2015 Paper 2

A house is valued at £240 000. Its value is predicted to rise by 2.8% per annum.
Calculate its predicted value after 2 years.

A function is defined as $\displaystyle f(x)=3x+2.$
Given that $\displaystyle f(a)=23$, find $\displaystyle a.$

Triangle ABC is shown below.

Calculate the length of AB.

Find $\displaystyle |\mathbf{u}|$, the magnitude of vector $\displaystyle \mathbf{u}=\begin{pmatrix}6\\-13\\18\end{pmatrix}.$

The vectors $\displaystyle \mathbf{p}$ and $\displaystyle \mathbf{q}$ are shown in the diagram.

Find the resultant vector $\displaystyle \mathbf{p}+\mathbf{q}.$
Express your answer in component form.

The Earth is approximately spherical with a radius of 6400 kilometres.

(a)  Calculate the volume of the Earth giving your answer in scientific notation, correct to 2 significant figures.

(b)  The approximate volume of the Moon is $\displaystyle 2.2\times10^{10}$ cubic kilometres. Calculate how many times the Earth's volume is greater than the Moon's.

Express $\displaystyle \large\frac{5t}{s} \normalsize \div \large \frac{t}{2s^2}$
in its simplest form.

James paid £297.50 for a laptop in a sale. The discount in the sale was 15%.
Calculate the original price of the laptop.

The flag at each hole on a golf course is coloured red and blue.
The diagram below represents a flag.
Triangle QRT represents the red section.
PQTS represents the blue section.

Triangles PRS and QRT are mathematically similar.
The area of triangle QRT is 400 square centimetres.
Calculate the area of PQTS, the blue section of the flag.

The pendulum of a clock swings along an arc of a circle, centre O.

The pendulum swings through an angle of 65°, travelling from A to B.
The length of the arc AB is 28.4 centimetres.
Calculate the length of the pendulum.

The top of a table is in the shape of a regular hexagon. The three diagonals of the hexagon which are shown as dotted lines in the diagram below each have length 40 centimetres.

Calculate the area of the top of the table.

The diagram below shows the circular cross-section of a milk tank.

The radius of the circle, centre O, is 1.2 metres.
The width of the surface of the milk in the tank, represented by ML in the diagram, is 1.8 metres.
Calculate the depth of the milk in the tank.

In the diagram below P, Q and R represent the positions of Portlee, Queenstown and Rushton respectively.

Portlee is 25 kilometres due South of Queenstown.
From Portlee, the bearing of Rushton is 072°.
From Queenstown, the bearing of Rushton is 128°.
Calculate the distance between Portlee and Rushton.
Do not use a scale drawing.

A rectangular picture measuring 9 centimetres by 13 centimetres is placed on a rectangular piece of card.

There is a border $\displaystyle x$ centimetres wide on all sides of the picture.

(a)  (i) Write down an expression for the length of the card in terms of $\displaystyle x.$
      (ii) Hence show that $\displaystyle 4x^{2}+44x-153=0.$

(b)  Calculate $\displaystyle x$, the width of the border. Give your answer correct to one decimal place.