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Grade 10 · Mathematics

Grade 10 Mathematics diagnostic

16 questions on algebra, powers & roots, coordinate geometry, geometry, statistics & probability, quadratic equations and sequences & series, plus 2 from Grade 9. 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.

1Algebraf(t) = 4t + (1); g(t) = 8t + (-7). Find f(g(0)).
2AlgebraSolve: 15x + 5 = 4x + 181.
3Powers & rootsFind n: 12^3 ÷ 12^10 = 12^n.
4Powers & rootsFind n: 2^10 × 2^3 = 2^n.
5Coordinate geometryRotate (-7, 19) 90° counterclockwise about the origin. Give the new x-coordinate.
6Coordinate geometryFind the slope through (-4, 0) and (-3, 6).
7GeometryA shape has area 43 cm². All lengths are multiplied by 7. Find the new area in cm².
cm²
8GeometryA cone has radius 15 cm and height 81 cm. Use π = 3.14. Find its volume in cm³.
cm³
9Statistics & probabilityFind the population variance of 9, 12, 15, 18, 21. Divide by 5.
10Statistics & probabilityClub A has 12 bus users and 20 walkers. Club B has 13 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.

11Quadratic equationsFind the discriminant of 2x² + 8x + 17 = 0.
12Quadratic equationsThe graph y = 4x² + 32x + 3 has axis x = k. Find k.
13Sequences & seriesAn arithmetic sequence has first term 33 and common difference 10. Find term 12.
14Sequences & seriesFind the sum of the first 6 terms of an arithmetic sequence with first term 18 and common difference 4.

From Grade 9

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

15Algebra (Grade 9)y = kx. When x = 26, y = 104. Find y when x = 76.
16Percentages (Grade 9)A value increases from 810 to 866.7. What is the percentage increase?
%