Mathematics Grade 8 Practice Questions
1. Convert 0.2 ? into a fraction.
2. What is the decimal expansion of 5/6?
3. Which number is the closest approximation to π/4?
4. Without using a calculator, identify which point on the number line could be √3?.
a. Point A
b. Point B
c. Point C
d. Point D
5. Simplify 52x54x5-4x5-2.
6. Simplify (2/3)-3.
7. Solve the equation for x: x2=16
8. Solve the equation for x: x3=-27
9. What is the decimal notation of 7x10-4?
10. What is 0.0143 written in scientific notation?
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 5x6=0.83 ?
3. C: You can approximate ?=3.14. Then 3.14x4=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 nth 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
8. C: When solving an equation of the form xn=b, take the nth 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 = 3 √-27
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: 1.43x10-2 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.
Last Updated: 03/01/2017