Transcript Scale Factor (3)

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General Past Papers
by Topic 2000 - 2010
Basic Calculations (12)
Pythagoras Theorem (11)
Straight Line (14)
Angles (14)
Money & Percentages (44)
Trigonometry (12)
Linear Patterns (8)
Scale Factor (3)
Scientific Notation (10)
Algebra (12)
Symmetry (11)
Speed Distance Time (17)
Summary of General
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General Past Papers
by Topic 2000 - 2010
Combinations / Logic (14)
Proportion & Ratio (8)
Length Area Volume (29)
Scale Drawing (5)
Bearings (4)
Variation (3)
Negative Numbers (9)
Tolerance (1)
Probability (7)
Statistics Stem Leaf (6)
Statistics Mean F Table (4)
22-Mar-17
Created by Mr. Lafferty Maths Dept.
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m=0
m<0
m 
(0,c)
m>0
m = undefined
Graph of
y = mx + c
Possible values
for gradient
m>0
Note :
2y + 4x = 8
rearrange into
correct form
y = -2x + 4
Parallel lines
have same
gradient
y  y1
V
 2
H
x 2  x1
Straight Line
y = mx + c
m = gradient
m 
y  y1
V
 2
H
x 2  x1
c = y intercept (0,c)
e.g. 17.5% of 300
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
17.5 %
Without a
calculator
With a
calculator
e.g. 19% of £60
19
x 60 = £11.40
100
£52.50
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
x 100 =75%
4
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Complicated Linear Patterns
using diagrams and tables
Key-Points
Write down the 4 main steps
1.
Make a table
2.
Find the difference
3.
Write down part of formula
4.
Find the correction factor and
then write down the full formula
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Why is this not
scientific notation ?
4000
Write out in full
a not between
1 and 10
11 x1018
4 x103
1.1 x1019
a x 10n
a between 1 and 10
n is positive
LARGE numbers
Science
Scientific Notation
= Standard Form
Maths
SMALL numbers
a x 10n
a between 1 and 10
n is negative
0.0000006
Write out in full
6 x10-7
5 x10-6
0.5 x10-5
Why is this not
scientific notation ?
a is less than 1
a<1
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Pythagoras Theorem
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Finding hypotenuse c
c = a +b
2
2
2
c
b
a
Finding shorter side a
a = c -b
2
22-Mar-17
2
2
Compiled by Mr. Lafferty Maths Dept.
Finding
shorter side b
b =c -a
2
2
2
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Trigonometry
Sin x° =
Opp
Hyp
Cos x° =
Adj
Hyp
O
A
S HC H
Tan x° =
O
T A
Opp
Adj
Trigonometry
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Process
1.
Write down
SOH CAH TOA
2.
3.
Identify what you want to find
what you know
Copy this!
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Scale Factor applies to ANY SHAPES that are
mathematically similar.
b
7.5 cm
a
4 cm
3 cm
8 cm
2cm
10 cm
Given the shapes are similar, find the values a and b ?
4
Scale factor = RSF =
= 0.4
10
a is 8 x 0.4 = 3.2
10
Scale factor = ESF =
= 2.5
4
b is 2 x 2.5 = 5
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x2 + x + 3 + y + 9 – 2x - 4y
= x2 - x – 3y + 12
Note
x2 ≠ x
10x
5x 2 – 6xy
3y
HCF = 2x
divide each
term by HCF
2x(
-
)
Tidying up terms
Factorising
Algebra
Evaluating Expressions
a = 2 b = (-3) c = 4
= 2b - 3(a - c)2
= 2(-3) - 3(2 - 4)2
= 2(-3) - 3(-2)2
= -6 – 12
= -18
Removing single
bracket
BODMAS
9 - 3(8 - y) =9 - 24 + 3y
= -15 + 3y
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Balancing Method
Kirsty goes to the shops every week to buy some potatoes.
She always buys the same total weight.
One week she buys 2 large bags and 1 small bag.
The following week she buys 1 large bag and 3 small bags.
If a small bags weighs 4 kgs. How
much does a large bag weigh?
4
4
4
How can we go about
What instrument
solving this using
measures balance
balance ?
22-Mar-17
Created by Mr Lafferty Maths Dept
4
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Balancing Method
Take a small bag away
from each side.
Take a big bag away
from each side.
We can see that a big bag
is equal to
4 + 4 = 8 kg
22-Mar-17
Created by Mr Lafferty Maths Dept
4
4
4
4
Balancing Method
What symbol should
we use for the scales
?
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Lets solve it using maths.
Let P be the weigh
of a big bag.
P
P
4
We know that a small bag = 4
2P + 4 = P + 12
-4
-4
2P = P + 8
-P
-P
Subtract 4
from each side
Subtract P
from each side
P=8
22-Mar-17
Created by Mr Lafferty Maths Dept
P
4
4
4
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Careful with time units you
must work in decimal time and
convert back at the end.
Time Distance Speed
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Mixed Problems
D=S  T
D
S=
D
T
S T
T=
D
S
Simple way to remember the 3 formulae !
22-Mar-17
Created by Mr. Lafferty Maths Dept.
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Book Title
Book Title
Book Title
Total Cost
B
r
L
A =LxB
A =
h
πr2
h
A =Bxh
a
A = ½bh
V = πr2h
V = Area x H
Volume = Area x Height
Simple
Volume
Area & Volume
of a Prism
Composite
Volume
L
made up of
basic areas
h
V = L x BxH
V = Area x H
h
Composite
Areas
B
A = L x B + ½bh
L
B
Simple
Areas
b
A = ½(a + b) h
h
H
h
H
B
made up of
basic volumes
L
V = (LxBxH) + (½BhL)
V = Area x H
Calculate the area of the base
24 cm
30 cm
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Land
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Probability
We can normally attach a value
to the probability of an event happening.
To work out a probability
number of outcomes
P(A) =
Total number of possible outcomes
Probability is ALWAYS in the range 0 to 1
22-Mar-17
Created by Mr Lafferty Maths Dept
Probability
Number Likelihood Line
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1
0
2
0.1
Impossible
3
0.2
4
0.3
5
0.4
6
0.5
0.6
7
0.7
8
0.8
Evens
P=
Q. What is the chance of picking a number that is even ?P(E) =
Q. What is the chance of picking the number 1 ?
Created by Mr Lafferty Maths Dept
1
Certain
Q. What is the chance of picking a number between 1 – 8 ?
22-Mar-17
0.9
P(1) =
8
=1
8
4
= 0.5
8
1
= 0.125
8
Stem Leaf Graphs
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Construction of Stem and Leaf
A Stem – Leaf graph is another way of displaying information :
Ages
This stem and leaf graph shows
2 4 6 8
the ages of people waiting in a
3 0 1 3
queue at a post office
4 4 4 5 6 7 9
5 0 3 4 9
How many people in the queue? 20
6 1 4 5 6
How many people in their forties? 6
leaves
stem
n = 20 Key : 2 4 means 24
22-Mar-17
Created by Mr. Lafferty Maths Dept.
Frequency Tables
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Working Out the Mean
Example : This table shows the number No of
of coins in the pockets of some children. Coins
(c)
Adding a third column to this table
will help us find the total number of
coins and the ‘Mean’.
Mean Number of coins =
22-Mar-17
Freq.
(f)
fxC
1
5
5 x 1 =5
2
5
5 x 2 = 10
3
1
1x3=3
4
3
3 x 4 = 12
5
2
2 x 5 = 10
Totals
16
40
40
= 2.5 coins
16
Created by Mr. Lafferty Maths Dept.
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Scaled Drawings using Bearings
Make an accurate drawing of the plane journey
N
N
N
N
22-Mar-17
120o
45o
8km
120o
12km
45o
8km
12km
1cm represents 2km
Created by Mr. Lafferty Maths Dept.
Direct Variation
Harder Direct Variation
S4
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Q.
The cost (C) of producing a football magazine
varies as the square root of the number of
pages (P). Given 36 pages cost 48p to produce.
Find a formula connecting C and P.
Since C is directly proportional to “square root of” P
the formula is of the form
C
C =k P
√P
22-Mar-17
C = 40
P=2
48 = k 36
k = 48 ÷ 6 = 8
C =8 P
Direct Variation
Harder Direct Variation
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S4
Q.
How much will 100 pages cost.
C
C = 8 100
√P
C = 8 100 = 8  10 = 80p
22-Mar-17
Created by Mr. Lafferty Maths Dept.
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Tolerance
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S4
Tolerance is
written as
(50±2)mm
He might be prepared to accept any bolt as long as it
lies between 48mm and 52mm
This means he will accept a bolt which is
within 2mm of the 50mm he asked for.
This is referred to as the
TOLERANCE for the measurement.
22-Mar-17