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Further Mathematics Past Questions

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795 questions JAMB 2 WAEC 795 CUSTOM 2

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Question 381

waec 2006

If \(a = \begin{pmatrix} 3 \\ 2 \end{pmatrix}\) and \(b = \begin{pmatrix} -3 \\ 5 \end{pmatrix}\), find a vector c such that \(4a + 3c = b\).

A\(\begin{pmatrix} 3 \\ -1 \end{pmatrix}\)

B\(\begin{pmatrix} -5 \\ -1 \end{pmatrix}\)

C\(\begin{pmatrix} -5 \\ 1 \end{pmatrix}\)

D\(\begin{pmatrix} -5 \\ -9 \end{pmatrix}\)

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Question 382

waec 2006

The mean and median of integers x, y, z and t are 5 and z respectively. If x < y < z < t and y = 4, find (x + t).

A12

B11

C10

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Question 383

waec 2006

Find, in surd form, the value of \(\cos 165\).

A\(\frac{1}{4}(\sqrt{6} + \sqrt{2})\)

B\(\frac{1}{4}(\sqrt{6} - \sqrt{2})\)

C\(-\frac{1}{4}(\sqrt{6} - \sqrt{2})\)

D\(-\frac{1}{4}(\sqrt{6} + \sqrt{2})\)

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Question 384

waec 2006

The parallelogram PQRS has vertices P(-2, 3), Q(1, 4), R(2, 6) and S(-1,5). Find the coordinates of the point of intersection of the diagonals.

A\((-1, 5)\)

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

C\((0, 4\frac{1}{2})\)

D\((1\frac{1}{2}, 5)\)

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Question 385

waec 2006

A and B are two independent events such that \(P(A) = \frac{2}{5}\) and \(P(A \cap B) = \frac{1}{15}\). Find \(P(B)\).

A\(\frac{3}{5}\)

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

C\(\frac{1}{6}\)

D\(\frac{2}{15}\)

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Question 386

waec 2006

Find the coordinates of the centre of the circle \(4x^{2} + 4y^{2} - 5x + 3y - 2 = 0\).

A\((\frac{-5}{4}, \frac{3}{4})\)

B\((\frac{3}{8}, -\frac{5}{8})\)

C\((\frac{5}{8}, -\frac{3}{8})\)

D\((\frac{5}{4}, -\frac{3}{4})\)

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Question 387

waec 2006

Given that \(\begin{pmatrix} 1 & -3 \\ 1 & 4 \end{pmatrix} \begin{pmatrix} -6 \\ P \end{pmatrix} = \begin{pmatrix} 3 \\ -26 \end{pmatrix}\), find the value of P.

A-8

B-5

D-3

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Question 388

waec 2006

A force of 32 N is applied to an object of mass m kg which is at rest on a smooth horizontal surface. If the acceleration produced is 8\(ms^{-2}\), find the value of m.

A12

B16

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Question 389

waec 2006

Find the least value of the function \(f(x) = 3x^{2} + 18x + 32\).

C-3

D-2

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Question 390

waec 2006

Find the coordinates of the point on the curve \(y = x^{2} + 4x - 2\), where the gradient is zero.

A(-2, 10)

B(-2, 2)

C(-2, -2)

D(-2, -6)

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Question 391

waec 2006

The equation of the line of best fit for variables x and y is \(y = 19.33 + 0.42x\), where x is the independent variable. Estimate the value of y when x = 15.

A18.91

B19.75

C25.63

D38.23

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Question 392

waec 2006

In a firing contest, the probabilities that Kojo and Kwame hit the target are \(\frac{2}{5}\) and \(\frac{1}{3}\) respectively. What is the probability that none of them hit the target?

A\(\frac{1}{5}\)

B\(\frac{2}{5}\)

C\(\frac{3}{5}\)

D\(\frac{4}{5}\)

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Question 393

waec 2006

Age(in years)	1 - 5	6 - 10	11 - 15
Frequency	3	5	2

Calculate the standard deviation of the distribution.

A1.10

B2.36

C3.50

D7.50

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Question 394

waec 2006

A particle of mass 2.5 kg is moving at a speed of 12 m/s. If a force of magnitude 10 N acts against it, find how long it takes to come to rest.

A1.5 s

B3.0 s

C4.0 s

D6.0 s

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Question 395

waec 2006

The area of a sector of a circle is 3\(cm^{2}\). If the sector subtends an angle of 1.5 radians at the centre, calculate the radius of the circle.

A1 cm

B\(\sqrt{2}\) cm

C2 cm

D4 cm

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Question 396

waec 2006

Simplify \(8^{n} \times 2^{2n} \div 4^{3n}\)

A\(2^{-n}\)

B\(2^{1 - n}\)

C\(2^{n}\)

D\(2^{n + 1}\)

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Question 397

waec 2006

Which of the following is a singular matrix?

A\(\begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix}\)

B\(\begin{pmatrix} 2 & 1 \\ 3 & 2 \end{pmatrix}\)

C\(\begin{pmatrix} 3 & 8 \\ 5 & 16 \end{pmatrix}\)

D\(\begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix}\)

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Question 398

waec 2006

Simplify \(\frac{^{n}P_{4}}{^{n}C_{4}}\)

A24

B18

C12

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Question 399

waec 2006

A committee of 4 is to be selected from a group of 5 men and 3 women. In how many ways can this be done if the chairman of the committee must be a man?

A15

B40

C70

D175

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Question 400

waec 2006

The mean age of n men in a club is 50 years. Two men aged 55 and 63 years left the club, and the mean age reduced by 1 year. Find the value of n.

A30

B20

C18

D14

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