GCE Further Mathematics 2022
Past Questions

Given that sets A and B are subsets of the universal set U, which of the following is equivalent to $(A \cup B)'$?

Given that log 2 = 0.3010 and log 3 = 0.4771, find log 72.

Solve for x: $2^{2x} - 5(2^x) + 4 = 0$

If f(x) = 2x³ - 3x² + x - 5, find f(2).

If $(x - 2)$ is a factor of $f(x) = x^3 + kx^2 - 4x + 4$, find the value of $k$.

Express $\dfrac{5x - 1}{(x+1)(x-2)}$ in partial fractions.

When the polynomial $f(x) = x^3 - 2x^2 + ax + b$ is divided by $(x - 1)$, the remainder is 4, and when divided by $(x + 1)$, the remainder is -2. Find the values of $a$ and $b$.

Which of the following is the correct partial fraction decomposition of $\dfrac{7}{(x-1)(x+6)}$?

If A = [[3, 1], [2, 4]] and B = [[1, 2], [0, 3]], find AB.

The matrix $A = \begin{pmatrix} k & 2 \\ 3 & k \end{pmatrix}$ is singular. Find the values of k.

If p = 2i + 3j and q = 5i - j, find p · q (the dot product of p and q).

If the position vectors of points A and B are 3i + j and i + 5j respectively, find the unit vector in the direction of AB.

Given that vectors p = (k+1)i + 3j and q = 2i + (k-2)j are perpendicular, find the value of k.

Convert 210° to radians, leaving your answer in terms of π.

If $f(x) = \frac{3x^2 - 1}{x}$, find $f'(x)$.

Find the coordinates of the stationary point of the curve $y = x^2 - 4x + 7$.

Evaluate $\int_{0}^{2} (x^2 + 1)\, dx$

Find $\int \sin^2 x\, dx$

The mean of the numbers 3, 7, x, 11 and 9 is 8. Find the value of x.

The table below shows the scores of students in a test: Score: 1, 2, 3, 4, 5 and Frequency: 2, 5, 6, 4, 3. Find the median score.

A discrete random variable $X$ has the probability distribution: $P(X=x) = kx$ for $x = 1, 2, 3, 4$. Find the value of $k$.

2. (a) Rationalise the denominator and simplify: (4 + √5) / (√5 - 1), leaving your answer in the form p + q√5, where p and q are rational numbers. [5 marks] (b) (i) Show that log_a(x) = log_b(x) / lo…

The letters of the word DISTINCTION are to be arranged. (a) How many different arrangements of all the letters are possible? [4 marks] (b) How many of these arrangements begin and end with the letter …