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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 5 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 42. What is the number?
2PercentagesA value increases from 650 to 702. What is the percentage increase?
%
3AlgebraSolve: 14x + 5 = 2x + 113.
4AlgebraSolve for x: 23x = -276
5Powers & roots11^3 = ?
6Powers & rootsFind n: 18^2 ÷ 18^10 = 18^n.
7Coordinate geometryReflect (-12, -10) in x = -3. What is the new x-coordinate?
8Coordinate geometryRotate (10, 23) 90° counterclockwise about the origin. Give the new x-coordinate.
9GeometryA cone has radius 15 cm and height 57 cm. Use π = 3.14. Find its volume in cm³.
cm³
10GeometryA right triangle has legs 119 cm and 408 cm. Find the hypotenuse in cm.
cm
11Statistics & probabilityA score of 19 occurs 10 times; a score of 23 occurs 5 times. Find the mean as a fraction or decimal.
12Statistics & probabilityFind the median of 49, 58, 79, 50, 15.
13Quadratic equationsFind f(3) if f(x) = 3x² + 5x + 12.
14Quadratic equationsExpand (10x + 24)². What is the coefficient of x?

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 7×8×3 cm and 2×6×8 cm. Find their total volume in cm³.
cm³
16Percentages (Grade 8)Find 90% of 130.