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Free online GCSE video tutorials, notes, exam style questions, worksheets, answers for all topics in Foundation and Higher GCSE. The content is suitable for the Edexcel, OCR and AQA exam boards.

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Year 11 Topic list - may21 foundation RAG

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Ratio

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The first step is to work out how many equal parts there are.
The ratio is 2:1 so there are 3 (2 &plus; 1) equal parts

We now need to work out how much each of the parts is worth
We divide the £120 between the 3 parts
£120 ÷ 3 = £40
Each part is worth £40

Now we can work out how much Abbie and Ben get
Abbie has 2 parts so she gets £80 (2 × £40)
Ben has one part which is worth £40

You may find it useful to draw a diagram for ratio questions

Abbie has 2 parts and Ben has 1 part, we could represent this as 2 boxes for Abbie and 1 box for Ben:

Each box must have the same amount in it and the total in all 3 boxes must be £120. We share £120 out evenly between the boxes (£120 ÷ 3 = £40)

We can see that Abbie gets £80 (£40 &plus; £40) and Ben gets £40
Example 2: A, B and C share £240 in the ratio 4:3:1
Work out how much each of them get.
4 + 3 + 1 = 8
There are 8 equal parts

£240 ÷ 8 = £30
Each part is worth £30

A gets 4 × £30 = £120
B gets 3 × £30 = £90
C gets 1 × £30 = £30
Try these: Example 3: A and B share some money in the ratio 5:2
A gets £40
Work out how much B gets.
In this example we have not been given the total amount. We have been given the amount that A gets

A has £40 and that is 5 parts

Each part much be equal so each part is worth £40 ÷ 5
£40 &divide 5 = £8

Each part is worth £8 and B has two parts
£8 × 2 = £16
Example 4: C and D share some money in the ratio 3:5
The difference between the amount C gets and the amount D gets is £18
Work out how much each of them get.
In this example we have been given the difference between the amounts of money C and D get.

The difference between 3 parts and 5 parts is 2 parts. (5 − 3 = 2)
2 parts must be worth £18
£18 ÷ 2 = £9

Each part is worth £9

C gets 3 × £9 = £27
D gets 5 × £9 = £45
Try these:

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Maths revision video and notes on the topic of sharing between ratios.

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Ratio

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Two-way tables

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Maths revision video and notes on the topic of two way tables.

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Online learning platform

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Sparx Learning provides maths solutions to more than half of UK schools, several large International School Groups and many individual schools across the world. We now provide maths in 23 countries supporting over 2,000 schools, 35,000 teachers and 1.8 million students.

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For Secondary schools, Sparx Maths delivers personalised intelligent maths practice, that is proven to boost grades. We provide maths in 23 countries supporting over 2,000 schools, 40,000 teachers and 1.8million students.

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Watch the video clips and make notes. Work through the tasks set.

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Watch the video clips and make notes. Work through the tasks set.

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Probability

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Probability describes how likely something is to happen, it can be written as a fraction, a decimal or as a percentage.

Writing Probability and The Probability Scale

The probability scale runs from 0 to 1

0 represents something that is impossible
If something has a probability of 1 it is certain to happen

Here we have a fair spinner. (We say the spinner is fair if the chance of landing on each side is equal.)

2 of the 4 sides have a B on. We can say the probability of the spinner landing on B is which can be simplified to (or 0.5 or 50%)

The probability of getting any letter other than A, B or C is 0. It would be impossible for the spinner to land on D. We can mark D on the probability scale at 0.
Example 1: In a bag there are 5 red counters, 4 blue counters and 3 yellow counters
A counter is picked at random find the probability that the counter will be
a) Red
b) Blue
c) Yellow
The total number of counters in the bag = 5 + 4 + 3 = 12

a) 5 out of 12 counters are red
the probability of picking a red counter will be
b) 4 out of 12 counters are blue, the probability of picking a blue counter will be
c) 3 out of 12 counters are yellow, the probability of picking a yellow counter will be

+ + = 1

Because the counter can only be red or blue or yellow the three probabilities must add up to 1
The probabilities of all possible events will always add to 1 (or 100%) Example 2: The probability of it raining tomorrow is 60%. Work out the probability of it not raining tomorrow.
The probability of it raining and the probability of it not raining must add up to 1 (or 100%)

100% - 60% = 40%

The probability of it not raining = 40%
Example 3: The probability of Roger winning a tennis match is 7⁄ 12. Work out the probability of Roger not winning the tennis match.
The probability of Roger winning and the probability of Roger not winning must add up to 1

1 - =
Example 4: There are 20 pens in a box.
8 of the pens are black
3 of the pens are green.
The rest of the pens are red.
One of the pens is chosen at random
Find the probability that the pen is red.

We can work out how many red pens there are by calculating
20 - 8 - 3
20 - 8 - 3 = 9

There are 9 red pens and there are 20 pens in total
Try these:
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Maths revision video and notes on the topic of the probability scale and writing probability.

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Probability

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Watch the videos and complete the online questions set.

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20 quick questions

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Watch the video clips and complete the online tasks. Aim for at least 80% on MW. 

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Watch the video clips and complete the online tasks. Aim for at least 80% on MW. 

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Complete each one of the 20Q set in 10 minutes.

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Complete each one of the 20Q set in 10 minutes.

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Paper 3F

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Paper 2F

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Paper 1F

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Paper 3F Mark scheme

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Paper 3F Worked solutions

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Grade 2 Revision Cards

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Foundation Revision Cards Grade 2 Topics

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Revision cards

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Paper 2F Worked solutions

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Paper 1F Worked solutions

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paper 3F Worked solutions

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Paper 2F Worked solutions

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Two-way tables

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Student guide

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Paper 1F Worked solutions