Further Mathematics Past Questions

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

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

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

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

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

Given that 2x + 3y - 10 = 0 and 3x = 2y - 11, calculate the value of (x - y). 

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

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

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

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

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

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

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

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

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

Evaluate: \(^{lim}_{x \to 1} \begin{pmatrix} \frac{1 - x}{x^2 - 3x + 2} \end {pmatrix}\)

A uniform beam, PQ. is 100 m long and weighs 35 N. It is placed on a support at a point 40 cm from P. If weights of 54 N and FN are attached at P and Q respectively in order to keep it in a horizontal position, calculate, correct to the nearest whole number, the value of F.