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Grade 11 · Mathematics

Grade 11 Mathematics diagnostic

16 questions on algebra, geometry, statistics & probability, quadratic equations, sequences & series, trigonometry and introductory calculus, plus 2 from Grade 10. 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.

1AlgebraSolve for x: x + y = 31 and x − y = 17.
2Algebraf(x) = 13x + (28). Find f⁻¹(-232).
3GeometryA cone has radius 23 cm and height 63 cm. Use π = 3.14. Find its volume in cm³.
cm³
4GeometryA cone has radius 7 cm and height 48 cm. Use π = 3.14. Find its volume in cm³.
cm³
5Statistics & probabilityA score of 6 occurs 6 times; a score of 30 occurs 10 times. Find the mean as a fraction or decimal.
6Statistics & probabilityFind the population variance of -6, 3, 12, 21, 30. Divide by 5.
7Quadratic equationsFind the smaller root of (x − 8)(x − 9) = 0.
8Quadratic equationsThe graph y = 1x² + 13x + 7 has axis x = k. Find k.
9Sequences & seriesAn arithmetic sequence has first term 7 and common difference 13. Find term 19.
10Sequences & seriesFind the sum of the first 4 terms of a geometric sequence with first term 11 and ratio 2.
11TrigonometryIn a right triangle, the side opposite θ is 110 cm and the hypotenuse is 286 cm. Find sin θ as a fraction.
12TrigonometryIn a right triangle, the legs opposite and adjacent to θ are 7 cm and 34 cm. Find tan θ as a fraction.
13Introductory calculusEvaluate the definite integral of (20x + 2) from x = 2 to x = 7.
14Introductory calculusFor f(x) = 11x^5, find f′(5).

From Grade 10

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

15Coordinate geometry (Grade 10)Find only the x-coordinate of the midpoint of (28, -1) and (-2, 20).
16Statistics & probability (Grade 10)P(A) = 13/21. Find P(not A).