GCSE, F, C online test 1

Instructions
Q1 - scales

Sketch a scale like that below.

  number line
Mark your scale at:
a) 1.5 and label it A
b) 2.25 and label it B


Look at the circular scale below.
 scale
c) What is the reading on the scale.


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Q2 Conversion Graphs

The graph shows the change in human body temperature over one day
conversion graph
a) What was the temperature at 10am
b) What is the range of temperatures?


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Q3 Factors, primes, multiples

Look at the numbers below

 prime numbers

Which number is:
a) a multiple of 12
b) a factor of 21
c) a square number
d) the square root of 36


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Q4 Conversion graph

The conversion graph below is used to change between pounds and kilograms.

conversion graph

a) What is 5 kilograms in pounds

b) What is 40 pounds in kilograms

c) What is 100 kilograms in pounds


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Q5 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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Q6 Table of money items.

Laura bought some things from a shop.
Complete her bill:

ItemNo.Cost eachTotal
Bottle orange9£1.20£10.80
Crisps...£0.27 £4.05
Pair Jeans3£.....£34.50
Pair socks3£1.54£.....
Total cost£.....

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Q7 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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Q8 Construction

On paper, draw a horizontal line 5cm long. Label it AB.
Using a compass and pencil construct an angle of 60° at point A.


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Q9 Money Calculation

A shop pays all its workers the minimum national wage (MNW) set by the government.
There are different levels of MNW, depending on your age.
The current rates (from 1 October 2011) are:

£6.08 - the main rate for workers aged 21+
£4.98 - the 18-20 rate
£3.68 - the 16-17 rate for workers above school leaving age

Luke is 16 and Jane is 18. They both work in the shop on Saturday from 9am to 4pm.

How much more will Jane get than Luke


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Q10 Use of the Calculator

Use your calculator to work out:
calculations
square numbers
Give your answer to one decimal place


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Q11 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) Using your graph, estimate the stopping distance S for a car with a speed of 45mph

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Q12 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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Q13 Area and Locii

A plan of a swimming pool is shown below.

locii


a) Calculate the area of the swimming pool

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

b) Copy the plan using 2m=1cm and then draw these two areas accurately on the plan.


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Q14 Payslip calculations

Matt looked at his yearly income statement and noticed some missing values.
Copy the statement and use the formula below to complete it

payslip

His taxable pay is worked out using the tax code 747L.
This means, he doesn't pay tax on £7475 of his gross pay.

a) Taxable Pay = Gross Pay – £7475.
Work out Matt's Taxable Pay.

b) Matt's Income tax = 20% of Taxable Pay.
Work out Matt's Income tax.

c) Matt's Total Deductions = Income Tax + NI (national Insurance)
Work out Matt's Total Deductions.

d) Net Pay = Gross pay – Total deductions.
Work out Matt's Net Pay.

e) What % of his gross pay is deducted.


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Q15 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.

a) Calculate the area of the track.
Give your answer to nearest whole number

b) Calculate the perimeter of the track.

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Q15b Fractions

The Olympic Marathon is over 42 kilometres long. A runner can lose over 3 ½ litres of sweat during a marathon.

This water must be replaced and so cups of water are handed out along the race.
Each cup holds ⅛ litre.

a) How many cups of water should a runner drink during the race?

b) After drinking one litre of water approximately how far would a runner have gone. Give your answer to the nearest km.


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Q16 Bar Chart

The chart shows the number of cinema tickets sold at two cinemas in a week

graph

a) On which day were the same number of tickets sold at both cinemas

b) What was the total number of tickets sold at the Rave at the weekend

c) Work out the mean number of tickets sold at CineBlue for the seven days

The normal ticket price is £5.40 at CineBlue
On a Thursday CineBlue has a special offer - two tickets for the price of one

d) How much money did CineBlue take on Thursday


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Q17 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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Q18 Proportions

Laura wants to make her own custard. She uses the recipe below for 4 people

 300ml milk
 ½ tea spoon vanilla extract
 2 eggs, yolks only
 15 grams sugar

a) How much milk would she need to make custard for 10 people

b) How much vanilla essence would she need to make custard for 2 people
Give your answer as a fraction of a tea spoon


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Q19 Money Calculation

A group of 16 university students hired a mini-bus for the day.

The mini-bus cost £40 per day plus an extra charge for mileage.

Between 0-100 miles this was 82p per mile and above 100 miles it was 41 p per mile.

The mileage reading at the start of the trip was 32,863 and 33,050 at the end.

Each student paid £10.

How much profit or loss did the trip make?


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Q20 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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Q21 Probability I

Cyril had a pack of 48 playing cards.
Each card in the pack was either black or red with a circle, square, triangle or rectangle symbol shown below.

probability

Cyril picked one card at random.

a) What was the chance of picking a card with a triangle symbol Give your answer as a fraction in its simplest form

b) A black card was picked. What is the probability that it has a square symbol.

Cyril took the circle cards from the pack. They were numbered 10 to 19. He picked one card at random.

c) What is the probability of picking a card with a prime number


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Q21b Probability II

Cyril had another pack of 50 playing cards.
Each card was either green or blue with a circle, square, triangle or rectangle symbol, shown below.

probability


a) How many blue, triangle cards were in the pack


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Q22 Distance-time graph

The graph shows how far Bill travelled on his bike ride. The first part of his journey was uphill.

speed-distance

a) How many times did he stop for a rest?

b) Calculate Bill's speed for the parts of the graph labelled A and B. Give your answer in km per hour.

c) At 12:10 Bill rode home downhill at a speed of 26 km per hour. What time did he arrive home.


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