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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 1 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 = 28 and x − y = 22.
2Algebraf(t) = 3t + (5); g(t) = 7t + (1). Find f(g(-3)).
3GeometryA cone has radius 8 cm and height 45 cm. Use π = 3.14. Find its volume in cm³.
cm³
4GeometryA cone has radius 3 cm and height 6 cm. Use π = 3.14. Find its volume in cm³.
cm³
5Statistics & probabilityFind the population variance of 32, 34, 36, 38, 40. Divide by 5.
6Statistics & probabilityData: 44, 56, 68, 80, 92, 104, 116, 128. Using medians of the lower four and upper four values, find the interquartile range.
7Quadratic equationsFind f(-5) if f(x) = 2x² + 10x + 5.
8Quadratic equationsThe graph y = 8x² + 4x + 7 has axis x = k. Find k.
9Sequences & seriesAn arithmetic sequence has first term 39 and common difference 3. Find term 17.
10Sequences & seriesFind the sum of the first 6 terms of a geometric sequence with first term 3 and ratio 5.
11TrigonometryIn a right triangle, the legs opposite and adjacent to θ are 7 cm and 35 cm. Find tan θ as a fraction.
12Trigonometry315° equals kπ radians. Find k as a fraction or integer.
13Introductory calculusFor f(x) = 1x^5, find f′(1).
14Introductory calculusf(x) = 4x³ + 9x² + (-6)x. Find f′(6).

From Grade 10

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

15Statistics & probability (Grade 10)A bag has 8 red and 4 blue counters. Draw twice, replacing the first counter. What is the probability both are red? Give a simplified fraction.

Give your answer as a fraction, for example 3/4.

16Algebra (Grade 10)Solve: 9x + 19 = 2x + 68.