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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 4 of 5

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

1AlgebraSolve: 14x + 18 = 2x + 138.
2Algebraf(x) = 5x + (4). Find f⁻¹(54).
3Powers & rootsFind n: 18^3 ÷ 18^9 = 18^n.
4Powers & rootsFind n: 5^9 × 5^10 = 5^n.
5Coordinate geometryFind only the x-coordinate of the midpoint of (22, -11) and (17, 12).
6Coordinate geometryRotate (6, -11) 90° counterclockwise about the origin. Give the new x-coordinate.
7GeometryA cylinder has radius 13 cm and height 5 cm. Its volume is kπ cm³. Find k.
8GeometryA circle has radius 24 cm. Its area is kπ cm². Find k.
9Statistics & probabilityP(A) = 14/15. Find P(not A).
10Statistics & probabilityClub A has 22 bus users and 6 walkers. Club B has 7 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 smaller root of (x − 19)(x − 26) = 0.
12Quadratic equationsFind f(2) if f(x) = 1x² + 1x + 2.
13Sequences & seriesAn arithmetic sequence has first term 18 and common difference 2. Find term 6.
14Sequences & seriesA geometric sequence starts at 5, with common ratio 2. Find term 6.

From Grade 9

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

15Algebra (Grade 9)Solve for x: 11x = -462
16Percentages (Grade 9)A value increases from 300 to 402. What is the percentage increase?
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