Grade 8 Math: 10 Free Practice Questions

Answer: 10^6
10^3 ÷ 10^-3 = 10^(3-(-3)) = 10^6, which is 1,000,000 millimeters. Sanity check: a kilometer is far longer than a millimeter, so the count must be huge. If you got 10^0 you subtracted 3 from 3, and the negative powers come from reversing the division.

Answer: 3^7
3^5 × 3^2 = (5 factors of 3) × (2 factors of 3) = 7 factors of 3, so the exponents add: 3^7. The base stays 3. If you chose 3^10 you multiplied the exponents instead of adding them. If you chose 9^7 or 6^7 you combined the bases, but the base stays 3 and only the exponents combine.

Answer: 1 / (2 × 2 × 2 × 2)
A negative exponent means 'one divided by' the positive power: 2^-4 = 1/2^4 = 1/(2 × 2 × 2 × 2) = 1/16. If you chose −(2 × 2 × 2 × 2) you let the negative exponent change the sign of the value. If you chose 1 / (2 × 4) or 2 × (−4) you combined the base and exponent instead of repeating the base four times.

Answer: Point A
The answer is Point A. Use perfect squares: 3² = 9 and 4² = 16, so √10 is between 3 and 4. Point A sits at about 3.16, and 3.16² = 9.9856 is close to 10. If you chose Point B, near 2, that point has 2² = 4, which is not 10. Square the position you read; it should land near the number under the root.

Answer: 60
The solution is x = 60. Move the x-terms together and the constants together: x/3 - x/5 = 8. With the common denominator 15, the left side is 2x/15, so 2x = 120 and x = 60. If you chose 15, you added the two fractions instead of subtracting. If you chose 180, you added 8 to 16 when it needed to be subtracted. Check: 60/3 + 8 = 28 and 60/5 + 16 = 28.

Answer: 100π m³
The volume is 100π m³. The figure gives the diameter, 10 m, so the radius is 10 ÷ 2 = 5 m. The volume of a cylinder is V = π × r² × h, so V = π × 5² × 4 = 100π cubic m. If you chose 400π m³, you used 10 as the radius. If you chose 40π m³, you used 2πrh, which is a surface-area style formula. Volume is measured in cubic units, so the unit is m³.

Answer: Dilation, scale factor 2, from the origin
The answer is dilation, scale factor 2, from the origin. Follow vertex A: it moves from (1, 1) to (2, 2), and the other vertices follow the same rule, so the whole figure is carried exactly onto the image. If you chose "Translation: 1 unit right and 1 unit up", test it on A: that would land at (2, 2), not (2, 2). Check one vertex against each rule - the rule that sends it to the right place for EVERY vertex is the answer.

Answer: (1, 1)
B' is (1, 1). Vertex B is at (1, -1). Reflecting over the x-axis keeps the distance to the axis and puts the point on the other side: the y-coordinate changes sign, giving (1, 1). If you chose (-1, -1) you reflected over the other axis. Read the vertex off the grid first, then flip only the coordinate that measures distance from the mirror axis.

Answer: 5 × 10⁻¹ meters
Height = thickness × number of sheets. (1 × 10⁻⁴)(5 × 10³) = 5 × 10⁻¹ meters. That is 0.5 meter, about the height of a small table. Common mistake: adding −4 and 3 and getting a positive exponent.

Answer: Typist B, 64 words per minute
Typist B has the greater rate, 64 words per minute. For A the unit rate is the number multiplying x, which is 48. For B divide y by x: 192 ÷ 3 = 64. Comparing 48 and 64, 64 is larger. The y-values in the table, such as 384, are totals, not rates. Check: put x = 6 into y = 48x and compare 288 with B's 384.