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 3 of 5

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

1PercentagesA recipe ratio of rice to water is 1:2 by volume. Which instruction preserves it?

A. Use 3 cups rice and 4 cups water.B. Use 3 cups rice and 6 cups water.C. Use 4 cups rice and 5 cups water.D. Use 2 cups rice and 3 cups water.

2PercentagesA quantity starts at 3600, increases by 25%, then decreases by 40%. Find the final quantity.

Your answer

3AlgebraSolve for x: 8x + 74 = 154

Your answer

4Algebraf(x) = 13x + (-2). Find f⁻¹(349).

Your answer

5Powers & rootsFind n: 15^12 ÷ 15^5 = 15^n.

Your answer

6Powers & rootsFind n: 19^2 × 19^3 = 19^n.

Your answer

7Coordinate geometryFind only the x-coordinate of the midpoint of (-26, -19) and (-24, -8).

Your answer

8Coordinate geometryFind the slope through (-1, 1) and (5, 31).

Your answer

9GeometryA trapezoid has parallel sides 13 cm and 21 cm and height 22 cm. Find its area in cm².

Your answercm²

10GeometryA cone has radius 22 cm and height 90 cm. Use π = 3.14. Find its volume in cm³.

Your answercm³

11Statistics & probabilityA bag has 10 red and 13 blue counters. Draw twice, replacing the first counter. What is the probability both are red? Give a simplified fraction.

Your answer

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

12Statistics & probabilityClub A has 7 bus users and 9 walkers. Club B has 15 bus users. Given that a student is in Club A, what is the probability they use the bus? Give a simplified fraction.

Your answer

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

13Quadratic equationsFind the smaller root of (x − 8)(x − 15) = 0.

Your answer

14Quadratic equationsFind f(-6) if f(x) = 5x² + 8x + 7.

Your answer

From Grade 8

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

15Percentages (Grade 8)Find 18% of 420.

Your answer

16Geometry (Grade 8)Two interior angles of a triangle are 75° and 37°. Find the third angle in degrees.

Your answer°