StudyBrixFree worksheets, study guides and courses

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 2 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 + (7); g(t) = 7t + (4). Find f(g(6)).
2AlgebraFor real h(x) = √(x + 3), which is the domain?
3GeometryA cone has radius 18 cm and height 12 cm. Use π = 3.14. Find its volume in cm³.
cm³
4GeometryA cone has radius 14 cm and height 63 cm. Use π = 3.14. Find its volume in cm³.
cm³
5Statistics & probabilityA score of 3 occurs 5 times; a score of 18 occurs 7 times. Find the mean as a fraction or decimal.
6Statistics & probabilityClub A has 25 bus users and 8 walkers. Club B has 12 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 equationsFind the discriminant of 4x² + 3x + 5 = 0.
8Quadratic equationsThe graph y = 8x² + 20x + 10 has axis x = k. Find k.
9Sequences & seriesFind the sum of the first 5 terms of a geometric sequence with first term 11 and ratio 2.
10Sequences & seriesFind the sum of the first 21 terms of an arithmetic sequence with first term 1 and common difference 6.
11TrigonometryIn a right triangle, the legs opposite and adjacent to θ are 12 cm and 30 cm. Find tan θ as a fraction.
12TrigonometryIn a right triangle, the side opposite θ is 120 cm and the hypotenuse is 200 cm. Find sin θ as a fraction.
13Introductory calculusf(x) = 4x³ + 9x² + (-7)x. Find f′(6).
14Introductory calculusEvaluate the definite integral of 8x^1 from x = 0 to x = 3.

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 = 40 and x − y = 32.
16Quadratic equations (Grade 11)Find the smaller root of (x − 4)(x − 19) = 0.