Theory paper · 2 questions · partial

WAEC · 2017 · May/June · Further Maths · Paper 2

Topics include Factor theorem, Polynomials, Trigonometric identities, Stationary points, Coordinate geometry.

Our copy of this paper is missing questions 1, 2, 3, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15.

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Answer every question in order, timed if you like (suggested 30 min). You're marked when you hand in, then you see where to focus and the working for each question.

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Question 4

Polynomials & quadratic roots

If $(x + 1)$ and $(x - 2)$ are factors of the polynomial $g(x) = x^4 + ax^3 + bx^2 - 16x - 12$ , find the values of $a$ and $b$ .

(a)
Value of $a$
(b)
Value of $b$

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Move a and b until the curve passes through both marked points. Which values work?

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Question 9

(a)
Simplify $\dfrac{1}{1 - \cos\theta} + \dfrac{1}{1 + \cos\theta}$ and leave the answer in terms of $\sin\theta$ .
(b)
Find the equation of the line joining the stationary points of $y = x^2(x - 3)$ and the distance between them.

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Plot the curves, move them, and read values off the graph.

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