Edexcel GCSE Maths

Topic Questions

Ratio Toolkit

1a
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2 marks

Here are the ingredients needed to make 12 shortcakes.

Shortcakes

Makes 12 shortcakes

   50 g of  sugar
  200 g of  butter
200 g of  flour
10 ml of  milk

Liz makes some shortcakes.
She uses 25 ml of milk.

How many shortcakes does Liz make?
1b
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2 marks

Robert has   

500 g of sugar
1000 g of butter
1000 g of flour
500 ml of milk

Work out the greatest number of shortcakes Robert can make.

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2
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4 marks

Here is a list of ingredients for making 18 mince pies.

Ingredients for mince pies

225 g   of butter
350 g   of flour
100 g    of sugar
        280 g    of mincemeat
1    egg

Elaine wants to make 45 mince pies.

Elaine has

1 kg of butter
I kg of flour
500 g of sugar
600 g of mincemeat
6 eggs

Does Elaine have enough of each ingredient to make 45 mince pies?
You must show clearly how you got your answer.

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3
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3 marks

Here are the ingredients needed to make 8 shortbread biscuits.

Shortbread biscuits
makes 8 biscuits

120 g    butter
              60 g  caster sugar
180 g  flour

Tariq is going to make some shortbread biscuits.
He has the following ingredients

330g butter    200g caster sugar    450g flour

Work out the greatest number of shortbread biscuits that Tariq can make with his ingredients.
You must show all your working.

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4
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3 marks

160 cm of gold wire has a weight of 17.8 grams.

Work out the weight of 210 cm of the gold wire.

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5
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3 marks

There are 1200 students at a school.

Kate is helping to organise a party.
She is going to order pizza.

Kate takes a sample of 60 of the students at the school.
She asks each student to tell her one type of pizza they want.

The table shows information about her results.

Pizza Number of students
ham 20
salami 15
vegetarian 8
margarita 17

Work out how much ham pizza Kate should order.
Write down any assumption you make and explain how this could affect your answer.

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6
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3 marks

Rob is learning about the planets.

Rob makes a model of the Sun.
He also makes a model of the planet Jupiter.

Rob is going to hang the two models in the school hall.

Rob wants a distance of 16 m between the two models.
The real distance between the planet Jupiter and the Sun is 8 x 108 km

Work out the scale Rob should use.
Give your answer in the form 1 space colon space n

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7
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3 marks

The ratio of the number of boys to the number of girls in a school is 4: 5
There are 95 girls in the school.

Work out the total number of students in the school.

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8
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4 marks

5 schools sent some students to a conference.

One of the schools sent both boys and girls.
This school sent 16 boys.
The ratio of the number of boys it sent to the number of girls it sent was 1: 2

The other 4 schools sent only girls.
Each of the 5 schools sent the same number of students.

Work out the total number of students sent to the conference by these 5 schools.

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9a
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3 marks

Babajan makes breakfast cereal.
She mixes nuts, raisins and oats in the ratio 3 : 2 : 5 by weight.

On Monday, Babajan uses 60 grams of nuts.

Work out the weight of raisins and the weight of oats she uses to make the breakfast cereal.
9b
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3 marks

On Tuesday, Babajan makes 300 grams of the breakfast cereal.

500 grams of nuts cost £8

Work out the cost of the nuts used to make 300 grams of the breakfast cereal.

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10
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4 marks

Talil is going to make some concrete mix.
He needs to mix cement, sand and gravel in the ratio 1 : 3 : 5 by weight.

Talil wants to make 180 kg of concrete mix.

Talil has

15 kg of cement
85 kg of sand
100 kg of gravel

Does Talil have enough cement, sand and gravel to make the concrete mix?

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11a
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2 marks

Emma has a digital photo.

q11a-medium-3-1-ratio-toolkit-edexcel-gcse-maths

The photo has a width of 720 pixels.
The photo has a height of 540 pixels.

Write down the ratio of the width of the photo to the height of the photo.
Give your ratio in its simplest form.

11b
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2 marks

Emma wants the ratio of the width of the photo to the height of the photo to be 3 : 2
She reduces the number of pixels in the height of the photo.
The width of the photo is still 720 pixels.

The ratio of the width of the photo to the new height of the photo is 3 : 2

Work out the new height of the photo.

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12a
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3 marks

Deon needs 50g of sugar to make 15 biscuits.

She also needs
         three times as much flour as sugar
         two times as much butter as sugar

Deon is going to make 60 biscuits.

Work out the amount of flour she needs.
12b
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2 marks

Deon has to buy all the butter she needs to make 60 biscuits.
She buys the butter in 250 g packs.

How many packs of butter does Deon need to buy?

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13
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4 marks

A shop sells packs of black pens, packs of red pens and packs of green pens.

There are

      2 pens in each pack of black pens
      5 pens in each pack of red pens
      6 pens in each pack of green pens

On Monday,

number of packs
of black pens sold
: number of packs
of red pens sold
: number of packs
of green pens sold
= 7: 3 : 4


A total of 212 pens were sold.
Work out the number of green pens sold.

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14
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3 marks

Brendon, Asha and Julie share some money in the ratios 3 : 2 : 6
The total amount of money that Asha and Julie receive is $36

Work out the amount of money that Brendon receives.

$..................

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15
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3 marks

A plane has a length ofspace 73 spacemetres.

A scale model is made of the plane.
The scale of the model is 1 space colon space 200

Work out the length of the scale model.
Give your answer in centimetres.

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16
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3 marks

A football team played 55 games.

Each game was won, drawn or lost.

number of games won : number of games drawn : number of games lost = 6 : 3 : 2

Work out how many more games the team won than the team lost.

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17
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1 mark

Two wire shapes make an earring.
The shapes are

a circle with radius 21 mm

and

a quarter circle.

q12-paper-1h-nov-2020-aqa-gcse-maths

radius of circle : radius of quarter circle = 7 : 2

Show that the radius of the quarter circle is 6 mm

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18
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4 marks

White paint costs £2.80 per litre.
Blue paint costs £3.50 per litre.
White paint and blue paint are mixed in the ratio 3 : 2

Work out the cost of 18 litres of the mixture.

£........................

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19
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3 marks

Ed and Fay shared £330 in the ratio    7 : 4

Ed gives Fay some of his money.

Fay now has the same amount as Ed.

How much does Ed give Fay?

£...............................

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20
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3 marks

George is the manager of a shoe shop.
He samples 50 of his customers and asks them about the one style of shoe they would buy next.
The table shows his results.

Style of shoe Number of customers
Laced shoes 18
Boots 15
Sandals 8
Trainers 5
Other 4


George buys 1000 pairs of shoes with the number of each style based on his survey results.
How many pairs of sandals should he buy?
Write down any assumption you make about his sample.

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21
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3 marks

Reece and Sarah share some money in the ratio 9 : 16.

Reece says that Sarah gets more than 60% of this money.

Show that Reece is correct.

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22
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4 marks

Two bags each contain only red counters and yellow counters.

In Bag A, the ratio of red counters to yellow counters is 1 : 4.

In Bag B, 1 fourth of the counters are red.

i)
Sharon says

   "The proportion of the counters that are red is the same in both bags."

Explain why Sharon is not correct.

[1]
ii)
The number of counters in the two bags is the same.

Complete the table below to show how many counters of each colour could be in the bags.

  Red counters Yellow counters
Bag A    
Bag B    

[3]

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