WAEC SSCE - Further Mathematics - 2020 (Objective)

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

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 \((\sqrt{3})*(\sqrt{2})\)

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

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\(^{-2}\)]

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

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

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

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

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

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

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

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

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.

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

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

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

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.

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.

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

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

Consider the statements:

x: Birds fly

y:  The sky is blue

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

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

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? 

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

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

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

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

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

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

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. 

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.

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?

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

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

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

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

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