1. Standard Grade Prelim Revision
The topics we will be revising are:
1. Wednesday 17th November – Pythagoras
2. Monday 22nd November – Statistics
3. Tuesday 23rd November – Volume
4. Wednesday 24th November – Area
5. Thursday 25th November – Time / Distance / Speed
6. Monday 29th November – Linear Equations (Finding a Rule)
7. Tuesday 30th November – Probability
8. Wednesday 1st December – Calculating % (Non-Calculator)
9. Thursday 2nd December - Fractions
NOTE: We will try and stick to this schedule as far as we can.
Supported Study can and should be used for any other revising
MONDAY – THURSDAY 3:30PM – 4:45 PM

2. Right Angled Triangles
Standard Grade Prelim Revision
Pythagoras’ Theorem
Pythagoras’ Theorem can ONLY be used on
Right Angled Triangles

3. Pythagoras’ Theorem Standard Grade Prelim Revision The Hypotenuse
The name given to the longest side on a Right Angled Triangle,
and the side opposite the right angle is called?
The Hypotenuse

4. a² + b² = c² Pythagoras’ Theorem Standard Grade Prelim Revision c a b
Pythagoras’ Theorem allows us to calculate a missing length of a
right angled triangle when we know 2 of its lengths.
The formula is c
a² + b² = c² a b

5. Pythagoras’ Theorem Standard Grade Prelim Revision Example :
Calculate the length of the hypotenuse on each of the 3 right angled triangles below.
3.7cm
8cm
5cm
2.5cm
4cm
11cm

6. Pythagoras’ Theorem Standard Grade Prelim Revision
Is this triangle right angled? Explain with working
30cm
12cm
24cm

7. Pythagoras’ Theorem Standard Grade Prelim Revision
Pythagoras’ theorem can also be used to calculate one of the smaller
sides of a right angled triangle..
If a² + b² = c²
Then by using balance method c a
a² = c² - b² or b
b² = c² - a²

8. Pythagoras’ Theorem Standard Grade Prelim Revision
Calculate the lengths of the missing sides of these right angled triangles
15cm
4cm
9cm
24cm
11cm
8cm

9. Pythagoras’ Theorem Standard Grade Prelim Revision
A rectangular picture measuring 540mm by 200mm is placed
diagonally in a cuboid shaped box as shown
The box has 530mm by 200mm, Calculate the height of the box.

10. Pythagoras’ Theorem Standard Grade Prelim Revision What to remember :
1. Pythagoras can only be used on Right Angled Triangles.
2. If you are given a question with 2 given lengths and
a right angled triangle is involved, Pythagoras will be required.
3. When calculating a smaller side of a right angled triangle, always
take the other smaller side away from the hypotenuse

11. Starter Questions Standard Grade Prelim Revision BEANS
10cm
The cardboard box above contains 4 cans of baked beans (below).
Calculate the volume of one can of beans.
Calculate the volume of the box
5cm

12. Statistics Standard Grade Prelim Revision Construction of Scattergraph
When two quantities are strongly connected we say there is a
strong between them.
correlation
A is a line that leaves roughly half of the points on one side
of the line, and roughly half of the points on the other.
best fit line
Best fit line x x
Best fit line
Strong positive
correlation
Strong negative
correlation

13. Statistics Standard Grade Prelim Revision Construction of Scattergraph
Draw in the best fit line
Standard Grade Prelim Revision
From the best fit line, estimate the value of a car aged 5 years
Statistics
Construction of Scattergraph
Is there
a correlation?
If yes, what kind?
Age
Price
(£1000) 3 1 2 4 5 9 8 7 6
Strong negative correlation

14. Mean (Average) Find the mean of the set of data 1, 26, 3, 1, 2, 1, 1
Can you see that this is not the most suitable of averages since
five out of the six numbers are all below the mean of 5

15. Median (Average) = 6.5 Median = 1, 4, 5, 8, 10, 13 Median = 5 + 8 2
Find the median of the set of data 1, 13, 5, 8, 10, 4
Median = 1, 4, 5, 8, 10, 13
The median lies between 5 and 8 so……..
Median = 5 + 8
= 6.5 2

16. Mode (Average)
Find the mode of the set of data 1, 26, 3, 1, 2, 1, 1
Mode = 1

17. Range
Find the median of the set of data 1, 26, 3, 1, 2, 1, 1
Range = 26 – 1 = 25

18. Different Averages
Example :
Find the mean, median, mode and range for the set of data.
10, 2, 14, 1, 14, 7

19. Sum of Tally is the Frequency
12, 14, 12, 17, 9, 19, 21, 12, 22
Frequency tables
Raw data can often appear untidy and difficult to understand. Organising data into frequency tables can make it much easier to make sense of the data.
Data
Tally
Frequency
llll
represents a tally of 5
Sum of Tally is the Frequency

20. Frequency tables Diameter Tally Frequency 56 57 58 59 60 61 62 lll
llll 3 4 9 13 10 5 4
From the data, we can then calculate the Range, Mode and Median
Range = Largest - Smallest
Mode = Most common number =
= 59
= 6

21. Frequency tables 59 Diameter Tally Frequency 56 57 58 59 60 61 62 lll
llll 3 4 9 13 10 5 4
The median is harder to calculate……..
To calculate the median in a frequency table we add each frequency up…….
= 48
Then divide by 2……
48 ÷ 2 = 24
….therefore the median is the 24th value 59

22. We call this column the cumulative frequency column
Frequency Tables
Working Out the Mean
Example : This table shows the number
of brothers and sisters of pupils in an
S2 class.
No of Siblings (S)
Freq.
(f)
S x f
Adding a third column to this table
will help us find the total number of
siblings and the ‘Mean’. 9
0 x 9 =0 1 13
1 x 13 = 13 2 6
2 x 6 = 12
Total Cumulative frequency ÷ total Frequency column 3 1
3 x 1 = 3 5 1
5 x 1 = 5
Totals 30 33

23. Starter Questions Q1. Factorise a) 48 – 12s b) 3t + 27t c) 9x + 54
Q2. Calculate the height (h) of the tower h
48º
452m 23

24. A short cut ! Volume = 6 x 3 x 4 = 72 cm³ Volume = length x breadth
height
Area of rectangle
breadth
length
Volume = 6
x 3
x 4
= 72 cm³
Volume =
length
x breadth
x height

25. Example 1 27cm 5 cm 18 cm Working Volume = l x b x h V = 18 x 5 x 27
Heilander’s
Porridge Oats
V = 18 x 5 x 27
V = cm³
27cm
5 cm
18 cm

26. Example 2
Working
Volume = l x b x h
V = 2 x 2 x 2
V = 8 cm³
2cm

27. Liquid Volume Volume = l x b x h = 1 cm³
I’m a very small duck!
How much water does this hold?
1 cm
1 cm
1 cm
Volume = l
x b
x h
= 1 cm³
A cube with volume 1cm³ holds exact 1 millilitre of liquid.
A volume of 1000 ml = 1 litre.

28. Volume of a Cylinder Volume = Area x height = πr2 = πr2h h x h
The volume of a cylinder can be thought as being a pile
of circles laid on top of each other.
Volume = Area x height h
= πr2
x h
Cylinder
(circular Prism)
= πr2h

29. Volume of a Cylinder V = πr2h = π(5)2x10 = 250π cm
Example : Find the volume of the cylinder below.
5cm
Cylinder
(circular Prism)
10cm
V = πr2h
= π(5)2x10
= 250π cm

30. Surface Area of a Cylinder 2πr h Total Surface Area = 2πr2 + 2πrh
The surface area of a cylinder is made up of 2 basic shapes can you name them.
Cylinder
(circular Prism)
2πr
Curved Area =2πrh
Top Area =πr2
Roll out
curve side  h
Bottom Area =πr2
2 x Circles
Rectangle
Total Surface Area = 2πr2 + 2πrh

31. Surface Area of a Cylinder = 2π x (3 x 3) + 2π x 3 x 10
Example : Find the surface area of the cylinder below:
3cm
Surface Area = 2πr2 + 2πrh
10cm
= 2π x (3 x 3) + 2π x 3 x 10
= 2π x 9 + 2π x 30
Cylinder
(circular Prism)
= cm2

32. Surface Area of a Cylinder Radius = 1diameter 2
Example : A net of a cylinder is given below.
Find the curved surface area only!
6cm
Curved Surface Area = 2πrh
Rectangle
Only!!
= 2 x π x 3 x 9
9cm
= cm2