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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 4 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) = 3t + (10); g(t) = 7t + (-2). Find f(g(-2)).
2Algebraf(x) = 15x + (-16). Find f⁻¹(194).
3GeometryA cone has radius 17 cm and height 81 cm. Use π = 3.14. Find its volume in cm³.
cm³
4GeometryA cone has radius 23 cm and height 45 cm. Use π = 3.14. Find its volume in cm³.
cm³
5Statistics & probabilityHow many ordered selections of 3 distinct items can be made from 16 items without repetition?
6Statistics & probabilityFind the population variance of 35, 37, 39, 41, 43. Divide by 5.
7Quadratic equationsComplete x² + 74x + □ = (x + 37)².
8Quadratic equationsExpand (12x + 9)². What is the coefficient of x?
9Sequences & seriesAn arithmetic sequence has first term 17 and common difference 15. Find term 28.
10Sequences & seriesFind the sum of the first 29 terms of an arithmetic sequence with first term 8 and common difference 2.
11TrigonometryIn a right triangle, the legs opposite and adjacent to θ are 31 cm and 21 cm. Find tan θ as a fraction.
12Trigonometry330° equals kπ radians. Find k as a fraction or integer.
13Introductory calculusFind the limit of 5x² + 15 as x approaches -3.
14Introductory calculusEvaluate the definite integral of (22x + 3) from x = 4 to x = 8.

From Grade 10

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

15Statistics & probability (Grade 10)A bag has 11 red and 5 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.

16Coordinate geometry (Grade 10)Find only the x-coordinate of the midpoint of (-11, 11) and (16, -14).