turned the opposite way, which swaps the signs. To remember the direction, rotate the easy point (1, 0): clockwise it (1, 0) goes down to (0, -1), and the rule must reproduce that.

Answer: 22
Step 1: what would remain if the extra 5 coins were set aside first (90 − 5) = 85 Step 2: equal share for each of the 5 people from what's left (85 ÷ 5) = 17 Step 3: what the one person with the extra amount actually receives (17 + 5) = 22 So the answer is 22 — that person's total.

Answer: 1
Any nonzero number raised to the power 0 equals 1. For example 9^2 ÷ 9^2 = 1, and by the quotient rule it also equals 9^(2-2) = 9^0. If you chose 0 you treated the exponent as a multiplier, and if you chose 9 you ignored the exponent. Zero factors of 9 is an empty product, and an empty product is 1.

Answer: 1 × 10⁻³
Multiply the numbers and add the exponents. 4 × 2.5 = 10 and 5 + (-9) = -4, so the product is 10 × 10⁻⁴. Since 10 is not less than 10, rewrite it as 1 × 10¹, which makes the answer 1 × 10⁻³. Common mistake: multiplying the exponents instead of adding them, or forgetting to adjust the exponent when the number part reaches 10 or more.

Answer: Irrational, because √7 is irrational and 2 is a nonzero rational number.
The answer is irrational. 2 × √7 ≈ 5.29, and a nonzero rational number times an irrational number is irrational: if 2√7 were rational, dividing by 2 would make √7 rational, but 2² = 4 and 3² = 9 leave no square at 7. If you chose rational because 2 × 7 = 14, you multiplied 2 by the 7 under the root, but the 2 sits outside the root. Keep the coefficient outside when you test a root.

Answer: 0.031
Multiplying by 10⁻² shifts the decimal point of 3.1. A negative exponent of -2 moves the decimal point 2 places to the left. That gives 0.031. Common mistake: moving the decimal point the wrong way, or treating a negative exponent as a negative number.

Answer: 2.5 × 10⁴
Divide the numbers and subtract the exponents. 2 ÷ 8 = 0.25 and 7 − (2) = 5, so the quotient is 0.25 × 10⁵. Since 0.25 is less than 1, rewrite it as 2.5 × 10⁻¹, which makes the answer 2.5 × 10⁴. Common mistake: adding the exponents instead of subtracting, or leaving a number part that is less than 1.

Answer: 3^-3 < 3^-2
3^-3 = 1/27 and 3^-2 = 1/9, and 1/27 < 1/9. The others are false: 4^-2 = 1/16 < 1/4, 2^-1 = 1/2 < 1, and 5^-2 = 1/25 is not equal to 25. Convert every power to a fraction before comparing. With a base above 1, a more negative exponent always gives a smaller value, so a negative exponent never makes a power bigger than 1.