WAEC SSCE - Further Mathematics - 2023 (Objective)

Adu's scores in five subjects in an examination are 85, 84, 83, 86 and 87. Calculate the standard deviation.

If \(X\) and \(Y\) are two independent events such that \(P (X) = \frac{1}{8}\) and \(P (X ⋃ Y) = \frac{5}{8}\), find \(P (Y)\).

If\((\frac{1}{9})^{2x-1} = (\frac{1}{81})^{2-3x}\)find the value of x

In how many ways can a committee of 3 women and 2 men be chosen from a group of 7 men and 5 women?

\(Differentiate f (x) = \frac{1}{(1 - x^2)^5}\) with respect to \(x\).

\(Simplify: \frac{log √27 - log √8}{log 3 - log 2}\)

An exponential sequence (G.P.) is given by 8√2, 16√2, 32√2, ... . Find the n\(^{th}\) term of the sequence

Calculate, correct to one decimal place, the angle between 5 i + 12 j and -2 i + 3 j

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

Evaluate \(\int^1_0 x(x^2-2)^2 dx\)

Given that r = (10 N , 200º) and n = (16 N , 020º), find (3r - 2n).

The distance S metres moved by a body in t seconds is given by \(S = 5t^3 - \frac{19}{2} t^2 + 6t - 4\). Calculate the acceleration of the body after 2 seconds

Given that P = {x : 2 ≤ x ≤ 8} and Q = {x : 4 < x ≤ 12} are subsets of the universal set μ = {x : x ∈ R}, find (P ⋂ Q\(^1\)).

The velocity of a body of mass 4.56 kg increases from \((10 ms^{-1}, 060^o) to (50 ms ^{-1}, 060^o)\) in 16 seconds . Calculate the magnitude of force acting on it.

Find the equation of the normal to the curve y = \(3x^2 + 2\) at point (1, 5).

The probabilities that Atta and Tunde will hit a target in a shooting contest are \(\frac{1}{6}\) and \({1}{9}\) respectively. Find the probability that only one of them will hit the target.

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

If \(f : x → 2 tan x\) and \(g : x → √(x^2 + 8), find ( g o f )(45^o)\)

Express \(\frac{3}{3 - √6}\) in the form \(x + m√y\)

A linear transformation on the oxy plane is defined by \(P : (x, y) → (2x + y, -2y)\). Find \(P^2\)

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

Find the fifth term in the binomial expansion of \((q + x)^7\).

Given that \(sin x = \frac{4}{5}\) and \(cos y = \frac{12}{13}\), where x is an obtuse angle and y is an acute angle, find the value of sin (x - y).

Given that M is the midpoint of T (2, 4) and Q (-8, 6), find the length of MQ .

If \(3x^2 + p x + 12 = 0\) has equal roots, find the values of p .

Given that \(y^2 + xy = 5,find \frac{dy}{dx}\).

A particle began to move at \(27 ms^{-1}\) along a straight line with constant retardation of \(9 ms^{-2}\). Calculate the time it took the particle to come to a stop.

Solve 6 sin 2θ tan θ = 4, where 0º < θ < 90º

A function \(f\) is defined by \(f :x→\frac{x + 2}{x - 3},x ≠ 3\).Find the inverse of \(f\) .

Evaluate: \(\int(2x + 1)^3 dx\)

Given that \(\frac{3x + 4}{(x - 2)(x + 3)}≡\frac{P}{x + 3}+\frac{Q}{x - 2}\),find the value of Q.

Find the radius of the circle \(2x^2 + 2y^2 - 4x + 5y + 1 = 0\)

An exponential sequence (G.P.) is given by \(\frac{9}{2},\frac{3}{4},\frac{1}{8},\)....Find its sum to infinity.

The table shows the mark obtained by students in a test.

If the mean mark is 3, find the value of k.

If α and β are the roots of \(7x2 +12x - 4 = 0\),find the value of \(\frac{αβ}{(α + β)^2}\)

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

Consider the statements:
x: The school bus arrived late
y: The student walked down to school
Which of the following can be represented by y ⇒ x?

The table shows the operation * on the set {x, y, z, w}.

Find the identity of the element.

A uniform beam PQ of length 80 cm and weight 60 N rests on a support at X where | PX | = 30 cm. If the body is kept in equilibrium by a mass m kg which is placed at P , calculate the value of m
[Take g = 10 ms\(^{-2}\)]