1. Compiled by Mr. Lafferty Maths Dept.
Starter Questions
Q1. Solve the equation below bo ao
Q2. Find all the missing angles 12 5
Q3. Find the mean, median, mode and range
of the numbers below
10, 9, 10, 20, 11
Q4. Find
24-Feb-19
Compiled by Mr. Lafferty Maths Dept.

2. Compiled by Mr. Lafferty Maths Dept.
Statistics Revision
Example :
Find the mean, median, mode and range for the set of data.
3, 2, 7, 1, 15, 7, 6, 7
24-Feb-19
Compiled by Mr. Lafferty Maths Dept.

3. Compiled by Mr. Lafferty Maths Dept.
Frequency Tables
Working Out the Mean
Example : This table shows the number
of coins in the pockets of some children.
No of
Coins (x)
Freq.
(f)
(f) x (x)
Adding a third column to this table
will help us find the total number of
coins and the ‘Mean’. 1 5
5 x 1 =5 2 5
5 x 2 = 10 3 1
1 x 3 = 3 4 3
3 x 4 = 12 5 2
2 x 5 = 10
Totals 16 40
24-Feb-19
Compiled by Mr. Lafferty Maths Dept.

4. Cumulative Frequency Tables
Working Out The Median
Example : This table shows the number
of eggs laid by a clutch of chickens each
day over a seven day period.
Day
Freq.
(f)
Cum. Freq.
Total so far 1 2 2
A third column is added to keep a
running total. This makes it easier to
get the total number of items. 2 3 5 3 1 6
You have 1 minute to come up with a question you can easily answer from the table. 4 6 12 5 5 17 6 8 25 7 4 29
24-Feb-19
Compiled by Mr. Lafferty Maths Dept.

5. Compiled by Mr. Lafferty Maths Dept.
Stem Leaf Graphs
Construction of Stem and Leaf
A Stem – Leaf graph is another way of displaying information :
Ages
This stem and leaf graph shows
the ages of people waiting in a
queue at a post office 2 4 6 8 3 1 4 5 6 7 9 5 3 4 9
How many people in the queue? 20 6 1 4 5
How many people in their forties? 6
stem
leaves
Key : means 24
24-Feb-19
Compiled by Mr. Lafferty Maths Dept.

6. Compiled by Mr. Lafferty Maths Dept.
Stem Leaf Graphs
Construction of Stem and Leaf
Example : Construct a stem and leaf graphs for the following
weights in (kgs) :
Weight (kgs) 1 1 3 9 2 4 5 7 2 2 12 13 15 21 23 29 32 40 41 51 54 55 57 12 40 57 54 55 13 15 32 41 21 23 29 51 2 3 4 5
stem
leaves
Key : means 23
24-Feb-19
Compiled by Mr. Lafferty Maths Dept.

7. Solving Real-Life Problems
When coming across a problem involving finding a missing side in a right-angled triangle, you should consider using Pythagoras’ Theorem to calculate its length.
Example : A steel rod is used to support a tree
which is in danger of falling down.
What is the length of the rod?
15m 8m
rod
24-Feb-19
Compiled by Mr. Lafferty Maths Dept.

8. Length of the smaller side
To find the length of the smaller side of a right-angled triangle we simply rearrange Pythagoras Theorem.
Example : Find the length of side a ?
Check answer ! Always smaller than hypotenuse
20cm
12cm
a cm
24-Feb-19
Compiled by Mr. Lafferty Maths Dept.

9. Compiled by Mr. Lafferty Maths Dept.
Calculating Percentages
A Mini Cooper cost £ in 2005
At the end 2006 it will have fallen by 20%
What will the mini cooper worth at end 2006?
End 2006
Fall in value = 20% x £15 000
= 0.2 x £15 000
= £3 000
New value = Old value – Fall in value
= £ £3000
= £12 000
24-Feb-19
Compiled by Mr. Lafferty Maths Dept.

10. Hire Purchase www.mathsrevision.com Buying Products
Interest Free
20%
deposit
General
Buying Products
Hoover Cash Price £360 or
Interest Free
(Deposit + 10 equal monthly payments)
How much is the monthly payments.
Deposit =
20% of 360 = 36 x 2 = £72.00
Left to pay =
£360 - £72 = £288
Monthly Payment is =
£288 ÷ 10 = £28.80
24-Feb-19
Compiled by Mr. Lafferty Maths Dept.

11. Complicated Linear Patterns using diagrams and tables
General
Q. Find the rule (equation) connecting Tables and Chairs
Number of Tables (T) 1 2 3 4 5
Number of Chairs (C) 4 6 8 10 12 2 2 2 2
Step 1 : Fill in missing values
Step 2 : Find difference
Part of the Formula
Step 3 :
C = 2T
C = 2T + 2
Correction factor
Step 4 :
“add on 2”
24-Feb-19
Compiled by Mr. Lafferty Maths Dept.

12. Complicated Linear Patterns using diagrams and tables
General
Q. Find the rules given the tables. 2 4 5 1 3
Number of Dots 10 18 22 6 14
Number of Crosses
C = 4D + 2 2 4 5 1 3
Number of Stars 11 14 8
Number of Points
P = 3S - 1 2 4 5 1 3
Number of Balloons 9 17 21 13
Number of People
P = 4B + 1
24-Feb-19
Compiled by Mr. Lafferty Maths Dept.

13. Finding the equation of a Line
General
24-Feb-19
Compiled by Mr. Lafferty Maths Dept.

14. Compiled by Mr. Lafferty Maths Dept.
Straight Line
General 4 1 2 3 10 11 12 5 6 7 8 9 x y
Q. Plot the points below and
determine the equation. x 1 2 3 4 5 y 4 6 8 10 12
24-Feb-19
Compiled by Mr. Lafferty Maths Dept.

15. Compiled by Mr. Lafferty Maths Dept.
Straight Line
General 4 1 2 3 10 11 12 5 6 7 8 9 x y
Q. Given the graph fill in the
missing points.
Determine the equation of
the line. x 1 2 3 4 5 y 6 8 10 12 14
24-Feb-19
Compiled by Mr. Lafferty Maths Dept.

16. Compiled by Mr. Lafferty Maths Dept.
Direct Proportion
Direct Proportion
Example : On holiday I exchanged £50 for $75.
How many $ will I get for £900.
£ $
50  75
1  75 ÷ 50 = 1.5
900  1.5 x 900 = $1350
24-Feb-19
Compiled by Mr. Lafferty Maths Dept.

17. Compiled by Mr. Lafferty Maths Dept.
Direct Proportion
Direct Proportion
Example : I am back from holiday and want to
exchange $300 back to £’s at the same
rate as before.
How many £’s will I get back.
$ £
75  50
1  50 ÷ 75 =
300  x 300 =
£200
24-Feb-19
Compiled by Mr. Lafferty Maths Dept.

18. Compiled by Mr. Lafferty Maths Dept.
The Circle
Example : Find the area and circumference of the
circle and the missing angles ao , bo , co , do
Tangent line
Solution
Solution do bo co
50o ao
10cm
ao = 150o
bo = co = 65o
do = 40o
24-Feb-19
Compiled by Mr. Lafferty Maths Dept.

19. Compiled by Mr. Lafferty Maths Dept.
Scientific Notation
A very quick method for find the scientific notation:
Example : Write in scientific notation
2.74
Step 1 : move decimal point till it comes
between 1st and 2nd digits
Step 2 : now count how many places that you have
have moved the point. 6
Step 3 : finally write this number (6) as the power
of 10.
2.74 x 106
24-Feb-19
Compiled by Mr. Lafferty Maths Dept.

20. Scientific Notation www.mathsrevision.com Quick method for going from
scientific notation to number form:
Example : Write 5.78 x 104 in full
Step 1 : Write down 578 without the point.
Step 2 : Move the point 4 places to the right.
57800
2 zero’s are added for
blank spaces.
24-Feb-19
Compiled by Mr. Lafferty Maths Dept.

21. Scientific Notation www.mathsrevision.com
It is possible to write very small decimal numbers in
scientific notation
Example : Write in scientific notation
2.58
Step 1 : move decimal point till it is after
1st non zero digit
Step 2 : now count how many places that you have
moved the point. 2
Step 3 : finally write this number (2) as the
negative power of 10.
2.58 x 10-2
24-Feb-19
Compiled by Mr. Lafferty Maths Dept.

22. Scientific Notation www.mathsrevision.com Reversing the process
scientific notation to a very small decimal number
Example 1 : Write 1.7 x 10-3 in full
Simply move the point 3 places to the left
0.0017
Example 2 : Write 3.5 x 10-5 in full
Simply move the point 5 places to the left
Example 3 : Write 2.39 x 10-4 in full
Simply move the point 4 places to the left
24-Feb-19
Compiled by Mr. Lafferty Maths Dept.