Download CAH TOA SOH - Mathsrevision.com

For balance we have
Subtract 6
from each side
2
a
5a + 6 = 3a + 16
-6
Subtract 3a
from each side
Divide each
side by 2
a
-6
a
5a = 3a + 10
-3a
a
a
a
2
2
a
2
2
2 2
2
2
2 2
a
HCF = 2x
divide each
term by HCF
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x2 + x + 3 + y + 9 – 2x - 4y
= x2 - x – 3y + 12
Note
x2 ≠ x
10x2 – 6xy
2x( 5x - 3y )
Tidying up terms
A l2
Factorising
-3a
Algebra
2a = 10
a = 2 b = (-3) c = 4
a= 5
= 2b - 3(a - c)2
= 2(-3) - 3(2 - 4)2
= 2(-3) - 3(-2)2
= -6 – 12
= -18
Adult ticket price is £5
BODMAS
Rugby
75
Football
90
Cricket
45
Ice Hockey
60
9 - 3(8 - y) = 9 - 24 + 3y
30
Total
300
Pie Chart
0
0.5
Impossible
Evens
Not very likely
1
2
3
4
Number of Surfers
5
7
9
11 13
2
2
Step 3 : Correction factor “add on 2”
0
1
2
3
39
89
02 2
47 7 7
Find a number
so formula
works
Order
data
Stem Leaf
Remember
KEY
2
Half of 29
is 14.5
25
29
Distance
=
135miles
1
2 hrs
4
D
S=
T
D
S T
To change minutes to decimal hours
‘divide minutes by 60’
2hr 15 minutes to decimal is
2
15
= 2.25 hrs
60
Converting
Time
d
x
Best fit line
correlation
4
4

3 4 7
x
Rhombus and kite
x
Strong negative
correlation
D
T=
S
b
b
Parallelogram
1
A  Dd
2
x x
Best fit line
Trapezium
1
A  ( a  b) h
2
A  bh
Two key points when dealing with
right-angled triangles
The longest side in a right-angled triangle is called
The HYPOTENUSE
Pythagoras
Theorem The HYPOTENUSE is ALWAYS opposite the right angle
S3 Mathematics
General Course
c
b
(xz)2 = (xy)2 + (yz)2
x
c2 = a2 + b2
z
17.5 %
Mean from a
Frequency table
Adding
Subtracting
Mean =
1 1 5
 
2 3 6
Multiplication
1 3 3
 
2 5 10
Simple
fractions
= 2.5
16
Subtracting
1 1 Deal with
2  1 whole numbers
2 3
first
1 1
1



1
1
2 3
6
D
60km
T= =
= 1.5hrs
S 40km/hr
Same idea
for addition
T = 1hr 30mins
To change decimal time to minutes
‘multiply the decimal part by 60’
3.7 hrs to hours and minutes is
3 + 0.7  60 = 3 hrs 42 mins
Harder fractions
Top-heavy
first
Multiplication
1 1 3 5 15 1 7
1 1   
2 4 2 4 8 8
With a
calculator
1 4

2 5
1 5
5
 
8
2 4
Basic Rules of
Fraction
40
If distance is in
kilometres and time in
hours then speed is in
kilometres per hour
Without a
calculator
Flip and
change
the sign
16
Top-heavy
first
e.g. 19% of £60
19
x 60 = £11.40
100
Division
Trigonometry
1
2
3 5
1 1 

2
3
2 3
Flip and
change
the sign
3 3
9
 
2 5 10
Percentage
out of 100
Finding
Percentages
% profit or loss
I buy a CD for £4 and sell it for £7.
What is the percentage profit?
Profit made £3
3
4
x 100 =75%
xo
Adjacent
Process
Distance
Speed Time
£52.50
Perecentages
Division
2 1 1
 
3 2 6
40
10%  10
5%  half of 10%
1%  100
0.5%  half of 1%
2%  twice 1%
3%  3 times 1%
10%300 10 = £30
5% 30 2 = £15
2.5% 15
2 =£ 7.50
Statistics 2
How long did the bus journey
take if it travelled a total distance
of 60 km at an average speed
of 40 km/hr.
Units MUST
be consistent !!
S = 60mph
x
x
h
D
Fractions
Time
Distance
Speed Time
135
=
2.25
D
Opposite
D = S  T= 50  6.5 = 325km
D
S=
T
Median
D= S  T
A racing car travelled at 50 km/hr.
What is the distance covered
in 6 hours 30mins ?
x
a
e.g. 17.5% of 300
Median from a
Frequency table
5
17
Certain
Very likely
x
x x
x
b
d
Areas
1
bh
2
Any Type of Triangle
y
Statistics
12
1
b
A
h
a
Mean :
Sum of data Number of data
Median :
Middle value (ordered data)
Mode :
Most common number
Range :
Highest - Lowest
n = 11
6
36o
S = 2T + 3
Mode : 37
Range : 34
Median : 22
Key 1|9 = 19
72o
2
Linear
Patterns
S = 2T
Step 2 : Part of the Formula
Speed
2
54o
h
l
Statistics 1
Same difference
linear pattern
Step 1 : Find difference
Daniel drove from his house
to the Blackpool, a distance
of 135 miles. It took him
2hrs 15mins.
What was his average speed?
5
b
1
2
A  bh
Revision of Square, Rectangle and RAT.
Scattergraph
There are 3 red and 4 green balls in a bag.
Strong positive
What is the probability a green ball is picked.
P( green) 
o
108o 90
Statistics
Probability
Algebra
Solving Equations
75
x 360  90o
300
90
Football angle =
x 360  108o
300
45
Cricket angle =
x 360  54o
300
60
Ice Hockey angle =
x 360  72o
300
30
Squash angle =
x 360  36o
300
Rugby angle =
Squash
= -15 + 3y
A  l b
l
Favourite Sport
Removing single
bracket
Evaluating Expressions
Number of Tables
S3 General
NEED TO KNOW
4/30/2012
Mr. Lafferty
1.
Write down
(SOH)(
2.
3.
CAH)(
TOA)
Sin x =
Opp
Hyp
Cos x =
Adj
Hyp
Tan x =
Identify what you want to find
what you know
SOH CAH TOA
Opp
Adj