Standard Grade Prelim Revision The topics we will be revising are: 1. Wednesday 17 th November – Pythagoras 2. Monday 22 nd November – Statistics 3. Tuesday

Standard Grade Prelim Revision

The topics we will be revising are:

1. Wednesday 17th November – Pythagoras2. Monday 22nd November – Statistics3. Tuesday 23rd November – Volume4. Wednesday 24th November – Area5. Thursday 25th November – Time / Distance / Speed6. Monday 29th November – Linear Equations (Finding a Rule)7. Tuesday 30th November – Probability8. 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


Pythagoras’ Theorem

Pythagoras’ Theorem can ONLY be used on

Right Angled Triangles



The name given to the longest side on a Right Angled Triangle, and the side opposite the right angle is called?

The Hypotenuse



Pythagoras’ Theorem allows us to calculate a missing length of aright angled triangle when we know 2 of its lengths.

a

b

c

The formula is

a² + b² = c²



Example :Calculate the length of the hypotenuse on each of the 3 right angled triangles below.

4cm

5cm

11cm

8cm

2.5cm

3.7cm



Is this triangle right angled? Explain with working

30cm

12cm

24cm



Pythagoras’ theorem can also be used to calculate one of the smallersides of a right angled triangle..

a

b

c

If a² + b² = c²

Then by using balance method

a² = c² - b²

or

b² = c² - a²



Calculate the lengths of the missing sides of these right angled triangles

15cm

8cm

24cm4cm

11cm9cm



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.



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


Starter Questions

BEANS

The cardboard box above contains 4 cans of baked beans (below).i) Calculate the volume of one can of beans. ii) Calculate the volume of the box

10cm

5cm

Construction of Scattergraph

xxx x

x x

Strong positive correlation

xx

x xx

x

Strong negative correlation

Best fit line

Best fit line

When two quantities are strongly connected we say there is a strong between them.

A is a line that leaves roughly half of the points on one sideof the line, and roughly half of the points on the other.

Standard Grade Prelim RevisionStatistics

correlation

best fit line

Standard Grade Prelim RevisionStatistics

0

2

4

6

8

10

12

0 2 4 6 8 10 12

Ages (Years)

Car

pri

ces

(£1000)

Construction of Scattergraph

Is therea

correlation?If yes, what

kind?

AgePrice

(£1000)

3

1

1

2

3

3

4

4

5

9

8

87

6

5

5

4

2

Strong negative correlation

Draw in the best fit line

From the best fit line, estimate the

value of a car aged 5

years

1+1+1+1+2+3+26The Mean = =5

7

Find the mean of the set of data 1, 26, 3, 1, 2, 1, 1

Sum of all the data valuesThe Mean =

how many data values

Can you see that this is not the most suitable of averages sincefive out of the six numbers are all below the mean of 5

Mean (Average)

The Median = Put all data in order

then fi nd MI DDLE value

Median (Average)

Find the median of the set of data 1, 13, 5, 8, 10, 4

Median = 1, 4, 5, 8, 10, 13

Median = 5 + 82

= 6.5

The median lies between 5 and 8 so……..

Mode (Average)

The Mode = The number that appears

most of ten

Find the mode of the set of data 1, 26, 3, 1, 2, 1, 1

Mode = 1

Range

The Range = Largest value - Smallest value

Find the median of the set of data 1, 26, 3, 1, 2, 1, 1

Range = 26 – 1 = 25

Different Averages

Example :

Find the mean, median, mode and range for the set of data.

10, 2, 14, 1, 14, 7

48Mean= =8

6 Median=1,2, ,17,10 4,14Mode =14

Range =14 - 1=137 +10 17

=Median= =8.52 2

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.

Frequency tables

Data Tally Frequency

Sum of Tally is the Frequencyllll represents a tally of 5

12, 14, 12, 17, 9, 19, 21, 12, 22

Diameter Tally Frequency

56

57

58

59

60

61

62

3

4

9

13

5

10

4

lll

llll

llll

llll

llll

llll

llll llll lll

llll

llll

Frequency tables

From the data, we can then calculate the Range, Mode and Median

Range = Largest - Smallest

= 62 - 56= 6

Mode = Most common number

= 59

Diameter Tally Frequency

56

57

58

59

60

61

62

3

4

9

13

5

10

4

lll

llll

llll

llll

llll

llll

llll llll lll

llll

llll

Frequency tables

The median is harder to calculate……..

To calculate the median in a frequency table we add each frequency up…….

3 + 4 + 9 + 13 + 10 + 5 + 4= 48

Then divide by 2…… 48 ÷ 2 = 24 ….therefore the median is the 24th value

59

No of No of SiblingSiblings (s (SS))

Freq.Freq.

(f)(f)

Example : This table shows the numberof brothers and sisters of pupils in an S2 class.

9

6

1

30

1

13

0

1

2

3

5

Totals

Frequency Frequency TablesTables

Working Out the Mean

Adding a third column to this tablewill help us find the total number ofsiblings and the ‘Mean’.

0 x 9 =0

2 x 6 = 12

5 x 1 = 5

3 x 1 = 3

1 x 13 = 13

33

Mean Number of siblings =

33= =1.1 siblings

30

S x S x ff

We call this column the cumulative

frequency column

Total Cumulative frequency ÷ total Frequency column

23

Q2. Calculate the height (h) of the tower

Starter QuestionsStarter Questions

Q1. Factorise

a) 48 – 12s b) 3t + 27t c) 9x + 54

h

48º

452m

A short cut !

6 = 72 cm³ Volume =

length

x breadth x 4

x height

length

breadth

height

x 3 Volume =

3cm

4cm

6cmArea of rectangl

e

Volume = l x b x h

V = 18 x 5 x 27

V = 2430 cm³

Example 1

18 cm

5 cm

27cm

Heilander’sPorridge Oats

Working

Example 2

2cm

Volume = l x b x h

V = 2 x 2 x 2

V = 8 cm³

Working

1 cm

1 cm

1 cm

Volume = = 1 cm³ x h x b l

How much water does this hold?

A cube with volume 1cm³ holds exact 1 millilitre of liquid.A volume of 1000 ml = 1 litre.

I’m a very small duck!

Liquid VolumeLiquid Volume

Volume = Area x height

The volume of a cylinder can be thought as being a pile

of circles laid on top of each other.

= πr2

Volume of a CylinderVolume of a Cylinder

Cylinder(circular Prism)

x hh

= πr2h

V = πr2h

Example : Find the volume of the cylinder below.

= π(5)2x10

5cm


10cm

= 250π cm

Volume of a CylinderVolume of a Cylinder

Total Surface Area = 2πr2 + 2πrh

The surface area of a cylinder is made up of 2 basic shapes can you name them.

Curved Area =2πrhCylinder(circular Prism)

h

Surface Area Surface Area of a Cylinderof a Cylinder

Roll out curve side

2πrTop Area =πr2

Bottom Area =πr2

Rectangle

2 x Circles

Example : Find the surface area of the cylinder below:

= 2π x (3 x 3) + 2π x 3 x 10

3cm


10cm

= 2π x 9 + 2π x 30


Surface Area = 2πr2 + 2πrh

= 245.04cm2

Example : A net of a cylinder is given below.Find the curved surface area only!


9cm

Radius = 1diameter

2

Curved Surface Area = 2πrh6cm

= 2 x π x 3 x 9

= 169.64 cm2

Rectangle

Only!!

Documents

Standard Grade Prelim Revision The topics we will be revising are: 1. Wednesday 17 th November – Pythagoras 2. Monday 22 nd November – Statistics 3. Tuesday