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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 2 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) = 15x + (7). Find f⁻¹(442).
2AlgebraSolve for x: x + y = 33 and x − y = 13.
3Powers & rootsFind n: 2^4 ÷ 2^12 = 2^n.
4Powers & roots∛(-21952) = ?
5Coordinate geometryFind only the x-coordinate of the midpoint of (26, 11) and (-25, -4).
6Coordinate geometryRotate (21, -29) 90° counterclockwise about the origin. Give the new x-coordinate.
7GeometryA cylinder has radius 8 cm and height 19 cm. Its volume is kπ cm³. Find k.
8GeometryA circle has radius 21 cm. Its circumference is kπ cm. Find k.
9Statistics & probabilityWhich summary of 2, 3, 4, 5, 100 changes least if 100 becomes 1000?
10Statistics & probabilityData: 16, 19, 22, 25, 28, 31, 34, 37. Using medians of the lower four and upper four values, find the interquartile range.
11Quadratic equationsThe graph y = 1x² + 12x + 13 has axis x = k. Find k.
12Quadratic equationsComplete x² + 68x + □ = (x + 34)².
13Sequences & seriesFind the sum of the first 26 terms of an arithmetic sequence with first term 16 and common difference 1.
14Sequences & seriesAn arithmetic sequence has first term 31 and common difference 8. Find term 27.

From Grade 9

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

15Coordinate geometry (Grade 9)Reflect (-4, 6) in x = 0. What is the new x-coordinate?
16Percentages (Grade 9)A value increases from 610 to 622.2. What is the percentage increase?
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