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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 3 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 + (-8); g(t) = 3t + (6). Find f(g(0)).
2AlgebraIf f(x) = 2x + 1 and g(x) = x², find f(g(3)).
3GeometryA cone has radius 11 cm and height 15 cm. Use π = 3.14. Find its volume in cm³.
cm³
4GeometryA cone has radius 2 cm and height 72 cm. Use π = 3.14. Find its volume in cm³.
cm³
5Statistics & probabilityA score of 14 occurs 6 times; a score of 11 occurs 2 times. Find the mean as a fraction or decimal.
6Statistics & probabilityClub A has 23 bus users and 18 walkers. Club B has 9 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.

7Quadratic equationsThe graph y = 5x² + 10x + 12 has axis x = k. Find k.
8Quadratic equationsFind the discriminant of 4x² + 1x + 12 = 0.
9Sequences & seriesA geometric sequence starts at 9, with common ratio 3. Find term 7.
10Sequences & seriesFind the sum of the first 5 terms of an arithmetic sequence with first term 10 and common difference 5.
11TrigonometryIn a right triangle, the side opposite θ is 312 cm and the hypotenuse is 663 cm. Find sin θ as a fraction.
12TrigonometryIn a right triangle, the legs opposite and adjacent to θ are 8 cm and 3 cm. Find tan θ as a fraction.
13Introductory calculusFind the limit of 2x² + 16 as x approaches -4.
14Introductory calculusEvaluate the definite integral of (10x + 7) 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 (7x + 13)². What is the coefficient of x?
16Algebra (Grade 11)Solve for x: x + y = 45 and x − y = 33.