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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 1 of 5

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

1Algebraf(x) = 12x + (18). Find f⁻¹(294).
2AlgebraSolve for x: x + y = 52 and x − y = 24.
3Powers & rootsFind n: 16^2 × 16^5 = 16^n.
4Powers & rootsFind n: 18^7 ÷ 18^12 = 18^n.
5Coordinate geometryFind the slope through (5, -2) and (15, 78).
6Coordinate geometryRotate (-25, -16) 90° counterclockwise about the origin. Give the new x-coordinate.
7GeometryA cone has radius 18 cm and height 30 cm. Use π = 3.14. Find its volume in cm³.
cm³
8GeometryA right triangle has legs 84 cm and 112 cm. Find the hypotenuse in cm.
cm
9Statistics & probabilityP(A) = 13/27. Find P(not A).
10Statistics & probabilityData: 11, 16, 21, 26, 31, 36, 41, 46. Using medians of the lower four and upper four values, find the interquartile range.
11Quadratic equationsFind the smaller root of (x − 6)(x − 21) = 0.
12Quadratic equationsFind f(-7) if f(x) = 6x² + 6x + 14.
13Sequences & seriesAn arithmetic sequence has first term 8 and common difference 13. Find term 8.
14Sequences & seriesA geometric sequence starts at 12, with common ratio 2. Find term 5.

From Grade 9

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

15Geometry (Grade 9)Find the volume of a cuboid measuring 21 cm × 18 cm × 4 cm, in cm³.
cm³
16Statistics & probability (Grade 9)Find the mean of 39, 5, 21, 45.