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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 2 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 = 26 and x − y = -12.
2Algebraf(t) = 2t + (7); g(t) = 8t + (-3). Find f(g(7)).
3GeometryA cone has radius 11 cm and height 87 cm. Use π = 3.14. Find its volume in cm³.
cm³
4GeometryA cone has radius 25 cm and height 75 cm. Use π = 3.14. Find its volume in cm³.
cm³
5Statistics & probabilityData: 22, 23, 24, 25, 26, 27, 28, 29. Using medians of the lower four and upper four values, find the interquartile range.
6Statistics & probabilityClub A has 25 bus users and 5 walkers. Club B has 15 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 equationsExpand (1x + 30)². What is the coefficient of x?
8Quadratic equationsFind f(5) if f(x) = 1x² + 4x + 6.
9Sequences & seriesFind the sum of the first 6 terms of a geometric sequence with first term 3 and ratio 5.
10Sequences & seriesFind the sum of the first 7 terms of an arithmetic sequence with first term 1 and common difference 2.
11TrigonometryIn a right triangle, the legs opposite and adjacent to θ are 13 cm and 27 cm. Find tan θ as a fraction.
12TrigonometryIn a right triangle, the side opposite θ is 10 cm and the hypotenuse is 26 cm. Find sin θ as a fraction.
13Introductory calculusFor f(x) = x³, find the slope of the tangent at x = −2.
14Introductory calculusFind the limit of 2x² + 18 as x approaches -7.

From Grade 10

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

15Powers & roots (Grade 10)Find n: 18^7 ÷ 18^4 = 18^n.
16Coordinate geometry (Grade 10)Rotate (-26, -6) 90° counterclockwise about the origin. Give the new x-coordinate.