GCSE, H, C online test 1

Instructions


Q1 Conversion Graphs

The conversion graph is used to change between UK pounds (£) and two different currencies - the Euro (€) the US dollar ($)
conversion graph
a) Use the graph to change 7 UK pounds into Euros (€)
b) What is 10 US dollars ($) in UK pounds (£)
c) What is 5 Euros (€) in US Dollars ($)


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Q2 Transformation

Sketch the diagram below. Rotate the shape by 90° clockwise about the origin (0, 0). Label it shape Y

rotation


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Q3 Table data

The table shows the number of students in each class who have extra tuition.

table

What percentage of the students in the school have maths tuition. Give your answer to the nearest whole number.


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Q4 Area

A plan of a bedroom is shown.

bedroom

Carpet comes in a 4 metre roll and costs £15 per square metre.
Underlay goes under the carpet and comes in 1 metre squares.
Underlay costs £6 per square metre.

Gripper rod which go around the perimeter of the room hold the carpet in place
Gripper rods cost 50 pence per metre.

The carpet fitter charges £50 to fit the carpet.
Work out the total cost of fitting a carpet.


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Q5 Draw a graph

a) Use the equation to complete the table of values.

x 02030405060
y0  75120 240


b) Now get some graph paper and plot the x, y co-ordinates and draw the graph


The stopping distance S (in feet) of a car is calculated using this formula :
 equation  where x is the speed in mph.


c) Estimate the speed of a car with a stopping distance of 60 feet

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Q6 Area and Perimeter

In 2012, the United Kingdom hosted the Olympic Games in London. A standard running track is shaped like this:

The track is made from two semi-circles at each end joined by two straights.

For the inside running lane, the radius of each circle is 36.80m and the two straights are 84.39m each as shown below.

Calculate the perimeter of the track.

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Q7 Length of a diagonal

Sylvia had a cylindrical pencil-case.
The case had a tight top that fitted snugly.
She wanted to put a 12 cm pencil in her pencil-case.


 pythagoras

Will the pencil fit in the pencil-case, diagonally with the top on. Explain.
Ignore the width of the pencil.


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Q8 Volume
volume

A carton of custard is in the shape of a cuboid as shown.

The carton was 12cm high, 7.5cm wide and 4.5cm deep.

a) Work out the volume of the carton.


The custard company wants to design a new larger carton to hold 1000cm3 of custard.


The base of the carton is a square and the height is 10cm more than the width as shown.


The volume of a carton is given by
V = x3 + 10x2 where x is the base width

b) Using trial and improvement work out x when V = 1000cm3
Give your answer to one decimal place.


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Q9 Substitution in formula

This formula converts temperature in degrees Centigrade to degrees Fahrenheit
 

a) Use the formula to convert 90° C to °F

b) David measured the temperature of some water. It was 128° F.
Calculate the temperature in °C


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Q10 Speed distance

A party of teachers travelled by car from Toddington to Ripon to attend a conference.
They drove 288 km at an average speed of 60 mph.
They stopped on route for a 25 minute break.
They needed to be at the conference 10 minutes before it started at 12:00

Using 5 miles = 8 kilometres, what is the latest time they must leave Toddington.
Give your answer in terms of the 24 hour clock.


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Q11 Area, distance and speed

A farmer needed to harvest the crops in a field.
The field was 200m by 120m
The farmer used a combine harvester with a blade cutting width of 4m for each cut across the field


a) How many cuts would the farmer need to make to harvest the field

The combine harvester had a speed of 4.8km per hour.

b) How long would it take the farmer to harvest crops in the field.
Give your answer in hours and minutes


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Q12 Area and Locii

A plan of a swimming pool is shown below. One dimension is missing.

locii


One area of the pool is for toddlers and another area is for adults only.
The toddler's paddling area is within 5m of the corner J
The adult area is within 4m of the side ML
The area that is left over shows where children are allowed to swim

Calculate the area where children are allowed to swim.
Give your answer to 3 significant figures.


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Q13 Interest rate

Poppy wanted to work out how much the monthly repayments would be on her fixed interest rate mortgage. She found a formula on the internet compound interest
M =  The monthly payment
P =  The amount of money being borrowed
n =  The number of months of the mortgage
i =  The interest per month and is calculated by converting the interest rate to a decimal and then dividing by 12.

a) Calculate the monthly repayments on a mortgage of £100,000 at an interest rate of 4% over 25 years.
Give your answer to the nearest £
b) Using your answer to a) work out the total amount paid over the 25 years.
Give your answer to the nearest thousand


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Q14 angles, Sectors
sector

In the Olympic Games the landing area for the discus event is a sector of a circle.

The length of the sector is 80m (L) and the two sector lines, at a distance of 80m, are spaced 48m apart. (W)

a) What is the ratio of the width W to the length L
Give your answer in its simplest form

b) Calculate the angle marked as x
Give your answer to 1 decimal place.

c) What is the area of the discus sector to 3 significant figures


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Q14b angles, Sectors
shot put

Refer to your answer in c above to answer this question.

The shot put is a similar sector as the discus, but the two sector lines, are spaced 15m apart.

What is the area of the shot put sector to 3 significant figures

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Q15 Simultaneous Equations

Laura bought some plates and cups at two car boot sales.
At Leicester she bought 2p plates and 3c cups. In total she bought 66 items.
At Nottingham she bought 3p plates and 2c cups. In total she bought 69 items.


a) State this information as a pair of simultaneous equations.

b) Solve your simultaneous equations to work out how many cup and plates she bought at Leicester.

The price paid for the cups was the same at both locations and the price paid for the plates was the same at both locations
For the 66 items at Leicester she paid £36.00
For the 69 items at Nottingham she paid £39.00


c) Work out how much she paid per cup and per plate


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Q16 Bearings

A helicopter flies from Birmingham (X) on a bearing of 056° for 56 km to Loughborough (Y).
bearings
It then flies 85 km on a bearing of 146° to Bedford(Z).

a) Work out y, the distance from Bedford(Z) to Birmingham(X)?
Give your answer to the nearest kilometre

b) What is the bearing of Birmingham(X) from Bedford(Z).
Give your answer to the nearest degree


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Q17 Circle Theorems

ABCD is a cyclic quadrilateral.
Angle AOB is 104° , DCB is 95°
O is the centre of the circle.
circle theorem


a) Work out the size of the angle DOB marked 'b'
Give a reason for your answer

b) Work out the size of the angle ADO, marked 'a'
Give a reason for your answer


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Q18 Histogram

The table and histogram show information about the age of passengers on a bus. Get Pdf


a) Use the histogram to complete the table

Time (t years)Frequency
0< t ≤ 1011
10< t ≤ 1516
15< t ≤ 30 
30< t ≤ 5024
50< t ≤ 60 
60< t ≤ 7033

b) Use the table to complete the histogram


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Q19 Bounds

Sylvia runs 100 metres in a time of 25.6 seconds.
The distance of 100 metres was measured to the nearest metre.
The time of 25.6 seconds was measured to the nearest tenth of a second.

a) What is the upper bound for the distance of 100 metres

b) What is the lower bound for the time of 25.6 seconds

c) Calculate the lower bound for Sylvia's average speed Show all the figures on your calculator display


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Q20 3D Pythagoras

The floor of a room is 6 m by 4 m, and its height is 3 m


pythagoras

Find the distance from a corner point on the floor to the opposite corner point on the ceiling.
Give your answer correct to 1 decimal place


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Q21 Algebra

A six sided shape is shown below with all the corners as right angles.
Measurements are in centimetres.

algebra quadratic

The area of the shape is 18 cm2

a) Show that 3x2 + 5x – 28 = 0

b) Find the height of the shape


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