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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 2 of 5

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

1PercentagesA value increases from 30 to 34.8. What is the percentage increase?
%
2PercentagesA quantity starts at 5400, increases by 50%, then decreases by 25%. Find the final quantity.
3Algebray = kx. When x = 15, y = 105. Find y when x = 60.
4AlgebraSolve for x: 7x = 301
5Powers & rootsFind n: 3^8 ÷ 3^3 = 3^n.
6Powers & roots∛(-1331) = ?
7Coordinate geometryFind the slope through (-7, -7) and (-3, 17).
8Coordinate geometryReflect (-10, 6) in x = 5. What is the new x-coordinate?
9GeometryA cylinder has radius 7 cm and height 22 cm. Its volume is kπ cm³. Find k.
10GeometryA right triangle has legs 168 cm and 576 cm. Find the hypotenuse in cm.
cm
11Statistics & probabilityClub A has 22 bus users and 10 walkers. Club B has 18 bus users. Given that a student is in Club A, what is the probability they use the bus? Give a simplified fraction.

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

12Statistics & probabilityFind the mean of 14, 37, 30, 25.
13Quadratic equationsFind f(0) if f(x) = 5x² + 6x + 13.
14Quadratic equationsFind the smaller root of (x − 17)(x − 30) = 0.

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 11×10×2 cm and 6×4×4 cm. Find their total volume in cm³.
cm³
16Algebra (Grade 8)What comes next? 86, 92, 98, 104, …