West African Examinations Council
WASSCE Further Mathematics · Paper 2 — Essay
Written answers, marked against a rubric.
8 exam-style questions, written to the West African Examinations Council format and free to read. The answers are here too — what they do not tell you is how many you would get right with a clock running.
1. The scores of eight students are 12, 15, 18, 20, 22, 25, 28 and 30.
(a) Calculate the mean and the standard deviation, correct to two decimal places. [12 marks]
(b) Calculate the median and the interquartile range. [6 marks]
(c) State one advantage of the standard deviation over the range. [2 marks]
2. Given a = 3i + 4j and b = −2i + 5j:
(a) Find a + b and |a + b|. [7 marks]
(b) Find the scalar product a·b and hence the angle between a and b, correct to the nearest degree. [10 marks]
(c) State the condition for two vectors to be perpendicular. [3 marks]
3. (a) Differentiate y = 3x⁴ − 2x² + 7x − 1 with respect to x. [5 marks]
(b) Find the coordinates of the turning points of y = x³ − 3x² + 4 and determine their nature. [12 marks]
(c) State what the second derivative tells you about a curve. [3 marks]
4. (a) Evaluate the integral of (3x² − 4x + 1) with respect to x between x = 1 and x = 3. [8 marks]
(b) Find the area enclosed between the curve y = x² and the line y = 4. [10 marks]
(c) State one practical use of definite integration. [2 marks]
5. (a) Expand (1 + 2x)⁵ in ascending powers of x. [8 marks]
(b) Use your expansion to estimate (1.02)⁵ correct to four decimal places. [7 marks]
(c) State one limitation of using the expansion for large values of x. [5 marks]
6. (a) Given that f(x) = 2x³ − 5x² + x + 2, show that (x − 2) is a factor of f(x). [6 marks]
(b) Hence factorise f(x) completely. [8 marks]
(c) Solve f(x) = 0. [6 marks]
Reading these is not the same as sitting them.
Every question above is answerable given time. The exam does not give you time. Sit the whole paper on the real clock and the number you get back is the one that means something.
Sit it against the clock — freeExampaper is an independent study service. It is not affiliated with, endorsed by, or connected to WAEC, NECO, JAMB or any examination body. Exam names and subject titles are used only to describe what each paper is for.