WAEC SSCE - Further Mathematics - 2020 (Objective)

P(3,4) and Q(-3, -4) are two points in a plane. Find the gradient of the line that is normal to the line PQ. 

If the sum of the roots of 2x\(^2\) + 5mx + n = 0 is 5, find the value of m.

A three-digit odd number less than 500 is to be formed from 1,2,3,4 and 5. If repetition of digits is allowed, in how many ways can this be done?

Consider the statements:

x: Birds fly

y:  The sky is blue

Which of the following statements can be represented as x \(\to\) y?

In which of the following series can be the formula S = \(\frac{a}{1 - r}\) where a is the first term and r is the common ratio, be used to find the sum of all the terms? 

Given that F = 3i - 12j, R = 7i + 5j and N = pi + qj are forces acting on a body, if the body is in equilibrium. find the values of p and q.

Differentiate \(\frac{x}{x + 1}\) with respect to x. 

If  \(\begin{pmatrix} p+q & 1\\ 0 & p-q \end {pmatrix}\) = \(\begin{pmatrix} 2 & 1 \\ 0 & 8 \end{pmatrix}\)

Find the values of p and q

Calculate the variance of \(\sqrt{2}\), (1 + \(\sqrt{2}\)) and (2 + \(\sqrt{2}\)) 

Given that X  : R \(\to\) R is defined by x = \(\frac{y + 1}{5 - y}\) , y \(\in\) R, find the domain of x.

A circle with centre (5,-4) passes through the point (5, 0). Find its equation.

A stone was dropped from the top of a building 40m high. Find, correct to one decimal place, the time it took the stone to reach the ground. [Take g = 9.8ms\(^{-2}\)]

Given that 2x + 3y - 10 and 3x = 2y - 11, calculate the value of (x - y). 

If X = \(\frac{3}{5}\) and cos y = \(\frac{24}{25}\), where X and Y are acute, find the value of cos (X + Y). 

The distance(s) in metres covered by a particle in motion at any time, t seconds, is given by S =120t - 16t\(^2\). Find in metres, the distance covered by the body before coming to rest.

Given that P = {x : 1 \(\geq\) x \(\geq\) 6} and Q = {x : 2 < x < 10}. Where x are integers, find n(p \(\cap\) Q) 

Find the unit vector in the direction opposite to the resultant of forces.  F\(_1\) = (-2i - 3j) and F\(_2\) = (5i - j)

Which of the following is not an equation of a circle?

If the binomial expansion of (1 + 3x)\(^6\) is used to evaluate (0.97)\(^6\), find the value of x. 

In what interval is the function f : x -> 2x - x\(^2\) increasing? 

Find the inverse of \(\begin{pmatrix} 3 & 5 \\ 1 & 2 \end{pmatrix}\)

The variables x and y are such that y =2x\(^3\) - 2x\(^2\) - 5x + 5. Calculate the corresponding change in y and x changes from 2.00 to 2.05.

Simplify; \(\frac{\sqrt{5} + 3}{4 - \sqrt{10}}\) 

If cos x = -0.7133, find the values of x between 0\(^o\) and 360\(^o\) 

Find the nth term of the linear sequence (A.P) (5y + 1), ( 2y + 1), (1- y),...

If log 5(\(\frac{125x^3}{\sqrt[ 3 ] {y}}\) is expressed in the values of p, q and k respectively.

A function f defined by f : x -> x\(^2\) + px + q is such that f(3) = 6 and f(3) = 0. Find the value of q.

If \(\int^3_0(px^2 + 16)dx\) = 129. Find the value of p.

A binary operation * is defined on the set of real number, R, by \(x*y = x^2 - y^2 + xy\), where \(x, \in R\). Evaluate \((\sqrt{3})*(\sqrt{2})\)

\({\color{red}2x} \times 3\)

Determine the coefficient of x\(^3\) in the binomial expansion of ( 1 + \(\frac{1}{2}\)x) 

If V = plog\(_x\), (M + N), express N in terms of X, P, M and V

Calculate, correct to two decimal places, the area enclosed by the line 3x - 5y + 4 = 0 and the axes.

A force of 230N acts in its direction 065\(^o\). Find its horizontal component.

Calculate the probability that the product of two numbers selected at random with replacement from the set {-5,-2,4, 8} is positive

A bag contains 5 red and 5 blue identical balls. Three balls are selected at random without replacement. Determine the probability of selecting balls alternating in color.

If \(\frac{6x + k}{2x^2 + 7x - 15}\)  = \(\frac{4}{x + 5} - \frac{2}{2x - 3}\). Find the value of k. 

Find the angle between i + 5j and 5i - J

Find the median of the numbers 9,7, 5, 2, 12,9,9, 2, 10, 10, and 18.

In how many ways can the letters of the word MEMBER be arranged?