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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 4 of 5

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

1PercentagesA model starts with 3200 units and grows by 25% each year for 2 years. Find the final number of units.
2Percentages75% of a number is 375. What is the number?
3AlgebraSolve for x: 28x = 1204
4AlgebraSolve for x: x + y = 13 and x − y = -1.
5Powers & rootsFind n: 19^3 ÷ 19^10 = 19^n.
6Powers & rootsFind n: 14^7 × 14^9 = 14^n.
7Coordinate geometryFind only the x-coordinate of the midpoint of (18, -19) and (14, 2).
8Coordinate geometryReflect (20, -5) in x = 7. What is the new x-coordinate?
9GeometryA shape has area 74 cm². All lengths are multiplied by 5. Find the new area in cm².
cm²
10GeometryA circle has radius 3 cm. Its area is kπ cm². Find k.
11Statistics & probabilityA score of 29 occurs 4 times; a score of 29 occurs 3 times. Find the mean as a fraction or decimal.
12Statistics & probabilityFind the median of 47, 28, 4, 78, 98.
13Quadratic equationsFind the smaller root of (x − 18)(x − 24) = 0.
14Quadratic equationsExpand (5x + 29)². What is the coefficient of x?

From Grade 8

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

15Statistics & probability (Grade 8)Find the range of: 107, 54, 71, 5, 116, 149.
16Algebra (Grade 8)What comes next? 27, 47, 67, 87, …