WAEC SSCE - Further Mathematics - 2017 (Objective)

Simplify \(\frac{1}{(1-\sqrt{3})^{2}}\)

A circle with centre (4,5) passes through the y-intercept of the line 5x - 2y + 6 = 0. Find its equation.

Solve \(3^{2x} - 3^{x+2} = 3^{x+1} - 27\)

Find the coordinates of the centre of the circle \(3x^{2}+3y^{2} - 4x + 8y -2=0\)

If \(\begin{pmatrix}  2  &  1 \\  4 & 3 \end{pmatrix}\)\(\begin{pmatrix}  5 \\ 4 \end{pmatrix}\)  = k\(\begin{pmatrix}  17.5 \\ 40.0 \end{pmatrix}\), find the value of k.

If \(B = \begin{pmatrix}  2 & 5  \\  1 & 3  \end{pmatrix}\), find \(B^{-1}\).

Given that a = 5i + 4j and b = 3i + 7j, evaluate (3a - 8b).

Find the 21st term of the Arithmetic Progression (A.P.):  -4, -1.5, 1, 3.5,...

A fair die is tossed twice. What is its smple size?

Differentiate \(\frac{5x^{3} + x^{2}}{x}, x\neq 0\) with respect to x.

A force (10i + 4j)N acts on a body of mass 2kg which is at rest. Find the velocity after 3 seconds.

Given that \(f(x) = \frac{x+1}{2}\), find \(f^{1}(-2)\).

A straight line 2x+3y=6, passes through the point (-1,2). Find the equation of the line.

A curve is given by \(y = 5 - x - 2x^{2}\). Find the equation of its line of symmetry.

Evaluate \(\int_{-1}^{0} (x+1)(x-2) \mathrm{d}x\)

If \((2x^{2} - x - 3)\) is a factor of \(f(x) = 2x^{3} - 5x^{2} - x + 6\), find the other factor

The 3rd and 7th term of a Geometric Progression (GP) are 81 and 16. Find the 5th term.

How many ways can 6 students be seated around a circular table?

A binary operation \(\Delta\) is defined on the set of real numbers, R, by \(a \Delta b = \frac{a+b}{\sqrt{ab}}\), where a\(\neq\) 0, b\(\neq\) 0. Evaluate \(-3 \Delta -1\).

Given that \(f(x) = 5x^{2} - 4x + 3\), find the coordinates of the point where the gradient is 6.

Simplify \(\frac{\sqrt{128}}{\sqrt{32} - 2\sqrt{2}}\)

Given the table above as the result of tossing a fair die 150 times, find the mode.

\(\alpha\) and \(\beta\) are the roots of the equation \(2x^{2} - 3x + 4 = 0\). Find \(\alpha + \beta\).

If \(log_{y}\frac{1}{8}\) = 3, find the value of y.

If \(x^{2} - kx + 9 = 0\) has equal roots, find the values of k.

Given that \(\sin x = \frac{5}{13}\) and \(\sin y = \frac{8}{17}\), where x and y are acute, find \(\cos(x+y)\).

The velocity, V, of a particle after t seconds, is \(V = 3t^{2} + 2t - 1\). Find the acceleration of the particle after 2 seconds.

\(\alpha\) and \(\beta\) are the roots of the equation \(2x^{2} - 3x + 4 = 0\). Find \(\frac{\alpha}{\beta} + \frac{\beta}{\alpha}\)

If P = \({n^{2} + 1: n = 0,2,3}\) and Q = \({n + 1: n = 2,3,5}\), find P\(\cap\) Q.

Express cos150° in surd form.

Given that \(f(x) = 2x^{2} - 3\) and \(g(x) = x + 1\) where \(x \in R\). Find g o f(x).

Given the table above as the results of tossing a fair die 150 times. Find the probability of obtaining a 5.

Given that \(\frac{6x+m}{2x^{2}+7x-15} \equiv \frac{4}{x+5} - \frac{2}{2x-3}\), find the value of m.

The function f: x \(\to \sqrt{4 - 2x}\) is defined on the set of real numbers R. Find the domain of f.

If \(y = \frac{1+x}{1-x}\), find \(\frac{dy}{dx}\).

In a class of 10 boys and 15 girls, the average score in a Biology test is 90. If the average score for the girls is x, find the average score for the boys in terms of x.

Find the coefficient of \(x^{4}\) in the expansion of \((1-2x)^{6}\).

There are 7 boys in a class of 20. Find the number of ways of selecting 3 girls and 2 boys

Find the magnitude and direction of the vector \(p = (5i - 12j)\)

Given that \( a = \begin{pmatrix} 2 \\ 3 \end{pmatrix}\) and \(b = \begin{pmatrix} -1 \\ 4 \end{pmatrix}\), evaluate \((2a - \frac{1}{4}b)\).