Eduqas GCSE Maths Component 1H Higher June 2017 question paper

Sasha is carrying out a survey into the amount of chocolate teenagers eat in a day.

Explain why this is a biased question.

State one other criticism of the question.

2. (a) Solve 7 x + 2 = 3 x + 4.

Solve 3 – 2(x – 9) = 5x.

Solve 7 – 3x < 1.

Represent your answer to part (c)(i) on the number line below.

The scale drawing below shows a lake. There are two small islands in the lake at A and B. The lifeguard station is marked at C.

Swimming is only allowed in the area of the lake that is, • nearer to A than it is to B and • less than 60 metres from C.

Using a ruler and a pair of compasses, show accurately on the diagram the area where swimming is allowed. Shade the area where swimming is allowed.

Use the scale 1 cm represents 10 m.

4.

Work out the column vector p + 3q.

Twenty people go on a trip to the seaside.

Of these 20 people • 13 swim in the sea • 17 go to the funfair • 2 do not swim in the sea or go to the funfair.

Complete the Venn diagram below to show this information.

One person is chosen at random.

Find the probability that this person swims in the sea and goes to the funfair.

One person is chosen at random from those who swim in the sea.

Find the probability that this person does not go to the funfair.

Make y the subject of this formula.

9 x = p (8 + y) + 5

A shop sells Brand X trainers in three colours only.

The proportion of gold trainers sold is 0·04. The proportion of black trainers sold is 5 times the proportion of lime trainers.

Find the proportion of black trainers sold.

9. (a) The diagram shows a large shipping container at rest on horizontal ground.

The weight of the container is 32 000 N.

Work out the pressure exerted on the ground by the shipping container.

Give your answer in N/m².

A table is at rest on horizontal ground. The table has 4 legs. Each leg has a height of 50 cm. The volume of material in one leg is 450 cm³. The table weighs 54 N.

By considering the base of the table legs, work out the pressure exerted on the ground by the table. Give your answer in N/cm².

You must show all your working.

State one assumption you have made in your answer to part (b).

How would your answer to part (b) change if you had not made this assumption?

10. (a) Show that the interior angle of a regular octagon is 135°.

The shaded shape is formed by cutting a kite from a regular octagon as shown in the diagram. Prove that y = 2x – 135.

You must give reasons to support your statements.

Gabby buys a chest of drawers and a computer desk to fit side by side between two walls in her

The width of the chest of drawers is 45 cm, correct to the nearest cm. The width of the computer desk is 60 cm, correct to the nearest cm. The two walls are 1·2 m apart, correct to the nearest 10 cm.

Calculate the least possible width of the gap remaining when Gabby’s furniture is in place.

The table shows information about the length (in minutes) of phone calls made between two college friends during March.

Call length, c (minutes)	0 c 5	5 c 10	10 c 20	20 c 30	30 c 60
Frequency	3	4	7	12	6
Frequency density

Complete the frequency density row in the table above.

Draw a histogram to illustrate the data in the table.

Estimate the fraction of calls that lasted for more than 35 minutes.

During one of the months, the college friends had examinations.

Compare the two histograms and explain which month this is likely to be.

13. (a) Evaluate each of the following.

Complete the following statement:

Space for working:

The diagram shows the points P (1, – 4) and Q (7, q), joined by a straight line.

Find the value of q.

The line L₁ is parallel to the line PQ and passes through the point (3, 0).

Where does the line L₁ cross the y-axis?

The line L₂ is perpendicular to the line PQ and passes through the point (–5, 1).

Find the equation of L₂.

Find SOQ.

Give a reason for your answer.

Find SRQ.

Calculate the size of OSR.

The diagram shows points A, B, C and D on the circumference of a circle. AC and BD intersect at the point E.

Show clearly that triangle AEB is similar to triangle DEC.

Give a reason for each step of your answer.

16. (a) Simplify each of the following.

Tom says:

Show that Tom’s statement is incorrect.

Give the reasons to support your decision.

In this question all dimensions are in centimetres.

The diagram shows a sketch of two circles, both with centre O.

The line AB is a chord of the outer circle and a tangent to the inner circle. The length of AB is 24. The equation of the outer circle is x² + y² = 13².

Find the equation of the inner circle.

The diagram shows a sketch of the graph of y = f (x).

The point A has coordinates (1, 0) and the point B has coordinates (0, 2).

Sketch the graph of y = –f(x) on the axes below.

You must indicate the coordinates of the new positions of the points A and B.

Sketch the graph of y = f(x) – 3 on the axes below.

You must indicate the coordinates of the new positions of the points A and B.

Water in a tank is x cm deep.

The tank has a tap which is slightly open. The rate, R cm³ per minute, at which the volume of water decreases is proportional to the square root of x. When the water is 81 cm deep, the volume of water decreases at the rate of 900 cm³ per minute.

Find the rate at which the volume of water decreases when the depth of the water is

9 cm.

Find the depth of the water when the rate at which the volume of water decreases is

400 cm³ per minute.

The functions g (x) and h (x) are defined, for x > 2, by

g(x) = x² – 1, h(x) = 3x.

Find the value of hg(9).

Find and simplify an expression for gh(2x).

A manufacturer wants to test the performance of a new fuel.

In the test, a total of 20 litres of the fuel is shared between a car and a motorbike.

The car uses x litres of fuel in the test.

Write an expression in terms of x for the number of litres used by the motorbike.

Show that x satisfies the equation