Notesale: Turn your study into money

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Mathematics and Numeracy

Supporting learning at home

HOW CAN YOU HELP?
Practise the number facts regularly with your child
Support them in the use of homework diary and class notes
Ensure that they check off answers with small tick and complete any
corrections
Support their organisation - pencil/rubber/ruler/jotters and a scientific
calculator to class (Casio FX83GTPlus Scientific Calculator is best)
Encourage their best presentation
Ensure they attempt all questions
Step-by-step, vertical working where possible
Support the use of the common language and methodology
Regular revision and use of online learning resources including GLOW

Time: Encourage your child to use a watch or clock to tell the time,
provide timed activities and read timetables
Calendars: Plan family birthdays on a calendar & do a birthday
countdown
...

Estimating: plan for activities in advance like calculating the number of
rolls of paper or paint required to decorate a room, the length of time
activities may take
...
e
...
using the information gathered from reading
newspapers, using the internet and watching TV to draw conclusions and make
choices that involve numeracy
...
It is not enough just
to learn the stations eg
...

Length
 height and length in cm and m
...

Progression in this topic will be able to estimate areas in m2 and lengths in m and mm
...

e
...


34 + 28 = 34 + 30  2
163  47 = 163  50 + 3
23  3 = (20  3) + (3  3)
68 + 4 = (68 +2) + 2

Decimal Notation
All pupils should be familiar with decimal notation for money although they may use incorrect notation
...
They may need to be reminded for example that 15 metres
is 150 centimetres not 105 centimetres
...
g
...

They may also have problems with comparing the size of decimal numbers and may believe that 2 ·36 is
bigger than 2·8 because 36 is bigger than 8
...
g
...
8

→ 238 (to nearest whole number)
→ 240 (to nearest 10)
→ 200 (to nearest 100)

Rounding to 1 decimal place (to 1 d
...
)
5
...
3 (to 1 d
...
)
11
...
0 (to 1 d
...
)
Rounding to more than 1 decimal place/to significant figures (to s
...
)
6
...
246 (to 3 d
...
25 (to 3 s
...
They should be able to use
calculators for standard form
...
4208, (i
...
the calculator
display)

Very large or very small numbers can be written in standard form
a x 10b
where 1 ≤ a < 10
2 000 000 = 2 x 106
3 700 000 000 = 3·7 x 109
0·00000009 = 9 x 10-8
0·000000859 = 8·59 x 10-7

LANGUAGE OF ARITHMETIC
Avoid the use of the word ‘sum’ to mean a maths question
...

e
...
3  2 = 6 + 4 = 10  7 = 3

It is important that pupils write such calculations correctly
...
g
...

There is no problem with calculations such as:
34 + 28 = 30 + 20 + 4 + 8 = 50 + 12 = 62
because each part of the equation has the same value
...

e
...


1576  312



1600  300 = 1300

ADD AND SUBTRACT
It may be best to avoid the use of “and” when meaning addition e
...
“4 and 2 is 6”
Subtraction is by ‘decomposition’
The algorithms can be laid out as follows:
The “carry” digit usually sits above the line
...


3 456 + 975

6 286  4 857

Estimate
3 500 + 1 000 = 4 500

Estimate
6 300  4 900 = 1 400

3

4
 1 91
4 4

5
71
3

6
5
1

5



6
4
1

1

2
8
4

7

8
5
2

1

6
7
9

MULTIPLYING AND DIVIDING BY 10, 100, 1000
The rule for multiplying by 10 is that each of the digits moves one place to the left
...
In division, the digits move to the right
...
Decimal points do not move
...
g
...
e
...


H
2

260  10 = 26
T
U

6
0

2
6


1
10

1
100

H
4

439  100 = 439
1
T
U
 10
3
9

4
 3

1
100

9

Using the rule of adding or removing zeros can be confusing because it only works for some numbers
...

Problems sometimes arise however with the less able student who applies this technique to decimals and writes 35  10 = 350
...
Start as “8 divided by 6”
...

 When multiplying by two digits, the algorithm can be laid out as follows:

4 7
×54 6
2 8 2
2 31 5 0
2 6 3 2
3

ORDER OF OPERATIONS
BOMDAS: The order of operations
Brackets
Off
Multiply
Divide
Add
Subtract
Examples

30  4  3
 30  12
 18

30  50  (2  8)
 30  50  10
 30  5
 35

The important facts are that brackets are done first, then powers, multiplication and division
and finally addition and subtraction
...


UP +

A negative number is less than zero
...

POSITIVE

A positive number is more than zero
...

The negative sign goes in front of a negative number
...

° is the symbol for degree
...

6 degrees Celsius is the same as 6°C
...

Positive temperatures are called above freezing
...

A number line can be of help when ordering numbers
...

Moving to the left, numbers getting smaller
...
g
...

Starting
point

Distance
to move
Direction

10 9 8 7 6 5 4 3 2 1

3

4

5

6

7

8

Care should be taken with the use of language
...
‘Minus’ is used as a verb, indicating the
operation of subtraction
...

e
...
(i)
(ii)

5 + (6) = 5  6 = 11

Read as: ‘6 minus
negative 3’
or ‘6 subtract
negative 3’

6 – (3) = 6 + 3 = 9

When multiplying positive and negative numbers, if both numbers are positive or both
numbers are negative, the answer will be positive
...


(i) (3)  (2) = 9 (ii) (8)  4 = 2

Fraction of a Quantity
Unitary fraction of a quantity

Simple fractions of a quantity

1
of £18
6
 £18  6
 £3

Simple fractions of a quantity

2
of 24
3
 24  3  2
 16

For a lower ability group
1
of 24
3
 24  3
8

then
2
of 24
3
 8 2
 16

 dividing by ½ is the same as multiplying by 2
 Numerator means top number
 Denominator means bottom number

2
3
 24  3  2
 16
24 

Rules of Fractions
Addition
 Find lowest common denominator
 Change tops (numerator)
 Add tops only
3 2 4  3

4
4
This is known as converting
from a mixed number to an
improper fraction (top heavy
fraction)

Example
3 2
2 
4 3
11 2
 
4 3
33 8


12 12
41
7

3
12
12

2

Multiply
 Simplify where possible
 Multiply top with top
 Multiply bottom with bottom
Examples

3 5

4 6
1 5
 
4 2
5

8

2
3
10
 15
3
1
 18
3

53

Subtraction
 Find lowest common denominator
 Change tops (numerator)
 Subtract tops only
Example
7 5
1 
8 6
15 5


8 6
45 20


24 24
25
1

1
24
24
Expert groups – Rules of Fractions

Divide




Flip second
Change to multiply

Example
8 4

9 3
8 3
 
9 4
2 1
 
3 1
2

3

Percentages
(with a calculator)
Pupils will be shown to set out examples in the following way:

27% of £469
27

 £469
100
 27  100  £469
 0
...
63
The more able pupils are encouraged to convert the percentage to a decimal as the first line of working, for example

27% of £469
 0
...
63
 percent means ‘out of 100’ and of means multiply
 Pupils benefit from showing working vertically with one ‘=’ sign per line
 Pupils should be discouraged from using the % button on a calculator

Percentages
(without a calculator)
Pupils will be shown to calculate amount using the following
1%

1
33 1 % 1
100
3
3
10% 1
66 2 % 2
10
3
3
20% 1
Table 2
5
25% 1
5%
10% ÷ 2
4
2∙5%
5% ÷ 2
50% 1
2
Table 3
75% 3
4
Table 1
Lower ability pupils experience more success when they associate percentages with fractions of a pound in pence eg
...


Most percentages will be found using multiples of 10% and/or 1%
Examples
A
...
Find 17∙5% of £220
10%
5%
2∙5%
17∙5%

is 22
is 11
is 5∙5
is 38∙5

It is useful to reinforce that 10% can be found by dividing by 10
Many pupils try to divide by 1 to find 1%

C
...

Pupils will be shown to simplify ratios like fractions
...


= 2:5

A ratio in which one of its values is ‘1’, is called a unitary ratio e
...
1:12
Ratio Calculations should be set out in a table and pupils should put their working at the side
...
If there are 35 dogs in the shelter how many
cats are there?

Ratio and Proportion (2)
If sharing money in given ratios pupils must:
● Calculate the number of shares by adding the parts of the ratio together
...

● Multiply each ratio by the value of one share to find how the money has been split
...
How much does Jack receive
and how much does Jill receive?
Solution Number of shares
value of 1 share
Jack’s share
Jill’s share

=
=
=
=

2+3
£35 ÷ 5
2 x £7
3 x £7

=5
= £7
= £14
= £ 21
...

● Divide by the given amount to find the unitary value
...

● Write final answer under the table
...
Find the cost of 4 textbooks
...
50
£11
...
00

The cost of 4 textbooks = £46
...

With inverse proportion as one quantity increases the other decreases
...

● Multiply to find out how long/much the unitary value will be
...


Example
If it takes 5 men 12 hours to paint a fence, how long would it take 6 men?
Solution
Men
5

Hours
12

→

1

→

5 x 12 = 60

6

→

60 ÷ 6 = 10

It takes 6 men 10 hours to paint the fence
...


Time – 12hour – 24hour
Pupils should be aware that using am and pm is very important when stating time in 12 hour
notation
...
All times written in
24 hour notation should have 4 digits
...
g
...
00am → 0800 hrs
10
...
15pm → 1715 hrs
noon)

(5 hours and 15 minutes after 1200, 12

Converting 24 hr → 12 hr
e
...
0240 → 2
...
45pm

Time Intervals
Pupils will be shown how to work out time intervals by “counting on”
...
g
...
25pm to 7
...
25pm

7
...
g
...
40am to 3
...
40am

Total:

20 mins

9
...
00pm

23 mins

3
...


6 hours 43 mins

e
...
Calculate how long it is from 2250 to 0210
2250

Total:

10 mins

3 hours 20 mins

2300

3 hours

0200

10 mins

0210

Time – Converting units
Converting hours and mins ↔ decimals
Pupils should already know:
• 30 mins = ½ hour = 0•5 hrs
• 15 mins = ¼ hour = 0•25 hrs
• 45 mins = ¾ hour = 0•75 hrs
Hours, mins

decimals

Rule
converting minutes to decimal hours → divide by 60
e
...

24 minutes = 24/60 of an hour = 0•4 hr
3 hours 13 mins
= [3 + (13/60)]hrs
= [3 + 0•22]hrs
= 3•22hrs ( to 2 d
...
)

Decimals

hours, mins

Rule
converting decimals hours to minutes → multiply by 60
e
...
0•15 hr = (0•15 x 60) mins = 9 minutes
...


Time, Distance, Speed

D
S T

Average Speed

=

Distance
Time

Distance = Average Speed x Time

Time

= Distance
Speed

Please NOTE – in Physics, pupils will use V instead of S for average
speed
...

Have the pupils rewrite expressions with the like terms gathered together as in the second line of
examples 2, 3 & 4 below, before they get to their final answer
...
It does not matter where the operator and term (−7x) are moved within the
expression
...


Example 1
Simplify
x  2 x  5x
 8x

Example 2
The convention in Maths is
to write the answer with the
letters first, in alphabetical
order, followed by number
...


Simplify

3  5x  4  7 x
 5x  7 x  3  4
 2 x  7

or

3  5x  4  7 x
 3  4  5x  7 x
 7  2x

5m  3n  2m  n
 5m  2m  3n  n
 3m  2n

5m  3n  2m  n
or  3n  n  5m  3n
 2n  3m

Algebra – Evaluating Expressions
If x = 2, y = 3 and z = 4
Find the value of: (a) 5x −2y

This line where the
substitution takes place
must be shown
...


(b) x + y – 2z

(c) 2(x + z) – y

(d) x2 + y2 + z2

a )5 x  2 y
 5 2  23
 10  6
4
b) x  y  2 z
 2  3  2  ( 4 )
 5  (8)
 13
c ) 2( x  z )  y
 2(2  ( 4))  3
 2  ( 2 )  3
 4  3
 7
d )x2  y 2  z 2
 2 2  3 2  ( 4 ) 2
 4  9  16
 29

There is a bracket
around the −4 as
mathematicians do not
write two operators side
by side
...
Expand 5(x + 2)

Example 3
...
Multiply out 4(2p – 7)

Example 4
...
Multiply ( x  3)( x  4)

 x 2  3x  4 x  12
 x  7 x  12
2

Example 2
...
This process is called factorising
For example: 2(x + 3) = 2x + 6 so, in reverse 2x + 6 = 2(x + 3)
2 is the highest factor of 2x and 6, so 2 goes outside the bracket
...

a – 4 is then required inside the bracket
...

Example 1
...
Factorise 18w2 – 12w

‘What is the highest number to go into 9x and 15?’ 3
‘Are there any letters common to 9x and 15?’ No
So only 3 comes before a bracket
...
6w ( )

‘What is required in the bracket so that the 9x can be found?’ 3x
3(3x + )

‘What is required in the bracket so that the 18w2 can be found?’3w
6w(3w – )
‘What is required in the bracket so that the 12w can be found?’ 2
6w(3w – 2)

‘What is required in the bracket so that the 15 can be found?’ 5
3(3x + 5 )
9x + 15
= 3(3x + 5)
Check by multiplying out

18w2 – 12w
= 6w(3w – 2)

Factorising Algebraic Expressions
2
2
Difference of Two Squares (a  b )

Example 1
...
Factorise x 2  4
x2  4
 ( x  2)( x  2)

Example 3
...
Factorise 4 x 2  25
4 x 2  25
 (2 x  5)(2 x  5)

Example 5
...
Factorise 2 x 2  32

2 x 2  32
 2( x 2  16)
 2( x  4)( x  4)

Trinomial Expressions (Quadratic Expressions)
Factorising ax2 + bx + c Algebraic Expressions
Worked Example
Draw up a table
...

The numbers on the r
...
s
...

In this case, 2+3 = 5 so the trinomial can be factorised as

( x  2)(x  5)
Example 1
...
Factorise x 2  4x  5

x 3
x 1

x 5 -5
x -1 1

x 2  4x  3
 ( x  3)( x  1)

x 2  4x  5
 ( x  5)( x  1)

Example 2
...
Factorise x 2  x  12

x -3
x -1
x  4x  3
 ( x  3)( x  4)
2

These answers can be checked by
multiplying out the brackets
using the box method
...
g
...
Factorise 6x2 + 4x – 16

Example 1
...

3x
x

-8
1

-4
2

-2
4

-1
8

From the table we can use:
3x
x

-4
2

6x  4x  2x

YES

6 x 2  4 x  16
 2(3x  4)( x  2)

Algebra – Solve Simple Equations
The method used for solving equations is balancing
...
It is useful to use scales like the ones below to introduce this
method as pupils can visibly see how the equation can be solved
...
Pupils need to be able to deal with numbers set out in a table horizontally, set out in a table vertically or given as a sequence
...


Using Formulae
Pupils meet formulae in ‘Area’, ‘Volume’, ‘Circle’, ‘Speed, Distance, Time’ etc
...
e
...


Example :
Find the area of a triangle with base 8cm and height 5cm
...


Rearranging Formulae
Pupils are taught the balance method of transforming formulae which involves carrying out the same
operation on both sides of the equation
...

e
...
(i)

V = IR
...


V  IR
V
R
I
(ii)

I

v2 = u2 + 2as
...


v 2  u 2  2as
v 2  u 2  2as
v2  u 2
a
2s

u2
2s

When using a formula, pupils may find it easier to substitute known values before carrying out the
transformation
...

3
e
...
The volume of a sphere is given by the formula
Find the radius of the sphere when the volume is 75 cm3
...

They should know the following facts:
Length
10 mm
= 1 cm
100 cm
= 1 m
1 000 m = 1 km

Mass
1 000 g
= 1 kg
1 000 kg = 1 tonne

Capacity
1 000 ml = 1 litre
1 cm3 = 1 ml

Pupils are encouraged to develop an awareness of the sizes of units and an ability to make
estimates in everyday contexts
...


Reading Scales
Pupils of lower ability often have difficulty in reading scales on graphs
...
It may help if they begin by
counting the number of divisions between each number on the scale and then determine what
each division of the scale represents
...
It is usually easiest to begin by converting all of the units of length to the units that
are required for the answer, before doing any calculation
...

Length
1km= 1,000 m
1m = 100 cm
1cm=10 mm

Area
1km2 = 1 000 000 m2
1m2 = 10 000 cm2
1cm2 = 100 mm2

NOTE: km means kilometre, m is metre, cm is centimetre
m2 is read as square metres NOT metres squared
m3 is read as cubic metres NOT metres cubed

Volume
1km3=1 000 000 000 m3
1m3 = 1 000 000 cm3
1cm3 = 1 000 mm3

Area and Volume (2)
Arearectangle = length x breadth = L x B = LB

Areakite or rhombus = ½ x d1 x d2

Volumecube = length3 = L3

Areatriangle = ½ base x height = ½ bh

Areatrapezium

1
= ( a  b) h
2

Volumecuboid = length x breadth x height = LBH

Volumecylinder =

r 2 h

Volumecone =

Volumesphere =

4 3
r
3

Volumeprism = Area of cross-section x height = Ah

1 2
r h
3

Plotting Points and Drawing Graphs
When drawing a diagram on which points are to be plotted, some pupils will need to be reminded that
numbers on the axes are written on the lines not in the spaces
...
g
...


e
...


(i)

(ii)

In an experiment in which the temperature is taken every 5 minutes the
horizontal axis would be used for time and the vertical axis for
temperature
...


Coordinates
 Practice drawing vertical and horizontal lines on the existing lines using a ruler and pencil
 Mark a dot at the centre of the paper (the origin)
 Draw a horizontal line (x-axis) and vertical line (y-axis) through the origin and extend in both
directions to form 4 quadrants (-10 to 10)
 Label axes
 Write y-axes scale on left of axis
 Write x-axis scale below x-axis
 A coordinate is plotted by identifying position on the x-axis then the position on the y-axis (along
the corridor, up the stairs OR horizontal then vertical OR right/left then up/down)
 A coordinate is stated in this form (x, y)

Information Handling
Terminology and Methodology

Discrete Data
Discrete data can only have a finite or limited number of possible values
...


Continuous Data
Continuous data can have an infinite number of possible values within a selected range
e
...
temperature, height, length
...
g
...


0

10
0 - 10

11 - 20

20

30

21 - 30

40

50

31 - 40 41 - 50




Non-Numerical Data (Nominal Data)
Data which is non-numerical
...
g
...

Tally Chart/Table (Frequency table)
A tally chart is used to collect and organise data prior to representing it in a graph
...

Mean: add up all the values and divide by the number of values
...

Median: is the middle value or the mean of the middle pair of an ordered set of values
...
In society average is commonly used to refer
to the mean
...
g
...

2 , 2 , 3 , 3 , 3 , 4 , 5 , 6 , 8
 The mode is 3 because 3 is the value which occurs most often
...

In the example above the range = 8 – 2 = 6
Standard Deviation
The Standard Deviation indicates how much, on average, the data points differ from the
mean
...

Type of data
Nominal (can count but not order or measure)
when the data is about personal opinions or
results where the most common is the important
conclusion to draw, rather an accurate exact
“average”
Ordinal (can count, order but not measure) when
the data has a bell shape, with the middle values
being the most common
Interval/ratio when the data are all as expected,
without any outliers (not skewed)
Interval/ratio (skewed)

Best measure of central tendency

Mode

Median
Mean
Median

Mean from a frequency table

Calculate the mean number of books carried by the girls in the group
...
We label
these two columns and “f”
...

Then we add up the numbers in the second and third columns (
and
)
...


No
...
7 (to 1 dp)

Mean =

Median from a frequency table
Calculate the median number of books carried by
the girls in the group
...


No
...


Frequency ( )
1
2
3
5
5
6
2
1

Median =

cf
1
3
6
11
16
22
24
25

(where n is the number of values)

There are 25 girls in the group
...

The 13th value (girl) is between the 11th and 16th value in the cf column, therefore it falls in the
highlighted row
...


Standard Deviation
Standard Deviation
The Standard Deviation indicates how much, on average, the data points differ from the mean
...

The two formulae for standard deviation are given in National 5 exam papers, they do not need to be
memorised
...


Method 2 (formula 2)
Method 1 (formula 1)
(i)
(ii) Make a table with three columns
x
(x x )²
39
-2
4
39
-2
4
40
-1
1
41
0
0
43
2
4
44
3
9
= 22
S =
S =
S =
S = 2
...
1 (to 1 dp)

Normal Distribution
A probability distribution that plots all of its data values in a symmetrical fashion and
most of the results are situated around the probability's mean
...


Examples:
Heights of people
Errors in measurements
blood pressure

Describing the distribution of Data

Symmetrical distribution

Widely spread distribution

Uniform distribution

Tightly clustered distribution

Skewed to the right distribution

Skewed to the left distribution

Scattergraphs
Scatter graphs are used to show whether there is a relationship between two
sets of data
...
As one quantity increases so does the other
A negative correlation
...

No correlation
...


Cost of ticket
Negative correlation

Annual Income
No correlation

Drawing a Line of Best Fit
A line of best fit can be drawn to data that shows a correlation
...
The line should go
through the mean point and should have approximately the same number of data points
on either side
...
7
Height = 165

180
175
170
165
160
155
150
4

5

6 7 8 9 10 11 12 13
Shoe Size

Graphs, charts and tables
Good graphs, charts and tables are powerful tools for displaying large
quantities of data and help turn information into knowledge
...


Why are these graphs
misleading?

Graphs, Charts and Tables
Graph
Pictograms
A pictogram uses an icon to
represent a quantity of data
values in order to decrease the
size of the graph
...

Linegraph
A line graph can be used as an
initial record of discrete data
values
...

Piechart
A piechart displays data as a
percentage of the whole
...
A total data number
should be included
...
A total data
number should be included
...

Categories are of continuous
measure such as time, inches,
temperature, etc
...
A double bar
graph can be used to compare two
data sets
...

Compound/ Comparative Bar
graph

Line Graph
A line graph plots continuous data
as points and then joins them with
a line
...

Combination of Bar Graph and
Line Graph

Visually strong
Can compare to normal curve
Usually vertical axis is a frequency
count of items falling into each
category

Cannot read exact values because
data is grouped into categories
More difficult to compare two
data sets
Use only with continuous data

Visually strong
Can easily compare two or three
data sets

Graph categories can be
reordered to emphasize certain
effects
Use only with discrete data

a bar graph that compares two
or more quantities simultaneously

Graph categories can be
reordered to emphasize certain
effects
Use only with discrete data

Can compare multiple continuous
data sets easily
Interim data can be inferred
from graph line

Use only with continuous data
Can sometimes have two
different vertical scales to
represent the different
quantities

Can illustrate continuous data
sets and discrete data set on
same graph
Can demonstrate the correlation
of two variables such as
temperature and rainfall

Frequency Polygon
A frequency polygon can be made
from a line graph by shading in the
area beneath the graph
...

Scattergraph
A scattergraph displays the
relationship between two factors
of the experiment
...

Stem and Leaf Plot
Stem and leaf plots record data
values in rows, and can easily be
made into a histogram
...

Box plot
A boxplot is a concise graph
showing the five point summary
...


Visually appealing

Shows a trend in the data
relationship
Retains exact data values and
sample size
Shows minimum/maximum and
outliers
Concise representation of data
Shows range, minimum &
maximum, gaps & clusters, and
outliers easily
Can handle extremely large data
sets
Shows 5-point summary and
outliers
Easily compares two or more
data sets
Handles extremely large data
sets easily

Anchors at both ends may imply
zero as data points
Use only with continuous data

Hard to visualize results in large
data sets
Flat trend line gives inconclusive
results
Data on both axes should be
continuous
Not visually appealing
Does not easily indicate
measures of centrality for large
data sets

Not as visually appealing as
other graphs
Exact values not retained

Probability : Terminology and Methodology
This is the chance that a particular outcome will occur, measured as a ratio of the total possible outcomes
...

It always lies between 0 and 1
0 meaning impossible (could not happen)
1 meaning certain (will definitely happen)
Probability of an event happening =

number of favourable outcomes
number of possible outcomes

Calculating Probability
Example
A boy tossed a coin
...


What is the probability that it is heads?

What is the probability a green ball is picked?

P (heads) = 1/2

P(green) = 4 / 3+4 = 4 / 7

Speed Distance and Time
The study of the relationships between speed, distance and time
...
We would use the substitution
method again when taking on a problem in this field
...

Speed = Distance
Time
Speed = 20
4
Speed = 5 miles per hour
It is important to remember to check the units being used in these calculations, mph, seconds, etc as this will change the
difficulty of the question
...

There are three main formulas used in Right Angled triangle Trigonometry, and these are known as the Trig ratios
...
(Highlighted above
...
We would use the
substitution and rearranging method as seen in the following examples
...


Step 1: Draw the triangle and label the sides H, O and A
...
Tick off what you know the
value of and dot what you are trying to find
Step 3: State formula, substitute values and calculate answer

Trigonometry
Worked Example 2: Calculating the size of an Angle
Find the size of angle xo in this triangle
...

(N
...
Notice as the angle is in a different position, the sides
change according to it)
Step 2: Write down SOH CAH TOA
...

This can be done easily using the calculator Shift/2nd function button must be pressed before Cos to give the correct
answer

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