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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 3 of 5

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

1AlgebraSolve: 7x + 3 = 3x + 11.
2AlgebraFor p(x) = x² + 1, calculate p(−3) − p(3).
3Powers & rootsFind n: 15^9 × 15^7 = 15^n.
4Powers & roots∛(-17576) = ?
5Coordinate geometryFind only the x-coordinate of the midpoint of (15, -19) and (0, -6).
6Coordinate geometryFind the slope through (-4, 0) and (-3, 6).
7GeometryA shape has area 66 cm². All lengths are multiplied by 2. Find the new area in cm².
cm²
8GeometryA right triangle has legs 145 cm and 348 cm. Find the hypotenuse in cm.
cm
9Statistics & probabilityFind the population variance of 70, 72, 74, 76, 78. Divide by 5.
10Statistics & probabilityClub A has 22 bus users and 10 walkers. Club B has 18 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 8x² + 19x + 12 = 0.
12Quadratic equationsThe graph y = 4x² + 7x + 10 has axis x = k. Find k.
13Sequences & seriesFind the sum of the first 28 terms of an arithmetic sequence with first term 15 and common difference 6.
14Sequences & seriesAn arithmetic sequence has first term 32 and common difference 7. Find term 21.

From Grade 9

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

15Percentages (Grade 9)25% of a number is 255. What is the number?
16Statistics & probability (Grade 9)Find the median of 72, 72, 70, 51, 85.