2025 Paper 1

Expand and simplify $\displaystyle (x+3)(x+5)+4(x-2)$

Ten pupils record the length of time, in minutes, it takes them to walk to school one morning.
3  11  13  15  15  16  17  18  19  22
Calculate the interquartile range of these times.

In a sale, the price of a wedding dress is reduced by 20%.
The sale price of the dress is £720.
Calculate the price of the dress before the sale.

Triangle ABC is shown in the diagram.

• AB = BC = 6 centimetres.
$\displaystyle \bullet \quad \sin B = \frac{2}{3}.$
Calculate the area of the triangle.

The diagram shows the straight line passing through points A and B.

Find the equation of the line AB.
Give the equation in its simplest form.

A function is defined as $\displaystyle f(x)=3x+7$.
(a)  Evaluate $\displaystyle f(6).$
(b)  Given that $\displaystyle f(p)=19$, find the value of $\displaystyle p.$

Part of the graph of $\displaystyle y=2\sin(x-30)^{\circ}$ is shown in the diagram.

The graph has a maximum turning point at A.
State the coordinates of A.

The diagram shows a parabola with equation of the form $\displaystyle y=(x+a)^{2}+b$.

(a)  State the value of $\displaystyle a.$
(b)  State the value of $\displaystyle b.$

Determine the nature of the roots of the function $\displaystyle f(x)=3x^{2}+2x+1.$

Express $\displaystyle \frac{6}{\sqrt{10}}$ with a rational denominator.
Give your answer in its simplest form.

Vectors $\displaystyle \mathbf{p}$ and $\displaystyle \mathbf{q}$ have components $\displaystyle \mathbf{p}=\begin{pmatrix}5\\ 2\end{pmatrix}$ and $\displaystyle \mathbf{q}=\begin{pmatrix}1\\ -3\end{pmatrix}.$
Draw the resultant vector $\displaystyle \mathbf{p}+\mathbf{q}$ on the grid.

Express $\displaystyle \frac{5}{x-1}-\frac{4}{x},$ $\displaystyle x \neq 1, x \neq 0$ as a single fraction in its simplest form.

The diagrams of a rectangle and square are shown below.

(a)  Find an expression for the area of the rectangle.
(b)  Given that the area of the rectangle is equal to the area of the square, show that $\displaystyle x^{2}-x-6=0.$
(c)  Hence find, algebraically, the length and breadth of the rectangle.