Grade 8 Math: 10 Free Practice Questions

Answer: 3.2
The answer is 3.2. Since 3² = 9 and 4² = 16, √10 is between 3 and 4, and a closer calculation gives √10 ≈ 3.16228, which rounds to 3.2 at the tenths place. If you chose 5.0, you divided 10 by 2 instead of finding the number that multiplies by itself to make 10. Check by squaring: 3.2² = 10.24 is close to 10.

Answer: Grade 7 40% vs Grade 8 20%: there may be an association
The careful sentence reports the two percents and says 'may be an association'. The relative frequencies are 24 ÷ 60 = 40% and 4 ÷ 20 = 20%. A table can show that two variables go together, but it cannot show that one makes the other happen, so words like 'makes' overstate it. 'All' is false, because only 40% fit, and 'share no students' contradicts the table, which has students in both columns.

Answer: 5
The input is x = 5. Set the rule equal to 11, so 3x - 4 = 11. Add 4 to both sides to get 3x = 15, then divide by 3 to get x = 5. Check: f(5) = 3 times 5 - 4 = 11. Tempting wrong answers: 29 comes from computing 3 times 11 - 4, which treats 11 as the input, and 7 comes from just adding 4 and ignoring the 3. Check by substituting back.

Answer: 3
The solution is x = 3. Move the x-terms to one side by subtracting 3x from both sides, leaving 4x + 5 = 17. Subtract 5 to get 4x = 12, then divide by 4 to get x = 3. If you chose 6/5, you added the x-terms instead of subtracting them. If you chose 11/2, you added 5 when you should have subtracted it. Check: both sides equal 26.

Answer: y is a function of x, but x is not a function of y
Check each direction by looking for a repeated first number. Reading from x to y, the inputs 1, 2, 3 and 4 are all different, so y is a function of x. Reading from y to x, the input 5 is paired with two values of x, so x is not a function of y. Tempting wrong answer: both, because every x has a y. Check: swap the columns and repeat the test.

Answer: 7
They cost the same after 7 visits. Let x be the number of visits and set the costs equal: 32 + 5x = 4 + 9x. Subtract 5x from both sides to get 32 = 4 + 4x, then subtract 4: 28 = 4x, so x = 7. If you chose 28, you stopped before dividing by 4. If you chose 9, you added the starting costs. Check: both plans cost 67.

Answer: 120 nanometers
Divide the length in meters by the size of a nanometer. 1.2 × 10⁻⁷ ÷ 10⁻⁹ = 1.2 × 10² = 120. The virus is 120 nanometers long, which is easier to say than 0.00000012 meter. Common mistake: getting the exponent difference wrong: −7 − (−9) is 2, not −16 or 16.

Answer: 16 cm
The missing leg is 16 cm. The hypotenuse is 34, so c² = a² + b² and the missing leg satisfies b² = 34² − 30² = 1156 − 900 = 256, giving b = 16. If you chose √2056, you added the squares, which would only be right when finding the hypotenuse. If you chose 256, you forgot the final square root. Check: 30² + 16² = 34².

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: 15
The smallest number is 15. Let the numbers be x, x + 1 and x + 2. Their sum is 3x + 3 = 48. Subtract 3 to get 3x = 45, then divide by 3 to get x = 15. The numbers are 15, 16 and 17. If you chose 16, you found the middle number by dividing 48 by 3. If you chose 17, you gave the largest. Check: 15 + 16 + 17 = 48.