2016 WAEC SSCE Further Mathematics Past Questions

2016

A particle is projected vertically upwards from the ground with speed \(30ms^{-1}\). Calculate the :(a) maximum height reached by the particle;(b) time taken by the particle to return to the ground;(c) time(s) taken for…

2016

Four vectors \(r = \alpha i + \beta j\), where \(\alpha \text{ and } \beta\) are constants, \(s = 2i -j, m = 3i + 2j\) and \(n = i + j\) are such that the magnitude of r is three times as s and is parallel to the vactor…

2016

(a) Two Mathematics books, 5 different Physics books and 3 different Chemistry are to be arranged on a shelf. How many arrangements are possible if ;(i) books on the same subject must stand together? (ii) only the Physic…

2016

The table shows the distribution of marks scored by some students in a test.Marks1-1011-2021-3031-4041-5051-6061-7071-8081-9091-100No. of students31741859711510164216(a)(i) Construct a cumulative frequency table for the…

2016

(a) If \(^{k}P_{2} = 72\), find the value of k.(b) Solve the equation : \(2\cos^{2} \theta - 5\cos \theta = 3; 0° \leq \theta \leq 360°\)

2016

(a)(i) Write down the expansion of \((1 + x)^{7}\) in ascending powers of x.(ii) If the coefficients of the fifth, sixth and seventh terms in the expansion in (a)(i) above form a linear sequence(A.P), find the common dif…

2016

(a) Without using mathematical tables or calculator, evaluate \(\frac{\frac{3}{2}\log 27 - 3\log 5\sqrt{5}}{\log 0.6}\)(b) Two linear transformations A and B in the \(O_{xy}\) plane, are defined by :\(A : (x, y) (x + 2y,…

2016

Given that \(p = \begin{pmatrix} 5 \\ 3 \end{pmatrix}, q = \begin{pmatrix} -1 \\ 2 \end{pmatrix}\) and \(r = \begin{pmatrix} 17 \\ 5 \end{pmatrix}\) and \(r = \alpha r + \beta q\), where \(\alpha\) and \(\beta\) are scal…

2016

(a) A body of mass 3kg moves with a velocity of 8ms\(^{-1}\). It collides with a second body moving in the same direction with a velocity of 5ms\(^{-1}\). After collision, the bodies move together with a velocity of 6ms\…

2016

The mean of the numbers 1, 4, k, (k + 4) and 11 is (k + 1). Calculate the :(a) value of k ;(b) standard deviation.

2016

The probabilities that Ago, Sulley and Musa will gain admission to a certain university are \(\frac{4}{5}, \frac{3}{4}\) and \(\frac{2}{3}\) respectively. Find the probability that :(a) none of them will gain admission ;…

2016

When \(f(x) = 2x^{3} + mx^{2} + nx + 11\) is divided by \(x^{2} + 5x + 1\), the quotient is \(2x - 5\) and the remainder is \(30x + 16\). Find the values of m and n.

2016

(a) If \(f(x + 2) = 6x^{2} + 5x - 8\), find \(f(5)\).(b) Express \(\frac{7\sqrt{2} + 3\sqrt{3}}{4\sqrt{2} - 2\sqrt{3}}\) in the form \(p + q\sqrt{r}\), where p, q and r are rational numbers.

2016

Given that (5, 2), (-4, k) and (2, 1) lie on a straight line, find the value of k.

2016

A binary operation \(\) is defined on the set, R, of real numbers by \(m n = m + n + 2\). Find the :(a) identity element under the operation ;(b) inverse of n under the operation .

2016

A ball falls from a height of 18m above the ground. Find the speed with which the ball hits the ground. \([g = 10ms^{-2}]\)

2016

A man of mass 80kg stands in a lift. If the lift moves upwards with acceleration 0.5\(ms^{-2}\), calculate the reaction from the floor of the lift on the man. \([g = 10ms^{-2}]\)

2016

A force 10N acts in the direction 060Â° and another force 6N acts in the direction 330Â°. Find the y component of their resultant force.

2016

A body of mass 10kg moving with a velocity of 5\(ms^{-1}\) collides with another body of mass 15kg moving in the same direction as the first with a velocity of 2\(ms^{-1}\). After collision, the two bodies move together…

2016 WAEC SSCE Further Mathematics Past Questions

A particle is projected vertically upwards from the ground with speed \(30ms^{-1}\). Calculate the :(a) maximum height reached by the particle;(b) time taken by the particle to return to the ground;(c) time(s) taken for…

Four vectors \(r = \alpha i + \beta j\), where \(\alpha \text{ and } \beta\) are constants, \(s = 2i -j, m = 3i + 2j\) and \(n = i + j\) are such that the magnitude of r is three times as s and is parallel to the vactor…

(a) Two Mathematics books, 5 different Physics books and 3 different Chemistry are to be arranged on a shelf. How many arrangements are possible if ;(i) books on the same subject must stand together? (ii) only the Physic…

The table shows the distribution of marks scored by some students in a test.Marks1-1011-2021-3031-4041-5051-6061-7071-8081-9091-100No. of students31741859711510164216(a)(i) Construct a cumulative frequency table for the…

(a) If \(^{k}P_{2} = 72\), find the value of k.(b) Solve the equation : \(2\cos^{2} \theta - 5\cos \theta = 3; 0° \leq \theta \leq 360°\)

(a)(i) Write down the expansion of \((1 + x)^{7}\) in ascending powers of x.(ii) If the coefficients of the fifth, sixth and seventh terms in the expansion in (a)(i) above form a linear sequence(A.P), find the common dif…

(a) Without using mathematical tables or calculator, evaluate \(\frac{\frac{3}{2}\log 27 - 3\log 5\sqrt{5}}{\log 0.6}\)(b) Two linear transformations A and B in the \(O_{xy}\) plane, are defined by :\(A : (x, y) (x + 2y,…

Given that \(p = \begin{pmatrix} 5 \\ 3 \end{pmatrix}, q = \begin{pmatrix} -1 \\ 2 \end{pmatrix}\) and \(r = \begin{pmatrix} 17 \\ 5 \end{pmatrix}\) and \(r = \alpha r + \beta q\), where \(\alpha\) and \(\beta\) are scal…

(a) A body of mass 3kg moves with a velocity of 8ms\(^{-1}\). It collides with a second body moving in the same direction with a velocity of 5ms\(^{-1}\). After collision, the bodies move together with a velocity of 6ms\…

The mean of the numbers 1, 4, k, (k + 4) and 11 is (k + 1). Calculate the :(a) value of k ;(b) standard deviation.

The probabilities that Ago, Sulley and Musa will gain admission to a certain university are \(\frac{4}{5}, \frac{3}{4}\) and \(\frac{2}{3}\) respectively. Find the probability that :(a) none of them will gain admission ;…

When \(f(x) = 2x^{3} + mx^{2} + nx + 11\) is divided by \(x^{2} + 5x + 1\), the quotient is \(2x - 5\) and the remainder is \(30x + 16\). Find the values of m and n.

(a) If \(f(x + 2) = 6x^{2} + 5x - 8\), find \(f(5)\).(b) Express \(\frac{7\sqrt{2} + 3\sqrt{3}}{4\sqrt{2} - 2\sqrt{3}}\) in the form \(p + q\sqrt{r}\), where p, q and r are rational numbers.

Given that (5, 2), (-4, k) and (2, 1) lie on a straight line, find the value of k.

A binary operation \(*\) is defined on the set, R, of real numbers by \(m * n = m + n + 2\). Find the :(a) identity element under the operation ;(b) inverse of n under the operation .

A ball falls from a height of 18m above the ground. Find the speed with which the ball hits the ground. \([g = 10ms^{-2}]\)

A man of mass 80kg stands in a lift. If the lift moves upwards with acceleration 0.5\(ms^{-2}\), calculate the reaction from the floor of the lift on the man. \([g = 10ms^{-2}]\)

A force 10N acts in the direction 060Â° and another force 6N acts in the direction 330Â°. Find the y component of their resultant force.

A body of mass 10kg moving with a velocity of 5\(ms^{-1}\) collides with another body of mass 15kg moving in the same direction as the first with a velocity of 2\(ms^{-1}\). After collision, the two bodies move together…

Find the unit vector in the direction of \(-2i + 5j\).

A binary operation \(\) is defined on the set, R, of real numbers by \(m n = m + n + 2\). Find the :(a) identity element under the operation ;(b) inverse of n under the operation .