## Question

The diagram shows the map of part of an orienteering course.

Sanji runs from the start, S, to the point A.

Write **SA** as a column vector.

### Solution

As Sanji runs **3** units in the left (**-ve**) direction and **4** units in the upward (**+ve**) direction. So the column vector is

-3 |

4 |

## Question

When Ali takes a penalty, the probability that he will score a goal is 4/5.

Ali takes 30 penalties.

Find how many times he is expected to score a goal.

### Solution

$$ \text{No. of times, Ali is expected to goal } = {4 \over 5} × 30 = 24$$24 times he is expected to score a goal.

## Question

The ratio of Anne’s height : Ben’s height is 7 : 9.

Anne’s height is 1.4 m.

Find Ben’s height.

### Solution

Ben's height = 1.8 m

## Question

The distance between the centres of two villages is 8 km.

A map on which they are shown has a scale of 1 : 50 000.

Calculate the distance between the centres of the two villages on the map.

Give your answer in centimetres.

### Solution

According to the map scale, 1 centimetre = 500 metre = 50000 centimetres

and we know that 8 kilometre = 800000 centimetres

Distance between two villages on map = 16 centimetres

## Question

The bar chart shows the favourite colours of students in a class.

**(a)** How many students are in the class?

**(b)** Write down the modal colour.

### Solution

**(a)** From bar chart, frequency against each colour represents the no. of students.
By adding these frequencies, we have, 4 + 2 + 6 + 8 + 5 = 25

Hence the no. of students in the class = 25

**(b)** The modal colour is green, having the highest frequency.

## Question

Use your calculator to find

$$ \sqrt{45 × 5.75 \over 3.1 + 1.5} $$### Solution

$$ \sqrt{45 × 5.75 \over 3.1 + 1.5} $$ $$ = \sqrt{258.75 \over 4.6} $$ $$ = \sqrt{56.25} $$ $$ = 7.5 $$## Question

**(a)** Calculate 60% of 200.

**(b)** Write 0.36 as a fraction.

Give your answer in its lowest terms.

### Solution

**(a)**

**(b)**

## Question

A circle has a radius of 50 cm.

**(a)** Calculate the area of the circle in cm^{2}.

**(b)** Write your answer to part (a) in m^{2}.

### Solution

**(a)**

Radius of the circle = 50 cm

$$ \text{Area of the circle } = \pi r^2 $$ $$ \text{Area of the circle } = 3.142 × 50^2 \text{ } = 7855 $$Area of the circle = 7855 cm^{2}

**(b)**

Area of the circle = 0.7855 m^{2}

## Question

The graph shows the temperature in Paris from 6 am to 6 pm one day.

**(a)** What was the temperature at 9 am?

**(b)** Between which two times was the temperature decreasing?

**(c)** Work out the difference between the maximum and minimum temperatures shown.

### Solution

**(a)**

The temperature at 9 am is 15 ^{o}C

**(b)**

Between 2 pm and 6pm, the temperature was decreasing.

**(c)**

From graph,

the maximum temperature = 27.5 ^{o}C

the minimum temperature = 12.5 ^{o}C

Difference between maximum and minimum temperatures

= 27.5 ^{o}C - 12.5 ^{o}C

= 15 ^{o}C

## Question

**(a)** Write down the mathematical name of a quadrilateral that has exactly two lines of symmetry.

**(b)** Write down the mathematical name of a triangle with exactly one line of symmetry.

**(c)** Write down the order of rotational symmetry of a regular pentagon.

### Solution

**(a)**

Rectangle or rhombus

**(b)**

Isosceles (triangle)

**(c)**

5

## Question

Without using your calculator, work out

$$ {1 \over 2} ({2 \over 3} + {1 \over 4}) $$Show all your working clearly and give your answer as a fraction.

### Solution

$$ {1 \over 2} ({2 \over 3} + {1 \over 4}) $$ $$ = {1 \over 2} ({8 + 3 \over 12}) $$ $$ = {1 \over 2} × {11 \over 12} $$ $$ = {11 \over 24} $$ $$ = 0.4583 $$## Question

The diagram shows the graph of y = (x + 1)^{2} for −4 ≤ x ≤ 2.

**(a)** On the same grid, draw the line y = 3.

**(b)** Use your graph to find the solutions of (x + 1)^{2} = 3.

Give each solution correct to 1 decimal place.

## Question

The front of a house is in the shape of a hexagon with two right angles.

The other four angles are all the same size.

Calculate the size of one of these angles.

## Question

**(a)** Expand and simplify.

2(3x – 2) + 3(x – 2)

**(b)** Expand.

x(2x^{2} – 3)

### Solution

**(a)**

2(3x – 2) + 3(x – 2)

= 6x – 4 + 3x – 6

= 9x – 10

**(b)**

x(2x^{2} – 3)

= 2x^{3} – 3x

## Question

The scatter diagram shows the marks obtained in a Mathematics test and the marks obtained in an
English test by 15 students.

**(a)** Describe the correlation.

**(b)** The mean for the Mathematics test is 47.3 .

The mean for the English test is 30.3 .

Plot the mean point (47.3, 30.3) on the scatter diagram above.

**(c) (i)** Draw the line of best fit on the diagram above.

**(ii)** One student missed the English test.

She received 45 marks in the Mathematics test.

Use your line to estimate the mark she might have gained in the English test.

## Question

**(a)**

In the diagram, AB is parallel to DE.

Angle ABC = 110°.

Find angle BDE.

**(b)**

TA is a tangent at A to the circle, centre O.

Angle OAB = 50°.

Find the value of

**(i)** y,

**(ii)** z,

**(iii)** t.

## Question

The diagram shows a ladder, of length 8 m, leaning against a vertical wall.

The bottom of the ladder stands on horizontal ground, 3 m from the wall.

**(a)** Find the height of the top of the ladder above the ground.

**(b)** Use trigonometry to calculate the value of y.

## Question

**(a)** Lucinda invests $500 at a rate of 5% per year simple interest.

Calculate the interest Lucinda has after 3 years.

**(b)** Andy invests $500 at a rate of 5% per year compound interest.

Calculate how much more interest Andy has than Lucinda after 3 years.