GCSE Mathematics

Practice Tests: Set 6

Paper 2H (Calculator)

Time: 1 hour 30 minutes

You should have: Ruler graduated in centimetres and millimetres, protractor, pair of compasses, pen, HB pencil, eraser, calculator. Tracing paper may be used.

Instructions

Use black ink or ball-point pen.

Fill in the boxes at the top of this page with your name,
centre number and candidate number.

Answer all questions.

Answer the questions in the spaces provided

– there may be more space than you need.

Calculators may be used.

Diagrams are NOT accurately drawn, unless otherwise indicated.

You must show all your working out.

Information

The total mark for this paper is 80

The marks for each question are shown in brackets
– use this as a guide as to how much time to spend on each question.

Advice

Read each question carefully before you start to answer it.

Keep an eye on the time.

Try to answer every question.

Check your answers if you have time at the end.

Answer ALL questions.

Write your answers in the spaces provided.

You must write down all the stages in your working.

1.	The width of a rectangle is a whole number of centimetres.

The length of the rectangle is 9 cm longer than its width.

The perimeter of the rectangle is less than 200 cm.

Find the greatest possible width of the rectangle.

…………………………………….. cm

(Total 4 marks)

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2.	A rugby team played six games.

The mean score for the six games is 14.5

The rugby team played one more game.

The mean score for all seven games is 16

Work out the number of points the team scored in the seventh game.

.......................... points

(Total 2 marks)

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3.	Here are four containers.

Water is poured into each container at a constant rate.

Here are four graphs.

The graphs show how the depth of the water in each container changes with time.

Match each graph with the correct container.

A and ..........................

B and ..........................

C and ..........................

D and ..........................

(Total 2 marks)

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4.	The diagram shows the positions of three turbines A, B and C.

A is 6 km due north of turbine B.

C is 4.5 km due west of turbine B.

(a)	Calculate the distance AC.

.............................................. km

(3)

(b)	Calculate the bearing of C from A.

Give your answer correct to the nearest degree.

.............................................. °

(4)

(Total 7 marks)

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5.	The diagram shows a prism.

All measurements are in centimetres.

All corners are right angles.

Find an expression, in terms of x, for the volume, in cm3, of the prism.

You must show your working.

Give your answer in its simplest form.

.......................................................

(Total 4 marks)

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6.	The diagram shows a triangle DEF inside a rectangle ABCD.

Show that the area of triangle DEF is 8 cm2.

You must show all your working.

(Total 4 marks)

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7.	Jarek uses the formula

Area = absinC

to work out the area of a triangle.

For this triangle,

a = 7.8 cm correct to the nearest mm.

b = 5.2 cm correct to the nearest mm.

C = 63° correct to the nearest degree.

Calculate the lower bound for the area of the triangle.

.............................................. cm2

(Total 3 marks)

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8.	The scatter graph shows some information about 10 cars.

It shows the time, in seconds, it takes each car to go from 0 mph to 60 mph.

For each car, it also shows the maximum speed, in mph.

What type of correlation does this scatter graph show?

..................................................

(1)

The time a car takes to go from 0 mph to 60 mph is 11 seconds.

(b)	Estimate the maximum speed for this car.

........................................ mph

(2)

(Total 3 marks)

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9.	Alex and Ben go to a cafe with some friends.

Alex buys 4 cups of coffee and 3 cups of tea.

He pays a total of £6.95

Ben buys 5 cups of coffee and 2 cups of tea.

He pays a total of £7.20

Work out the cost of each cup of coffee and the cost of each cup of tea.

Cup of coffee.............................................

Cup of tea.............................................

(Total 5 marks)

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10.

The graph of y = kx, where k is a positive constant, is shown above.

Find the value of k.

k = ..............................................

(Total 2 marks)

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11.	In the USA, Sam pays 20.88 US Dollars for 6 US gallons of petrol.

In Russia, Leon pays 800 Roubles for 25.58 litres of petrol.

Use the information in the table to compare the prices of petrol in the two countries.

1 US gallon = 3.79 litres

1 Euro = 40.63 Roubles

1 US Dollar = 0.77 Euros

(Total 5 marks)

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12.	Louise makes a spinner.

The spinner can land on green or on red.

The probability that the spinner will land on green is 0.7

Louise spins the spinner twice.

(a)	Complete the probability tree diagram.

(2)

(b)	Work out the probability that the spinner lands on two different colours.

.............................................

(3)

(Total 5 marks)

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13.	A trapezium ABCD has an area of 5√6 cm2.

AB = 4 cm.

BC = √3 cm.

DC = k cm.

Calculate the value of k, giving your answer in the form a√b – c, where a, b and c are positive integers. Show each step in your working.

k = ................................

(Total 3 marks)

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14.	The diagram shows a large tin of pet food in the shape of a cylinder.

The large tin has a radius of 6.5 cm and a height of 11.5 cm.

A pet food company wants to make a new size of tin.

The new tin will have a radius of 5.8 cm.

It will have the same volume as the large tin.

Calculate the height of the new tin.

Give your answer correct to one decimal place.

.......................................... cm

(Total 3 marks)

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15.	Prove that, for all positive values of n,

(Total 4 marks)

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16.	Make r the subject of the formula p =

r = .........................................................

(Total 4 marks)

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17.	The graph of y = f(x) is shown on the grid.

The graph G is a translation of the graph of y = f(x).

(a)	Write down, in terms of f, the equation of graph G.

y = .....................................................

(1)

The graph of y = f(x) has a maximum point at (−4, 3).

(b)	Write down the coordinates of the maximum point of the graph of y = f(−x).

(....................... , .......................)

(2)

(Total 3 marks)

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18.	A parachutist jumps out of a plane.

This graph shows information about the velocity, v m/s, of the parachutist t seconds after he jumped.

(a)	Work out an estimate for the acceleration of the parachutist when t = 8

.............................................................. m/s2

(3)

(b) Work out an estimate for the distance the parachutist falls in the first 6 seconds.

.............................................................. m

(3)

(Total 6 marks)

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19.	S is inversely proportional to the cube of t.

When t = 4, S =

Find the value of S when t = 8

..............................................

(Total 4 marks)

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20.	The line N is drawn below.

Find an equation of the line perpendicular to line N that passes through the point (0, 1).

..............................................

(Total 3 marks)

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21.	The points A, B and C lie in order on a straight line.

The coordinates of A are (2, 5)

The coordinates of B are (4, p)

The coordinates of C are (q, 17)

Given that AC = 4AB, find the values of p and q.

p = ..............................................

q = ..............................................

(Total 3 marks)

TOTAL FOR PAPER IS 80 MARKS