2025 Paper 2

The number of visitors to a zoo in 2024 was 118 750.
The number of visitors is expected to increase by 4% each year over the next two years.
Calculate the expected number of visitors in 2026.

A shop sells footballs in the shape of a sphere with diameter 21 centimetres.

Calculate the volume of the football.
Give your answer correct to 3 significant figures.

The mass of one atom of gold is $\displaystyle 3.27 \times 10^{-22}$ grams.
The mass of one atom of carbon is 6.1% of the mass of an atom of gold.
Calculate the mass of one atom of carbon.
Give your answer in scientific notation.

The weights, in kilograms, of a sample of rugby players in Scotland are shown.
93  103  99  105  88  106  92
(a)  Calculate the mean and standard deviation of these weights.

A sample of rugby players in France has a mean weight of 105 kilograms and a standard deviation of 5.9 kilograms.
(b)  Make two valid comments comparing the weights of the rugby players in the samples from Scotland and France.

Express $\displaystyle x^{2}+10x+19$ in the form $\displaystyle (x+a)^{2}+b.$

A party hat is made in the shape of a cone, as shown.

The piece of card used for making the hat is a sector of a circle, centre C.

The radius of the circle is 15 centimetres and angle ACB is 170°.
Calculate the area of the sector.

In the diagram, ABCDE is a regular pentagon.
• Angle EFA is 65°.
• FAB is a straight line.

Calculate the size of angle FEA.

The diagram shows a cuboid, KLMNOPQR, relative to the coordinate axes.

L has coordinates (0, 3, 12).
R has coordinates (4, 0, 0).
(a)  Write down the coordinates of M.
(b)  Calculate the length of the space diagonal OM.

Change the subject of the formula $\displaystyle B = \frac{1}{4}kc^{2}-3c$ to $\displaystyle k.$

On Bob's lorry there are 7 stacks of paving slabs and 3 stacks of edging blocks. The total weight is 2400 kg.
(a)  Write down an equation in $\displaystyle p$ and $\displaystyle e$ to illustrate this information.

Imran has 3 stacks of paving slabs and 4 stacks of edging blocks. The total weight is 1300 kg.
(b)  Write down an equation in $\displaystyle p$ and $\displaystyle e$ to illustrate this information.

Beth has 6 stacks of paving slabs and 5 stacks of edging blocks.
(c)  Calculate the total weight of the stacks on Beth's lorry.

Two model aircraft are mathematically similar.

The small model is 14 cm long, and the area of one wing is 24 cm². The large model is 31.5 cm long.
Calculate the area of one wing of the large model.

In the diagram A, B and C represent the positions of three checkpoints in an orienteering course.

• B is 250 metres east of A.
• The bearing of C from A is 131°.
• C is 200 metres from B.
Calculate the bearing of C from B.

Solve the equation $\displaystyle \frac{5x+1}{2}=\frac{4x}{3}+1.$

A ride at a theme park has a car attached to a rotating arm.

The starting position of car A is shown in the diagram.

The height, $\displaystyle h$ metres, of car A above the ground is given by $\displaystyle h=10-8\cos x^{\circ}.$
Calculate the two values of $\displaystyle x$ for which the height of car A is 13 metres above the ground.

In the diagram, $\displaystyle \vec{DG}$ and $\displaystyle \vec{GE}$ are represented by vectors $\displaystyle \mathbf{r}$ and $\displaystyle \mathbf{s}$ respectively. $\displaystyle \vec{DE}=3\vec{EF}.$

Express $\displaystyle \vec{GF}$ in terms of $\displaystyle \mathbf{r}$ and $\displaystyle \mathbf{s}.$
Give your answer in its simplest form.