Shortbread biscuits are made from flour, butter and sugar.
Their masses are in the ratio 4: 3: 2 respectively.
What fraction of a shortbread biscuit is made up of sugar?
[1]
1400 g of flour is used to make a batch of shortbread biscuits.
How many grams of butter is used for this batch of shortbread biscuits?
[2]
[4]
Regan caught 70 fish on a fishing trip.
He measured the length of each of the fish in centimetres.
The table shows his results.
| Length, l (centimetres) | Number of fish |
60  l  65 | 19 |
65  l  70 | 17 |
70  l  75 | 23 |
75 l  80 | 10 |
| 80 l 85 | 1 |
Calculate an estimate for the mean length of these fish.
[4]
Regan thinks that the median length of fish is in the group 70 l 
75. Is Regan correct?
Yes No
Give the reason for your answer.
[1]
Jan has a large piece of card.
The card has width 60 cm and length 96 cm.
She uses a machine to cut identical circles out of the card. Each circle has a radius of 6 cm.
Jan has cut five circles as shown on the diagram above. She continues in this way to cut as many circles as possible from the card.
What is the maximum number of circles Jan can cut out of the card?
[1]
Jan cuts out the maximum number of circles from the card.
What area of card is left over?
Area of card left over........
[4]
[2]
Solve 7x + 6 = 4x + 7.
[2]
Factorise y2 − 400.
[1]
[3]
The two shapes below are similar.
Find the value of r and the value of t.
[4]
Vaughan cycles down a track from the top of a mountain to the bottom.
The track goes down at an angle of 48° to the horizontal. Vaughan is 800 feet above ground level.
Vaughan cycles from the top of the track to the bottom of the track.
What distance has he cycled?
The distance Vaughan has cycled is........ feet.
[4]
State an assumption you have made in answering part (a).
[1]
If your assumption is not correct, what effect would this have on your answer to
part (a)?
[1]
He pays £1451.60 for a silver bar after a 5% discount has been applied.
What was the original cost of the silver bar?
[3]
The silver bar is in the shape of a cuboid and has the following dimensions: length 8·1 cm, width 7·3 cm and depth 4 cm. Bjorn melts down the silver bar and uses the silver to make 200 identical pieces of jewellery. The density of silver is 10·49 g/cm3. Calculate the mass of each piece of jewellery.
Give your answer in grams.
Each piece of jewellery has a mass of………........ ……….. g
[4]
[6]
Make e the subject of the formula.
g = 4 e − 3 f
[2]
[4]
The equation 2x3 − 3x2 − 2 = 0 has only one positive solution.
Akriti says,
Is Akriti correct?
Yes No
Show calculations and explain your decision.
[2]
The same home learning task was given to 50 Year 7 pupils in school A and 50 Year 7 pupils in school B.
The length of time, in minutes, each pupil took to complete the task was recorded.
The results for the pupils from school A are shown on the cumulative frequency diagram
Use the cumulative frequency diagram to answer the following questions about the pupils in school A.
What is the median time taken to complete the task?
[1]
Calculate the inter-quartile range of the times taken to complete the task.
Inter-quartile range........ minutes
[2]
What percentage of pupils took longer than 62 minutes to complete the home
learning task?
[2]
A summary of the results for the pupils in school B is shown in the table below.
| Least time | 12 minutes |
| Lower quartile | 31 minutes |
| Median | 45 minutes |
| Inter-quartile range | 24 minutes |
| Greatest time | 1 hour 5 minutes |
Draw a box plot to display the results for school B.
[3]
Make two comments to compare the results of school A and school B. One comment must include an appropriate average.
The other comment must include a measure of spread.
Comment 1
Comment 2
[2]
The diagram below shows a square-based pyramid.
The slant height of each triangular face is 12 cm.
Calculate the volume of the pyramid.
You must show all your working.
[5]
Cody has a bag containing 8 red sweets and 9 green sweets.
Cody randomly selects one sweet at a time and eats it.
Calculate the probability that the first two sweets Cody eats are red.
[2]
Calculate the probability that the first two sweets Cody eats are the same colour.
[2]
[6]
The hour hand has a length of 11 mm. Find the area of the sector covered by the hour hand as it moves through an
angle of 131°.
[2]
The minute hand of the watch has a length of y mm.
How far does the tip of the minute hand move in 21 minutes?
Give your expression in its simplest form in terms of π and y.
[2]
A car driver is having a tyre replaced at Edutyres Garage.
The waiting time, t minutes, is inversely proportional to the square of the number of mechanics, m, working that day.
If there are 3 mechanics working, the waiting time is 38 minutes.
Find a formula for t in terms of m.
[3]
The garage wants to reduce the waiting time to no more than 12 minutes.
What is the least number of mechanics that should be working to achieve this?
[2]
Calculate the size of CBD
.
CBD
=........ °
[7]
Complete the following table to show the inequalities that describe the shaded region
above.
[3]
The line AB is shown on the diagram.
Show that the equation of the perpendicular bisector of the line AB is 4y = x + 9.
[6]
For two events, A and B,
P(A
B) = 0·66, P(A
B) = 0·07 and P(AB′) = 0·31
[3]
Find P(A
B′).
[2]
Write y = x2 − 4x −1 in the form y = (x + a)2 + b, where a and b are constants.
[2]
[2]
[2]
The graph below shows a circle centred at the origin.
Write down the equation of the circle shown on the graph above.
[1]
Find the coordinates of the point of intersection of the tangent to the circle above at (0,5)
and the line y = 2 x + 3.
[2]
The paper as printed
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