WAEC SSCE - Further Mathematics - 2023 (Objective)

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

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

Find the identity of the element.

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

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

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

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).

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

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

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\(^1\)).

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

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

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

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

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

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

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

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

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

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

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

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

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

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?

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\(^{-2}\)]

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

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

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

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

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

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

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

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

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).

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.

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.

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

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

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

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 \(x\).

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.