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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 1 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) = 9t + (-5); g(t) = 5t + (7). Find f(g(2)).
2AlgebraFor real h(x) = √(x + 3), which is the domain?
3GeometryA cone has radius 21 cm and height 36 cm. Use π = 3.14. Find its volume in cm³.
cm³
4GeometryA cone has radius 6 cm and height 84 cm. Use π = 3.14. Find its volume in cm³.
cm³
5Statistics & probabilityData: 23, 26, 29, 32, 35, 38, 41, 44. Using medians of the lower four and upper four values, find the interquartile range.
6Statistics & probabilityFind the population variance of 28, 30, 32, 34, 36. Divide by 5.
7Quadratic equationsFind the discriminant of 4x² + 11x + 18 = 0.
8Quadratic equationsThe graph y = 10x² + 29x + 7 has axis x = k. Find k.
9Sequences & seriesAn arithmetic sequence has first term 8 and common difference 8. Find term 15.
10Sequences & seriesFind the sum of the first 18 terms of an arithmetic sequence with first term 18 and common difference 3.
11TrigonometryIn a right triangle, the legs opposite and adjacent to θ are 14 cm and 17 cm. Find tan θ as a fraction.
12TrigonometryIn a right triangle, the side opposite θ is 152 cm and the hypotenuse is 323 cm. Find sin θ as a fraction.
13Introductory calculusEvaluate the definite integral of (14x + 10) from x = 0 to x = 2.
14Introductory calculusf(x) = 7x³ + 10x² + (-5)x. Find f′(-4).

From Grade 11

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

15Algebra (Grade 11)Solve for x: x + y = 11 and x − y = 9.
16Quadratic equations (Grade 11)Find f(-7) if f(x) = 4x² + 6x + 14.