Mathematics Grade 8 Practice Questions

1. Convert 0.2 ? into a fraction.

1. ¹/₅ 
2. ¹¹/₅₀
3. ²/₉
4. ²/₇

2. What is the decimal expansion of ⁵/₆?

1. 0.(56)
2. 0.83
3. 0.56
4. 1.2

3. Which number is the closest approximation to ^π/₄?

1. 0.85
2. 1.0
3. 0.785
4. 1.273

4. Without using a calculator, identify which point on the number line could be √3?.

1. Point A
2. b. Point B
3. Point C
4. Point D

5. Simplify 5²x5⁴x5^-4x5^-2.

1. 1
2. 5
3. 0
4. 2.5

6. Simplify (²/₃)^-3.

1. ⁸/₂₇
2. ²⁷/₈
3. ^-8/₂₇
4. ^-27/₈

7. Solve the equation for x: x²=16

1. x=4
2. x=±4
3. x=8
4. x=±8

8. Solve the equation for x: x³=-27

1. x=-9
2. x=±9
3. x=-3
4. x=±3

9. What is the decimal notation of 7×10^-4?

1. 70,000
2. 7,000
3. 0.00007
4. 0.0007

10. What is 0.0143 written in scientific notation?

1. 1.43×10
2. 1.43×10²
3. 1.43×10^-1
4. 1.43×10^-2

Answers and Explanations

1. C: When converting a decimal whose value repeats itself indefinitely, write the repeating digit or digits in the numerator. In this problem, the repeating digit is 2. In the denominator, place 9 for every repeating digit, then reduce the fraction to lowest terms. In this problem a single 9 is in the denominator, so the answer is ²/₉. Another example is 0.‾24= ²⁴/₉₉=⁸/₃₃

2. B: 5/6 can be rewritten as 5×6=0.83 ?

3. C: You can approximate ?=3.14. Then 3.14×4=0.785

4. C: See that 2² =4 . Since 2² > 3, we know √2² > √3 which is to say √3 < 2. Similarly, see that √3 > 1. This means that √3 is between 1 and 2. The only point between those on the number line is point C.

5. A: When multiplying powers that have the same base, the exponents are added up, and the base remains the same. Here it would be: 5²+4+(-4)+(-2) )=5⁰. Then, using the zero exponent rule of a⁰=1 whenever a ≠ 0, we find that the answer is 5⁰=1

6. B: The negative exponent will take the reciprocal of the base, then the exponent will distribute to both the numerator and denominator and the powers will be simplified. (2/3)^-3=(3/2)³=3³/2₃ =27/8

7. B: When solving an equation of the form xⁿ =b, take the n^th root of both sides of the equation. If n is even, then it will need to be =±? ⁿ√ b , meaning there are two solutions, one positive and one negative. If n is even and b is less than zero, then no real solution exists. 
x²=16 
√(x² )=± √16
x=±4

8. C: When solving an equation of the form xⁿ=b, take the n^th root of both sides of the equation. If n is even, then it will need to be ±?ⁿ√b, and if n is odd, it is only the ⁿ√ b. If n is odd, then there is only one solution and the sign of the answer is the sign of b.
x³=-27 
√ x³ = ³ √-27
x=-3

9. D: Because the exponent of 10 is -4, the decimal which is located behind the 7 will move 4 spaces to the left, and any of the empty spaces will fill with 0’s. so 7x 10? ^-4=0.0007

10. D: 1.43×10^-2 is the same as 1.43x¹/₁₀₀ or .0143. To write a number in scientific notation, the form is ax10ⁿ, where 1 ≤ a < 10. The decimal needs to move two spaces to the right so that it is immediately to the right of the 1. To move the decimal 2 places, we multiply by 100, but we also need to multiply by 10^-2 to cancel. .0143=.0143x¹⁰⁰/₁₀₀=1.43x¹/₁₀₀=1.43 x?10^-2.