Grade 8 Math: 10 Free Practice Questions

Answer: 2
The solution is x = 2. Move the x-terms to one side by subtracting 2x from both sides, leaving 7x + 3 = 17. Subtract 3 to get 7x = 14, then divide by 7 to get x = 2. If you chose 14/11, you added the x-terms instead of subtracting them. If you chose 20/7, you added 3 when you should have subtracted it. Check: both sides equal 21.

Answer: 6.2 x 10^-4
The answer is 6.2 x 10^-4. Scientific notation needs a number from 1 up to (but not including) 10, multiplied by a power of ten. Moving the decimal point to make 6.2 takes 4 places, so the exponent is -4. If you chose 6.2 x 10^-5 you miscounted by one place, which is the most common error here. Count the places twice, and remember a number smaller than 1 always has a negative exponent.

Answer: 10√2
The hypotenuse is 10√2 units. With both legs equal to 10, c² = 10² + 10² = 200, so c = √200 = 10√2 because 200 = 100 × 2. If you chose 20, you added the legs. If you chose 200, you forgot the square root. Check: 10√2 is about 14.1, longer than a leg but shorter than the sum 20.

Answer: 7.8 x 10^6
The answer is 7.8 x 10^6. Scientific notation needs a number from 1 up to (but not including) 10, multiplied by a power of ten. Moving the decimal point to make 7.8 takes 6 places, so the exponent is 6. If you chose 7.8 x 10^7 you miscounted by one place, which is the most common error here. Count the places twice, and remember a number smaller than 1 always has a negative exponent.

Answer: 5
f(-2) = 5. Substitute -2 for x, giving 2 times (-2)² - 3. The square of -2 is positive 4, so the expression becomes 2 times 4 - 3 = 8 - 3 = 5. Tempting wrong answers: -11 comes from treating (-2)² as -4, 13 comes from squaring after multiplying, (2 times -2)² - 3, and -7 comes from skipping the square. Check: put the negative input in brackets before you square.

Answer: 3 × 10⁵
Divide the numbers and subtract the exponents. 9 ÷ 3 = 3 and 7 − (2) = 5, so the quotient is 3 × 10⁵. Common mistake: adding the exponents instead of subtracting, or leaving a number part that is less than 1.

Answer: 1.65 × 10⁷
The powers of ten match, so add the number parts: 9.5 + 7 = 16.5. The result is 16.5 × 10⁶. Writing 16.5 × 10⁶ with a number part from 1 to 10 gives 1.65 × 10⁷. Common mistake: adding or subtracting the number parts without first matching the powers of ten.

Answer: 6
The value is k = 6. Distribute k to get kx + 4k = 6x + 24. For both sides to be identical, the x-coefficients must match, so k = 6, and the constants must match: 4k = 24 is true when k = 6. If you chose 24, you matched the constant instead of the coefficient. If you chose 4, you used the number in the parentheses. Check by substituting k = 6 and simplifying.

Answer: When the input is 3, the output is 7
The notation f(3) = 7 says that the function f turns the input 3 into the output 7. The number in the brackets is the input, and the value after the equals sign is the output. Tempting wrong answer: f times 3. The brackets do not mean multiplication here, they hold the input. Check: read it aloud as f of 3 equals 7, and the point (3, 7) lies on the graph.

Answer: An acute triangle
The new triangle is an acute triangle. The new sides are 5, 6 and 7. Then 5² + 6² = 61 and 7² = 49. Since the sum of the squares of the shorter sides is greater than the square of the longest side, the triangle is acute. Adding the same amount to every side does not keep the right angle, only multiplying does. Test the numbers rather than trusting the pattern.