WAEC SSCE - Further Mathematics - 2023 (Objective)

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.

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 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\(^{-2}\)]

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

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 table shows the mark obtained by students in a test.

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

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?

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).

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

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\(^1\)).

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

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

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

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

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

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

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.

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

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).

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

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

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

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

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

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

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

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

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

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

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

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.

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

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

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

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

Find the identity of the element.

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

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

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

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