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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 3 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) = 4t + (-7); g(t) = 5t + (-1). Find f(g(3)).
2AlgebraSolve for x: x + y = 45 and x − y = 27.
3GeometryA cone has radius 20 cm and height 75 cm. Use π = 3.14. Find its volume in cm³.
cm³
4GeometryA cone has radius 9 cm and height 72 cm. Use π = 3.14. Find its volume in cm³.
cm³
5Statistics & probabilityClub A has 15 bus users and 17 walkers. Club B has 14 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.

6Statistics & probabilityHow many ordered selections of 5 distinct items can be made from 15 items without repetition?
7Quadratic equationsThe graph y = 8x² + 33x + 5 has axis x = k. Find k.
8Quadratic equationsFind the discriminant of 7x² + 18x + 16 = 0.
9Sequences & seriesFind the sum of the first 8 terms of an arithmetic sequence with first term 20 and common difference 6.
10Sequences & seriesFind the sum of the first 3 terms of a geometric sequence with first term 5 and ratio 3.
11TrigonometryIn a right triangle, the side opposite θ is 5 cm and the hypotenuse is 13 cm. Find sin θ as a fraction.
12TrigonometryIn a right triangle, the legs opposite and adjacent to θ are 8 cm and 18 cm. Find tan θ as a fraction.
13Introductory calculusFor f(x) = 11x^3, find f′(1).
14Introductory calculusFind the limit of 4x² + 17 as x approaches 8.

From Grade 10

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

15Coordinate geometry (Grade 10)Find the slope through (-2, -5) and (10, -65).
16Powers & roots (Grade 10)Find n: 6^12 ÷ 6^12 = 6^n.