2022 Paper 2

Expand and simplify $\displaystyle (3x-2)(2x^{2}+5x-1)$.

A company's annual profit at the end of 2021 was £215,000.
The profit is expected to increase by 3% each year.
Calculate the company's expected annual profit by the end of 2025.
Give your answer correct to the nearest thousand pounds.

A concrete gatepost is made in the shape of a cuboid with a sphere on top.

The sphere has diameter 0.4 metres.
The cuboid has a square base of length 0.48 metres.
The total height of the gatepost is 2.4 metres.
Calculate the volume of concrete needed to make a gatepost.

Moira buys 4 mangoes and 3 apples at a fruit shop.
The total cost is £4.25.
(a)  Write down an equation to illustrate this information.

Sami buys 5 mangoes and 2 apples in the same fruit shop.
The total cost is £4.70.
(b)  Write down an equation to illustrate this information.

(c)  Calculate, algebraically, the cost of a mango and the cost of an apple.

A school netball team recorded the number of sit-ups each player completed in a minute.
The numbers for the seven players were:
29  27  24  31  22  19  30
(a)  Calculate the mean and standard deviation of the numbers of sit-ups.

Some players in the school's hockey team also recorded the number of sit-ups they completed in a minute.
Their numbers gave a mean of 29 and a standard deviation of 3.2.
(b)  Make two valid comments comparing the numbers of sit-ups of the players in the netball team and the hockey team.

The diagram shows triangle FGH.

• FG = 25 centimetres
• FH = 32 centimetres
• Angle GFH = 58°
Calculate the area of triangle FGH.

Solve the equation $\displaystyle 4x^{2}+2x-7=0$.
Give your answers correct to 2 significant figures.

A train tunnel has a circular cross-section with a horizontal floor.
A diagram of the cross-section is shown below.

• The centre of the circle is O.
• Chord AB is 4 metres.
• The radius OA is 2.9 metres.
Calculate the height of the tunnel.

Solve the equation $\displaystyle 3\sin x^{\circ}+4=6$, for $\displaystyle 0 \le x \le 360$.

An attraction at a theme park has a carriage attached to an arm.
The arm swings from A to B along the arc of a circle, centre C, as shown in the diagram below.

• The length of the arm, CB, is 15 metres.
• The length of the major arc, AB, is 69.4 metres.
Calculate the size of the reflex angle ACB.

The diagram shows a cuboid, ABCDEFGH.

• The length of the cuboid, EH, is 24 centimetres.
• The breadth of the cuboid, HG, is 6 centimetres.
• The height of the cuboid, CG, is 8 centimetres.
Calculate the length of EC, the space diagonal of the cuboid.

Simplify $\displaystyle \frac{2ab+6a}{b^{2}-9}$.

Simplify $\displaystyle \frac{\sin x^{\circ}+2\cos x^{\circ}}{\cos x^{\circ}}$.

The width of a river is represented by BC in the diagram below.
AB represents a tree on the river bank.

• From C, the angle of elevation to A is 28°.
• From D, the angle of elevation to A is 12°.
• The distance from C to D is 15 metres.
• BCD is a straight line.
Calculate BC, the width of the river.