Grade 11 Maths Practice Paper 2

A Grade 11 CAPS-style Paper 2 practice test: standard deviation, equations of lines, reduction formulae, identities, general solutions, sine and cosine…

This practice paper samples every Grade 11 Paper 2 topic: statistics, analytical geometry, trigonometry (reduction, identities, general solutions and the triangle rules), circle geometry and measurement.

Give yourself an hour. Use the information sheet for the sine, cosine and area rules, and write a reason for every geometry statement.

Topics covered

  • Variance and standard deviation
  • Equation of a line and inclination
  • Reduction formulae
  • Trig identities
  • General solutions
  • Sine, cosine and area rules
  • Circle theorems
  • Volume and surface area of a sphere

Questions with worked answers

  • Question 1: Statistics (5 marks). For 4; 6; 7; 9; 14 find the mean and the standard deviation.
  • Question 2: Analytical geometry (5 marks). A(2; 3) and B(6; 7). (a) Find the equation of AB and its inclination. (b) Find the equation of the line through B perpendicular to AB.
  • Question 3: Trigonometry (5 marks). Simplify: cos(180° + x) · tan(360° − x) ÷ sin(180° − x)
  • Question 4: Trigonometry (4 marks). Prove that (1 − cos²x) ÷ (sin x · cos x) = tan x.
  • Question 5: Trigonometry (5 marks). Find the general solution of 2 cos x + 1 = 0.
  • Question 6: Trigonometry (5 marks). In △ABC, a = 9, B̂ = 40° and Ĉ = 75°. Find b.
  • Question 7: Trigonometry (3 marks). Find the area of a triangle with sides 7 cm and 10 cm and an included angle of 120°.
  • Question 8: Circle geometry (4 marks). O is the centre of a circle through A, B and C. AÔB = 2x + 20° and AĈB = 50°. Find x.
  • Question 9: Measurement (7 marks). A sphere has a radius of 6 cm. Find its volume and surface area, correct to two decimal places.

How to use this paper

  • For reduction, work out the quadrant and sign before simplifying.
  • In identity proofs, work on one side only.
  • Mark the radii and equal angles on circle diagrams first.

Frequently asked questions

Is this an official Grade 11 paper?

No. It is a Snap&Learn practice paper in the style of a CAPS Grade 11 Paper 2. Official November common papers are linked on the Grade 11 papers page.

Which Grade 11 Paper 2 topic is the biggest?

Trigonometry, at about 50 of 150 marks, followed by Euclidean geometry and measurement at about 50.

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