1. YEAR 10
REVISION BLASTER

2. GCSE MATHS REVISION UNIT 1 – all about DATA Probability Averages
Cumulative frequency
Histograms
Percentages

3. Probability

4. KEY POINTS The probability scale goes from 0 to 1.
Probability of a certain event = 1
Probability of an impossible event= 0
P(event)= No. of ways that event can happen
Total no. of ALL possible outcomes

5. 22 Sweets in a bag, 7 are red, 6 are blue, 9 are green.
What is the probability of randomly picking a blue sweet? 22 6
P(event)= No. of ways that event can happen
Total no. of ALL possible outcomes
P (BLUE) = =

6. Calculate the Probability of NOT picking a blue sweet.
P(event Not happening)=1 – P(event happening)
P (NOT BLUE) = 1 – P(picking blue)
P (NOT BLUE) = 1 –
P (NOT BLUE) =

7. Calculating the Probability of combined events.
STARTER:
P(garlic bread)=0.2; P(dough balls)= 0.8
MAIN:
P(pasta)=0.2; P(Salad)= P(Pizza) = 0.6
Calculate the probability of having; garlic bread followed by pizza.
Calculate the probability of having ANY starter followed by salad.

8. OR RULE= ADD PROBABILITIES
SO we add together the possibilities:
= 0.20
Probability of having ANY starter followed by salad is 0.20
There are TWO possibilities here; garlic bread and then salad, OR dough balls and the salad.
OR RULE= ADD PROBABILITIES
P(garlic bread)=0.2; P(dough balls)= 0.8
P(pasta)=0.2; P(Salad)= P(Pizza) = 0.6
Calculate the probability of having ANY starter followed by salad.
Calculate the probability of having; garlic bread followed by pizza.
MAIN
Pasta
Salad
0.2
0.6
STARTER
Answer= 0.12
0.2
0.2 x 0.2 = 0.04
Garlic Bread
0.6
0.2
0.2
0.2
Pizza
0.2 x 0.6 = 0.12
Pasta
Salad
0.2
0.6
AND RULE (Going ALONG the branches)
We MULTIPLY the Probabilities.
0.8
0.8
Dough
Balls
0.2
0.8 x 0.2 = 0.16
Pizza

9. Relative Frequency: An estimate for theoretical probability
Relative Frequency = Frequency of the event
Total Number of trials
Calculate the relative frequency of the toast landing jam side up.
No. of drops
No. of jam side up
Relative Frequency 12 6
12/6 =2

10. The relative frequency of seeing a red car go past your window is 0.6.
Relative Frequency = Frequency of the event
Total Number of trials
Frequency of the event =
0.6 x = Frequency
= Frequency
The relative frequency of seeing a red car go past your window is 0.6.
You watch 100 cars go past your window. How many would you expect to be red?
0.6
100

11. Probability Answers 1. (a) ½ (b) 300 2. (a) (i) 11/12 or 0.92
(ii) 8/12 or 2/3
(b) (i) 15/22 (allow 14 or 15 on top 22 or 21 on bottom)
(ii) 5/11 or any equivalent fraction
3. (a) 0.4 on first branch & all other branches correct
(b) (i) or 4/25 or 16 %
(ii) or 21/25 or 84 %
(a)
(b) 15
(c) More than expected with a suitable qualification (allow expect 10)

12. Averages

13. MEAN Mode Median 3+3+4+4+4+5+5+6+7=41 41 9 = 4.55…
3, 3, 4, 4, 4, 5, 5, 6, 7
3, 5, 4, 3, 5, 4, 4, 6, 7
3, 3, 4, 4, 4, 5, 5, 6, 7

14. Calculate the mean. Mean = sum of ALL the values = 140 = 1.84 21052639 10 15 17 20
Frequency 4 5 1
Numbers of sports played
TOTAL 76
Frequency x Numbers of sports played
0 × 20
= 0
1 × 17
= 17
2 × 15
= 30
3 × 10
= 30
4 × 9
= 36
5 × 3
= 15
6 × 2
= 12
140
Mean = sum of ALL the values
sum of frequencies
= 140 = 1.84 76

15. Javelin distances in metres
Calculate an estimate for the mean. 1
35 ≤ d < 40 3 10 12 8
Frequency
30 ≤ d < 35
25 ≤ d < 30
20 ≤ d < 25
15 ≤ d < 20
10 ≤ d < 15
5 ≤ d < 10
Javelin distances in metres 36
TOTAL
Midpoint
Frequency × midpoint
7.5
1 × 7.5
= 7.5
12.5
8 × 12.5
= 100
17.5
12 × 17.5
= 210
22.5
10 × 22.5
= 225
27.5
3 × 27.5
= 82.5
32.5
1 × 32.5
= 32.5
37.5
1 × 37.5
= 37.5
695
Mean = sum of ALL frequency x midpoint
sum of frequencies
= 695 = 19.3 36
055555…

16. Averages Answers 99.7 (allow 100) 2. (a) 131.6 (allow 131 to 132)
(b) 110 £ t < 130
3. (a) (allow 26)
(b) Frequency polygon from (10, 42) to (70, 3) joined with approximately straight lines
(c) Comment - eg. Higher mean on Saturday, or Larger range on Saturday, or More money spent on Saturday

17. Year 10 Unit 1 Exam. Tuesday 9th November- TOMORROW!!
AD BREAK
Year 10 Unit 1 Exam. Tuesday 9th November- TOMORROW!!
Don’t Forget: CALCULATORS
PEN
PENCIL
RULER
REVISE

18. CUMULATIVE FREQUENCY

19. The cumulative frequency is the RUNNING TOTAL OF FREQUENCIES
Used for finding the MEDIAN and UPPER AND LOWER QUARTILES

20. Marks in a Yr 10 Maths Test 2 2 13 32 68 110 141 154 160 11-20 21-30
Frequency
Cumulative Frequency
11-20
21-30 11
31-40 19
41-50 36 42
61-70 31
71-80 13
81-90 6 2 2 13
110 people scored 60 marks OR less 32 68
51-60
110
141
154
160

21. Plot the top value in each group against cumulative frequency

22. =65 -44 =21 Interquartile range
Median shows that ½ of people score less than 53 marks and ½ score more
Lower Quartile shows 25% of people scored 44 marks or less
Interquartile range
= =21
Upper Quartile shows 75% of people scored 65 marks or less

23. Cumulative Frequency Answers
1. (a) Any value from 55 to 57 inclusive
(b) 6 ± 0.4
2. (a) 12, 27, 56, 72, 83, 90
(b) Correct graph ‘increasing’ (S shape)
(c) (i) Median line from 45(.5)
e.g
(ii) IQR lines from Q1 (22.5) and Q3 (67.5) and subtract their answers (eg 16 – 20)
(d) Approx 48

24. HISTOGRAMS

25. Finding lengths given areas
If the width is 10
What must the height be to make an area of 25?
2.5 25
As 10 x 2.5 = 25 10

26. Bar Graphs
Bar graphs are great to use when you have equal class intervals:

27. Histograms
Histograms are used when you have different sized class intervals.
The area of the rectangle represents the frequency.
The width is the size of the class interval.
The height is what we call the frequency density.

28. We have different sized class intervals
The table below shows the number of kick-ups completed in a competition at a local primary school.
Number of kick-ups
Frequency
Frequency Density
0-5 10
5-15 25
15-30 45
30-40 15
Our class interval width is 5, and our frequency (area) is 10. 2
2.5
So, Frequency Density (height) = 10/5 3
1.5
We have different sized class intervals

29. 2 2.5 3 1.5 Number of kick-ups Frequency Frequency Density 0-5 10 5-1525
2.5
15-30 45 3
30-40 15
1.5

30. Estimate how many students managed ten kick-ups or less.
Frequency =
5 x 2.5 = 12.5
Frequency=
5 x 2 = 10
So, = 22.5
We can estimate that 22.5 students made ten kick-ups
or less.

31. Comparing Histograms and Bar Graphs

32. Histograms Answers 1. (a) 0.4, 0.4, 0.5, 0.1 (b) 21
(a) Correct histogram:
Widths: 15, 5, 5, 10, 15
Heights: 0.6, 4.2, 4.8, 3.1, 1
(b) 42

34. Percentage Increase and Decrease

35. Increase by 15% so 1.15 is the multiplier
Method 1
Find 15%
10% = £2 5% = £1 so 15% = £3
Now add it on to £20
£20 + £3 = £23
Method 2
I need to find 115% OF original amount
115% of £20 is
1.15 x £20 = £23
Increase by 15% so 1.15 is the multiplier

36. Decrease £60 by 5% Method 2 Method 1
A decrease of 5% is same as 95% of original amount
So 0.95 x £60 = £57
Method 1
Find 5% of £60
10% = £ % = £3
Subtract from £60
£60 - £3 = £57
95% of original amount means 0.95 is the multiplier

37. Compound Interest OR 1000 x 1.05 x 1.05 x1.05= 1.05 is the multiplier!
£1,000 in bank earns 5% interest per year. How much will you have in 3 years?
After 1 year 1000 x 1.05 = 1050
After 2 years 1050 x 1.05=
After 3 years x 1.05 =
OR 1000 x 1.05 x 1.05 x1.05=
1000 x 1.05³=£
1.05 is the multiplier!

38. Percentages Answers
1. £2140 (allow £140)
2. (a) 1.029
(b) (allow )
3. 1st year is £20; 2nd year is £20.80
Interest is £40.80 so Amir is wrong
4. (a) 2.04
(b) 6 (windmills)