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Grade 12 · Mathematics

Grade 12 Mathematics diagnostic

16 questions on algebra, geometry, statistics & probability, quadratic equations, sequences & series, trigonometry and introductory calculus, plus 2 from Grade 11. 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.

1Algebraf(t) = 5t + (-2); g(t) = 6t + (6). Find f(g(2)).
2AlgebraFor real log₂(x − 1), the domain is
3GeometryA cone has radius 11 cm and height 66 cm. Use π = 3.14. Find its volume in cm³.
cm³
4GeometryA cone has radius 23 cm and height 18 cm. Use π = 3.14. Find its volume in cm³.
cm³
5Statistics & probabilityClub A has 11 bus users and 3 walkers. Club B has 15 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.

6Statistics & probabilityData: 14, 16, 18, 20, 22, 24, 26, 28. Using medians of the lower four and upper four values, find the interquartile range.
7Quadratic equationsThe graph y = 8x² + 7x + 17 has axis x = k. Find k.
8Quadratic equationsFind the discriminant of 6x² + 12x + 7 = 0.
9Sequences & seriesFind the sum of the first 22 terms of an arithmetic sequence with first term 8 and common difference 8.
10Sequences & seriesA geometric sequence starts at 6, with common ratio 5. Find term 3.
11TrigonometryIn a right triangle, the side opposite θ is 39 cm and the hypotenuse is 65 cm. Find sin θ as a fraction.
12TrigonometryIn a right triangle, the legs opposite and adjacent to θ are 15 cm and 38 cm. Find tan θ as a fraction.
13Introductory calculusEvaluate the definite integral of 16x^1 from x = 0 to x = 1.
14Introductory calculusf(x) = 1x³ + 7x² + (2)x. Find f′(2).

From Grade 11

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

15Algebra (Grade 11)f(x) = 3x + (23). Find f⁻¹(-16).
16Quadratic equations (Grade 11)Find the smaller root of (x − 20)(x − 23) = 0.