Grade 9 · Mathematics

Grade 9 Mathematics diagnostic

16 questions on percentages, algebra, powers & roots, coordinate geometry, geometry, statistics & probability and quadratic equations, plus 2 from Grade 8. 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.

1Percentages10% of a number is 110. What is the number?

Your answer

2PercentagesA quantity starts at 600, increases by 20%, then decreases by 20%. Find the final quantity.

Your answer

3AlgebraSolve for x: 11x + 45 = 78

Your answer

4Algebraf(t) = 4t + (1); g(t) = 3t + (-2). Find f(g(-1)).

Your answer

5Powers & roots√144 = ?

Your answer

6Powers & rootsFind n: 14^12 ÷ 14^11 = 14^n.

Your answer

7Coordinate geometryFind only the x-coordinate of the midpoint of (25, 7) and (-26, 7).

Your answer

8Coordinate geometryRotate (-2, 25) 90° counterclockwise about the origin. Give the new x-coordinate.

Your answer

9GeometryA cylinder has radius 19 cm and height 27 cm. Its volume is kπ cm³. Find k.

Your answer

10GeometryA circle has radius 54 cm. Its area is kπ cm². Find k.

Your answer

11Statistics & probabilityFind the mean of 40, 8, 36, 10.

Your answer

12Statistics & probabilityA bag contains 25 red counters and 32 blue counters. One counter is drawn at random. What is the probability of red?

Your answer

13Quadratic equationsFind f(5) if f(x) = 6x² + 2x + 1.

Your answer

14Quadratic equationsExpand (10x + 17)². What is the coefficient of x?

Your answer

From Grade 8

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

15Geometry (Grade 8)Two non-overlapping rectangular boxes measure 3×9×6 cm and 7×5×3 cm. Find their total volume in cm³.

Your answercm³

16Arithmetic (Grade 8)(-19) × (-4) = ?

Your answer