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Further Mathematics Past Questions

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Question 191

waec 2016

Given that \(-6, -2\frac{1}{2}, ..., 71\) is a linear sequence , calculate the number of terms in the sequence.

A20

B21

C22

D23

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Question 192

waec 2016

The 3rd and 6th terms of a geometric progression (G.P.) are \(\frac{8}{3}\) and \(\frac{64}{81}\) respectively, find the common ratio.

A\(\frac{1}{3}\)

B\(\frac{2}{3}\)

C\(\frac{3}{4}\)

D\(\frac{4}{3}\)

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Question 193

waec 2016

Find the fourth term in the expansion of \((3x - y)^{6}\).

A\(-540x^{3}y^{3}\)

B\(-540x^{4}y^{2}\)

C\(-27x^{3}y^{3}\)

D\(540x^{4}y^{2}\)

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Question 194

waec 2016

Find the coefficient of \(x^{3}\) in the expansion of \([\frac{1}{3}(2 + x)]^{6}\).

A\(\frac{135}{729}\)

B\(\frac{149}{729}\)

C\(\frac{152}{729}\)

D\(\frac{160}{729}\)

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Question 195

waec 2016

Given n = 3, evaluate \(\frac{1}{(n-1)!} - \frac{1}{(n+1)!}\)

A\(12\)

B\(2\frac{1}{2}\)

C\(2\)

D\(\frac{11}{24}\)

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Question 196

waec 2016

Simplify \(\frac{^{n}P_{5}}{^{n}C_{5}}\).

A80

B90

C110

D120

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Question 197

waec 2016

If \(\log_{10}y + 3\log_{10}x \geq \log_{10}x\), express y in terms of x.

A\(y \geq \frac{1}{x}\)

B\(y \leq \frac{1}{x}\)

C\(y \leq \frac{1}{x^{2}}\)

D\(y \geq \frac{1}{x^{2}}\)

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Question 198

waec 2016

Solve for x in the equation \(5^{x} \times 5^{x + 1} = 25\).

A\(-2\)

B\(\frac{-1}{2}\)

C\(\frac{1}{2}\)

D\(2\)

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Question 199

waec 2016

If (2t - 3s)(t - s) = 0, find \(\frac{t}{s}\).

A\(\frac{3}{2}\) or \(1\)

B\(\frac{3}{2}\) or \(-1\)

C\(\frac{-3}{2}\) or \(-1\)

D\(\frac{-3}{2}\) or \(1\)

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Question 200

waec 2016

The remainder when \(x^{3} - 2x + m\) is divided by \(x - 1\) is equal to the remainder when \(2x^{3} + x - m\) is divided by \(2x + 1\). Find the value of m.

A\(\frac{-7}{8}\)

B\(\frac{-3}{8}\)

C\(\frac{1}{8}\)

D\(\frac{5}{8}\)

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Question 201

waec 2016

If the solution set of \(x^{2} + kx - 5 = 0\) is (-1, 5), find the value of k.

A-6

B-4

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Question 202

waec 2016

Factorize completely: \(x^{2} + x^{2}y + 3x - 10y + 3xy - 10\).

A(x + 2)(x + 5)(y + 1)

B(x + 2)(x - 5)(y + 1)

C(x - 2)(x + 5)(y + 1)

D(x - 2)(x - 5)(y + 1)

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Question 203

waec 2016

If \(y = 4x - 1\), list the range of the domain \({-2 \leq x \leq 2}\), where x is an integer.

A{-9, -1, 2,3, 4}

B{-9, -2, 0, 1, 7}

C{-5, -4, -3, -2}

D{-9, -5, -1, 3, 7}

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Question 204

waec 2016

If \(f(x) = \frac{4}{x} - 1, x \neq 0\), find \(f^{-1}(7)\).

A\(\frac{-3}{7}\)

B\(0\)

C\(\frac{1}{2}\)

D\(4\)

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Question 205

waec 2016

Consider the statements:

p : Musa is short

q : Musa is brilliant

Which of the following represents the statement "Musa is short but not brilliant"?

A\(p \vee q\)

B\(p \vee \sim q\)

C\(p \wedge \sim q\)

D\(p \wedge q\)

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Question 206

waec 2016

An operation * is defined on the set, R, of real numbers by \(p * q = p + q + 2pq\). If the identity element is 0, find the value of p for which the operation has no inverse.

A\(\frac{-1}{2}\)

B\(0\)

C\(\frac{2}{3}\)

D\(2\)

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Question 207

waec 2016

Express \(\frac{8 - 3\sqrt{6}}{2\sqrt{3} + 3\sqrt{2}}\) in the form \(p\sqrt{3} + q\sqrt{2}\).

A\(7\sqrt{3} - \frac{17\sqrt{2}}{3}\)

B\(7\sqrt{2} - \frac{17\sqrt{3}}{3}\)

C\(-7\sqrt{2} + \frac{17\sqrt{3}}{3}\)

D\(-7\sqrt{3} - \frac{17\sqrt{2}}{3}\)

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Question 208

waec 2016

If \(P = {x : -2 < x < 5}\) and \(Q = {x : -5 < x < 2}\) are subsets of \(\mu = {x : -5 \leq x \leq 5}\), where x is a real number, find \((P \cup Q)\).

A\({x : -5 < x < 5}\)

B\({x : -5 \leq x \leq 5}\)

C\({x : -5 \leq x < 5}\)

D\({x : -5 < x \leq 5}\)

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Question 209

waec 2015

Forces of magnitude 8N and 5N act on a body as shown above. Calculate, correct to 2 dp, the angle that the resultant makes with the horizontal.

A80.76°

B75.00°

C71.99°

D15.00°

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Question 210

waec 2015

Forces of magnitude 8N and 5N act on a body as shown above. Calculate, correct to 2 d.p., the resultant force acting at O.

A14.06N

B13.00N

C9.83N

D8.26N

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