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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 5 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) = 8t + (-7); g(t) = 2t + (-1). Find f(g(6)).
2AlgebraAn inverse function over a specified domain requires the original function to be
3GeometryA cone has radius 10 cm and height 51 cm. Use π = 3.14. Find its volume in cm³.
cm³
4GeometryA cone has radius 6 cm and height 57 cm. Use π = 3.14. Find its volume in cm³.
cm³
5Statistics & probabilityClub A has 10 bus users and 23 walkers. Club B has 14 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 & probabilityFind the population variance of 55, 56, 57, 58, 59. Divide by 5.
7Quadratic equationsThe graph y = 1x² + 6x + 7 has axis x = k. Find k.
8Quadratic equationsFind the discriminant of 2x² + 15x + 5 = 0.
9Sequences & seriesAn arithmetic sequence has first term 22 and common difference 4. Find term 28.
10Sequences & seriesA geometric sequence starts at 11, with common ratio 5. Find term 7.
11TrigonometryIn a right triangle, the legs opposite and adjacent to θ are 31 cm and 14 cm. Find tan θ as a fraction.
12TrigonometryIn a right triangle, the side opposite θ is 33 cm and the hypotenuse is 55 cm. Find sin θ as a fraction.
13Introductory calculusFind the limit of 6x² + 19 as x approaches -6.
14Introductory calculusEvaluate the definite integral of (24x + 15) from x = 2 to x = 8.

From Grade 11

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

15Quadratic equations (Grade 11)Expand (8x + 21)². What is the coefficient of x?
16Algebra (Grade 11)f(x) = 5x + (-14). Find f⁻¹(106).