2023 WAEC SSCE Further Mathematics Past Questions

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2023

(a) A see-saw pivoted at the middle is kept in balance by weights of Richard, John and Philip such that only Richard whose mass is 60 kg sits on one side. If they sit at distances 2 m , 3 m , and 4 m respectively f…

2023

(a) A particle of mass 2 kg moves under the action of a constant force, F N , with an initial velocity \((3 i + 2 j ) ms^{ -1}\) and a velocity of \((15 i - 4 j ) ms^{ -1}\) after 4 seconds . Find the: acceleration…

2023

(ai) A bag contains 16 identical balls of which 4 are green. A boy picks a ball at random from the bag and replaces it. If this is repeated 5 times, what is the probability that he: did not pick a green ball; (aii) A bag…

2023

(a) The table shows the distribution of marks scored by some candidates in an examination. Marks 11 - 20 21 - 30 31 - 40 41 - 50 51 - 60 61 - 70 71 - 80 81 - 90 91 - 100 Num of candidates 5 39 14 40 57 25 11 8 1…

2023

(a) Express \(\frac{8x^2 + 8x + 9}{(x - 1)(2x + 3)^2}\) in partial fractions. (b) The coordinates of the centre and circumference of a circle are (-2, 5) and \(6\pi\) units respectively. Find the equation of the circle.

2023

(ai) A quadratic polynomial, g (x) has (2x + 1) as a factor. If g (x) is divided by (x - 1) and (x - 2), the remainder are -6 and -5 respectively. Find; g (x); (aii) A quadratic polynomial, g (x) has (2x + 1) as a…

2023

(a) Find the derivative of \(4x-\frac{7}{x^2}\) with respect to \(x\), from first principle. (b) Given that \(\tan P =\frac{3}{x - 1}\) and \(\tan Q =\frac{2}{x + 1}\), find \(\tan (P - Q)\)  

2023

P is the mid-point of \(\overline{NO}\) and equidistant from \(\overline{MN}\) and \(\overline{MO}\) . If \(\overline{MN}\) = 8i + 3j and \(\overline{MO}\) = 14i - 5j, find \(\overline{MP}\) .

2023

(a) A bus travels with a velocity of \(6 ms ^{-1}\). It then accelerates uniformly and travels a distance of 70 m. If the final velocity is \(20 ms ^{-1}\), find, correct to one decimal place, the: acceleration; (b) A b…

2023

There are 6 boys and 8 girls in a class. If five students are selected from the class, find the probability that more girls than boys are selected

2023

(a)The table shows the distribution of heights ( cm ) of 60 seedlings in a vegetable garden. Heights(cm) 0.1 - 0.3 0.4 - 0.6 0.7 - 0.9 1.0 - 1.4 1.5 - 1.9 2.0 - 22 2.3 - 2.5 Frequency 6 9 12 1…

2023

(a) The first term of an Arithmetic Progression is -8, the last term is 52 and the sum of terms is 286. Find the: number of terms in the series; (b) The first term of an Arithmetic Progression is -8, the last term is 52…

2023

(a) The inverse of a function \(f\) is given by \(f^{-1}(x)=\frac{5x - 6}{4 - x},x ≠ 4\).Find the: function, \(f (x)\) (b) The inverse of a function \(f\) is given by \(f^{-1}(x)=\frac{5x - 6}{4 - x},x ≠ 4\).Find the:…

2023

The volume of a cube is increasing at the rate of \(3\frac{1}{2} cm ^3 s^{ -1}\). Find the rate of change of the side of the base when its length is 6 cm .

2023

If \(^9C_x = 4[^7C_{x - 1}]\), find the values of \(x\)

2023

If \((x - 5)\) is a factor of \(x^3 - 4x^2 - 11x + 30\), find the remaining factors.

2023

In how many ways can four Mathematicians be selected from six ?

2023

Find the coefficient of the \(6^{th}term\) in the binomial expansion of \((1 - \frac{2x}{3})10\) in ascending powers of \(x\).

2023

If m and ( m + 4) are the roots of \(4x^2 - 4x - 15 = 0\), find the equation whose roots are 2 m and (2 m + 8).

2023

Given that \(p = \begin{bmatrix} x&4\\3&7\end{bmatrix} Q =\begin{bmatrix} x&3\\1&2x\end{bmatrix}\) and the determinant of \(Q\) is three more than that of \(P\) , find the values of \(x\).

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2023 WAEC SSCE Further Mathematics Past Questions

(a) A see-saw pivoted at the middle is kept in balance by weights of Richard, John and Philip such that only Richard whose mass is 60 kg sits on one side. If they sit at distances 2 m , 3 m , and 4 m respectively f…

(a) A particle of mass 2 kg moves under the action of a constant force, F N , with an initial velocity \((3 i + 2 j ) ms^{ -1}\) and a velocity of \((15 i - 4 j ) ms^{ -1}\) after 4 seconds . Find the: acceleration…

(ai) A bag contains 16 identical balls of which 4 are green. A boy picks a ball at random from the bag and replaces it. If this is repeated 5 times, what is the probability that he: did not pick a green ball; (aii) A bag…

(a) The table shows the distribution of marks scored by some candidates in an examination. Marks 11 - 20 21 - 30 31 - 40 41 - 50 51 - 60 61 - 70 71 - 80 81 - 90 91 - 100 Num of candidates 5 39 14 40 57 25 11 8 1…

(a) Express \(\frac{8x^2 + 8x + 9}{(x - 1)(2x + 3)^2}\) in partial fractions. (b) The coordinates of the centre and circumference of a circle are (-2, 5) and \(6\pi\) units respectively. Find the equation of the circle.

(ai) A quadratic polynomial, g (x) has (2x + 1) as a factor. If g (x) is divided by (x - 1) and (x - 2), the remainder are -6 and -5 respectively. Find; g (x); (aii) A quadratic polynomial, g (x) has (2x + 1) as a…

(a) Find the derivative of \(4x-\frac{7}{x^2}\) with respect to \(x\), from first principle. (b) Given that \(\tan P =\frac{3}{x - 1}\) and \(\tan Q =\frac{2}{x + 1}\), find \(\tan (P - Q)\) &nbsp;

P is the mid-point of \(\overline{NO}\) and equidistant from \(\overline{MN}\) and \(\overline{MO}\) . If \(\overline{MN}\) = 8i + 3j and \(\overline{MO}\) = 14i - 5j, find \(\overline{MP}\) .

(a) A bus travels with a velocity of \(6 ms ^{-1}\). It then accelerates uniformly and travels a distance of 70 m. If the final velocity is \(20 ms ^{-1}\), find, correct to one decimal place, the: acceleration; (b) A b…

There are 6 boys and 8 girls in a class. If five students are selected from the class, find the probability that more girls than boys are selected

(a)The table shows the distribution of heights ( cm ) of 60 seedlings in a vegetable garden. Heights(cm) 0.1 - 0.3 0.4 - 0.6 0.7 - 0.9 1.0 - 1.4 1.5 - 1.9 2.0 - 22 2.3 - 2.5 Frequency 6 9 12 1…

(a) The first term of an Arithmetic Progression is -8, the last term is 52 and the sum of terms is 286. Find the: number of terms in the series; (b) The first term of an Arithmetic Progression is -8, the last term is 52…

(a) The inverse of a function \(f\) is given by \(f^{-1}(x)=\frac{5x - 6}{4 - x},x ≠ 4\).Find the: function, \(f (x)\) (b) The inverse of a function \(f\) is given by \(f^{-1}(x)=\frac{5x - 6}{4 - x},x ≠ 4\).Find the:…

The volume of a cube is increasing at the rate of \(3\frac{1}{2} cm ^3 s^{ -1}\). Find the rate of change of the side of the base when its length is 6 cm .

If \(^9C_x = 4[^7C_{x - 1}]\), find the values of \(x\)

If \((x - 5)\) is a factor of \(x^3 - 4x^2 - 11x + 30\), find the remaining factors.

In how many ways can four Mathematicians be selected from six ?

Find the coefficient of the \(6^{th}term\) in the binomial expansion of \((1 - \frac{2x}{3})10\) in ascending powers of \(x\).

If m and ( m + 4) are the roots of \(4x^2 - 4x - 15 = 0\), find the equation whose roots are 2 m and (2 m + 8).

Given that \(p = \begin{bmatrix} x&amp;4\\3&amp;7\end{bmatrix} Q =\begin{bmatrix} x&amp;3\\1&amp;2x\end{bmatrix}\) and the determinant of \(Q\) is three more than that of \(P\) , find the values of \(x\).

(a) Find the derivative of \(4x-\frac{7}{x^2}\) with respect to \(x\), from first principle. (b) Given that \(\tan P =\frac{3}{x - 1}\) and \(\tan Q =\frac{2}{x + 1}\), find \(\tan (P - Q)\)

Given that \(p = \begin{bmatrix} x&4\\3&7\end{bmatrix} Q =\begin{bmatrix} x&3\\1&2x\end{bmatrix}\) and the determinant of \(Q\) is three more than that of \(P\) , find the values of \(x\).