2024 Paper 2

Dougie pays £460 for a new laptop.
It is expected that the value of the laptop will depreciate by 26% each year.
Calculate the expected value of Dougie's laptop after 3 years.

An ant colony occupies an area of 250 hectares.
There is an average of $\displaystyle 1.22 \times 10^6$ ants per hectare.
Calculate the number of ants in the colony.
Give your answer in scientific notation.

In triangle ABC:
• AB = 25 metres
• AC = 18 metres
• BC = 34 metres.

Calculate the size of the shaded angle at A.

Solve, algebraically, the inequation
$\displaystyle 5(x-2)+4 < 7x+8.$

This year the cost of Charley's car insurance is £278.40.
This is an increase of 16% on last year's cost.
Calculate the cost of Charley's insurance last year.

(a)  Factorise $\displaystyle y^2-6y.$
(b)  Hence simplify $\displaystyle \frac{y^2-6y}{y^2-3y-18}.$

A paperweight is in the shape of a cuboid.
It consists of a hemisphere of red glass surrounded by clear glass.

The cuboid has height 4 centimetres and a square base of length 7 centimetres.
The hemisphere has diameter 6 centimetres.
Calculate the volume of clear glass in the paperweight.
Give your answer correct to 2 significant figures.

Solve the equation $\displaystyle 3x^2+8x+1=0.$
Give your answers correct to 2 decimal places.

Change the subject of the formula $\displaystyle f = \frac{2d+3}{e}$ to $\displaystyle d.$

Karen buys a door-number sign for her house.
The sign consists of parts of two identical circles.

AB is a chord to both circles.

• AB has length 15 centimetres.
• The radius AC has length 10 centimetres.
Calculate the width of the sign.

Solve the equation $\displaystyle 17 \sin x^{\circ} + 1 = 9$, for $\displaystyle 0 \le x < 360.$

Express $\displaystyle \frac{2}{x+5} + \frac{3}{x-4}$, $\displaystyle x \neq -5, x \neq 4$ as a single fraction in its simplest form.

In triangle ABC:

• AC = 22 centimetres
• angle BAC = 40°
• angle BCA = 30°
• BD is perpendicular to AC.
Calculate the length of BD.

The diagram shows a rhombus WXYZ with a diagonal ZX drawn.

$\displaystyle \vec{ZW}$ represents vector $\displaystyle \mathbf{a}$ and $\displaystyle \vec{ZX}$ represents vector $\displaystyle \mathbf{b}$.
(a)  Express $\displaystyle \vec{WX}$ in terms of $\displaystyle \mathbf{a}$ and $\displaystyle \mathbf{b}$.

M is the mid-point of XY.
(b)  Express $\displaystyle \vec{WM}$ in terms of $\displaystyle \mathbf{a}$ and $\displaystyle \mathbf{b}$. Give your answer in its simplest form.

The diagram shows a sector of a circle, centre C.

The radius of the circle is 12 centimetres.
The length of arc AB is 15 centimetres.
Calculate the area of the sector.

Express $\displaystyle 3\cos^2 x^{\circ} - 1$ in the form $\displaystyle a + b \sin^2 x^{\circ}.$
Show your working.