Grade 8 · Mathematics

Grade 8 Mathematics diagnostic

16 questions on arithmetic, percentages, algebra, powers & roots, coordinate geometry, geometry and statistics & probability, plus 2 from Grade 7. Answer what you can, then check your answers to see which topics are secure and what to practise next.

16 questions7 topicsAbout 20 minutesSet 1 of 5

Skip a question if you do not know the answer. It is better than guessing, because it shows what to practise.

1Arithmetic(-82) − (-27) = ?

Your answer

2Arithmetic70 + 15 × 18 = ?

Your answer

3PercentagesA value increases from 580 to 725. What is the percentage increase?

Your answer%

4PercentagesFind 65% of 190.

Your answer

5AlgebraEvaluate 6x + 5 when x = 1.

Your answer

6AlgebraSolve for x: 10x + 58 = 178

Your answer

7Powers & rootsFind n: 5^9 ÷ 5^12 = 5^n.

Your answer

8Powers & rootsFind n: 9^9 × 9^3 = 9^n.

Your answer

9Coordinate geometryRotate (-22, 13) 90° counterclockwise about the origin. Give the new x-coordinate.

Your answer

10Coordinate geometryFind only the x-coordinate of the midpoint of (-10, 14) and (21, 9).

Your answer

11GeometryA triangle has base 45 cm and perpendicular height 33 cm. Find its area in cm².

Your answercm²

12GeometryA cone has radius 22 cm and height 9 cm. Use π = 3.14. Find its volume in cm³.

Your answercm³

13Statistics & probabilityFind the range of: 113, 20, 34, 71, 94, 11.

Your answer

14Statistics & probabilityData: 36, 43, 50, 57, 64, 71, 78, 85. Using medians of the lower four and upper four values, find the interquartile range.

Your answer

From Grade 7

These questions check skills from the grade below, so gaps can be spotted early.

15Decimals (Grade 7)39.8 × 49 = ?

Your answer

16Percentages (Grade 7)Write 42% as a fraction in simplest form.

Your answer

Give your answer as a fraction, for example 3/4.