Download EVALUATE- work out CALCULATE – work out EXPRESS – show

PRIME NUMBERS CAN
ONLY BE DIVIDED BY
THEMSELVES AND 1
EVALUATE- work out
CALCULATE – work out
EXPRESS – show
PRODUCT- multiply
SUM/TOTAL- add
SIMPLIFY – make easier
A number with only
2 factors- 1 and itself
2 3 5 7 11 13 17 19 23 29 31 37 41…………
(Note 1 is not a prime number)
2
1
T
FACTORS OF 12
1 x 12 = 12
2 x 6 = 12
3 x 4 = 12
A factor is a number that will divide
exactly into a larger number
Are factors which are
also prime numbers
The factors of 12
are 1,2,3,4, 6 & 12
They can all
divide into 12
And the Factors
of 18 are..
1, 2, 3, 6, 9,and 18
Eg prime factors of 12 are 2×2×3
3
4
The lowest number that 2 or more given numbers can divide
into
Highest factor common to 2 numbers
Eg
Factors of 12
12
=2×2×3
and
Factors of 16
Factors common to both 12 and 16
16
= 2×2×2×2
Eg 12
Factors of 12= 2×2×3
=2×2
and
16
2×2×2×2
Factors of 16=
LCM 2×2×3×2×2 = 48
(ie both 12 and 16 divide into 48)
HCF = 2 X 2 = 4
What is a
multiple?
Multiples are the
results of when
you multiply
- list factors common to both numbers ( 2, 2) and then any additional
factors of both numbers (2,2,3)
5
6
2
are numbers multiplied by themselves
The multiples of
a number are
that number’s
times table
Square numbers are 4. 9, 16, 25, 36, 49, 64, 81, 100, 121, 144
eg
2 2
The multiples of 6 are: 12,18,24,30,36…
The multiples of 7 are: 14,21,28,35,42…
2
Eg square of 2 is 4 (2X2)
3 is 9 (3X3)
4 is 16 (4X4)
(multiplied by itself 3 times)
2
2x2x2=8
3x3x3=27
2
7
Cube Numbers are 8, 27, 64, 125, 216
8
RULES OF DIVISIBILITY
2
3
4
5
6
7
8
9
10
The answer is a number that has been
multiplied by itself
Eg Square root of 9 is 3 (3X3=9)
16 is 4 (4X4=16)
25 is 5 (5X5=25)
36 is 6
49 is 7
64 is 8
81 is 9
√
(The square root is the opposite of a Square Number)
9
Index Numbers or Powers
(indices)
2
3
33
34
35
= 3x3
= 3x3x3
= 3x3x3x3
= 3x3x3x3x3
The
The
The
The
The
÷
last digit is even (0,2,4,6,8)
sum of the digits is divisible by 3
last 2 digits are divisible by 4
last digit is 5 or 0
number is divisible by 3 and is even
The last 3 digits are divisible by 8
The sum of the digits is divisible by 9
The number ends in 0
10
Brackets
11
Indices
Division
Multiplication
Addition
Subtraction
12
Median = Middle value 3,3,3,4,6,7,9
Mode = Most common 3
Mean = Total of items
Think of
A la mode – in
fashion-
367 X 25
Eg
3,6,3,7,4,3,9
MULTIPLY
(367 X 20) + (367 X 5)
(multiply by 2 and add O)
Number of items
Multiply by 5
3+3+3+4+6+7+9 = 35 =
This is MEAN
13 !
I have to doT
the work!
5
7
eg
14
32.138 = 32.1
872.884 = 872.9
= 0.1
0.06
6 630
3 105
35
Add
Eg To 1 Decimal Place
Divide 630 by the Factors of 18 (6 and 3)
Divide answer by 3
13
Look at next number if it is 5 or more the
first number will
increase by 1
630 ÷ 18
Divide by 6
Multiply by 20
367
X 25
1835
7340
9175
15
IGNORE THE WHOLE NUMBERS- ONLY CONSIDER
THE NUMBERS AFTER THE DECIMAL PLACE
16
Look at 4th number- if
it is 5 or more the
third number will
increase by 1
Eg To 3 Significant figures (SF)
657.33 = 65700
432.87 = 43300
2.6582 = 2.66
0.5142 = 0.514
0.0387 = 0.039
Smaller than
Eg
Note: 0 after the decimal
place is significant
9
Bigger than
‹ 12
15
›
13
18
17
PERCENTAGE PROFIT
means out of 100
PePercentage
Decimal
60
100
=
60%
Actual profit(increase in price) X 100
Cost(original) price
Decimal – Divide by 100
60% = 0.60
Percentage – Multiply by 100
0.60 = 60%
(INCREASE)
PERCENTAGE LOSS
19
(DECREASE)
Actual loss(decrease in price) X 100
Cost(original) price
21
ADDING & SUBTRACTING
MULTIPLICATION & DIVISION
when the signs are NOT touching
Move up and down the Number line
If the signs are the same (both positive or both
negative), the answer will be positive.
If the signs are different (one positive and one
negative), the answer will be negative.
20 ÷ (-4) = -5
(-3) × (-5) = 15
Eg:
2 - 7 = -5
+
-1 -5 = -6
When the signs are touching
replace the 2 signs with 1 sign
- - = +
- + = + + = +
+ - = -
(-3) × 4 = - 12
6
–2(x – 3)
= –2x +
2
2
25
Eg: 5 - - 6 = 11
26
-4 + - 8 = -12
A
MULTIPLY BY 10- Move all numbers 1 place to Left
MULTIPLY BY 100- Move all numbers 2 places to Left
6. 274 X 10 = 62.74
6. 274 X 100 = 627.4
1 of 15 = 3
of 15=3
5
A
B
3
:
5 parts
in total
2
Each part is 3
sweets
Each part is 3 sweets
D IVIDE BY 100 – Move all numbers 2 places to Right
3. 62÷ 100 = .0362
B
Share 15 sweets between 2 children A and B
in the ratio 3:2
1
5
DIVIDE BY 10 – Move all numbers 1 place to Right
3. 62 ÷ 10 = .362
i
_
3 of 15
5
sweets
2
5
of 15 sweets
22
9 sweets
6 sweets
23
RULE 2
RULE 1
You can Multiply different and like terms together.
Always multiply the numbers together first
Then put in letters but leave out multiplication sign
3a x 5b x 2c = 30 abc
3a x 4a
= 12 a²
2a x 3b x 3a² = 18 a³b
You can only add or subtract LIKE TERMS
Eg
4y² + 3y
RULE 3
20 abc
4a
m and p are not like terms
43
Ratio of
With algebra we write division as a fraction
Divide the numbers first ( cancel if possible)
Cancel the letters where possible
20 abc
4a
cannot be added- y² and y are not like
terms
m + p =m+p
45
5x - 3x = 2x
3m + 2m = 5m
Red : Black
Black : Red
8 : 12
= 5bc
÷4
8 : 20
12 : 8
÷4
2 : 3
Red : All
÷4
÷4
3 : 2
÷4
÷4
2: 5
46
24
The length of the distance round a shape
The space within a shape (in square units)
PeRimeter reminds
us of PRison- the
guards patrol round
the outside
4 cms
5m
2 cms
4m
3m
6m
2m
8m
Area = 4X2 =8 square cms (cm²)
Perimeter= 5 + 4 + 3 + 2 + 8 + 6 = 28 Metres
29
28
A AREA OF TRIANGLE
½ Base X Perpendicular height
10 cms
15cm
8cm
12cm
vertices
10 cms
(corners)
8cms
12cms
edges
10cm
ArArea of Triangle
= 5 X 8= 40cm²
Area of Triangle
12 X 8 = 48cm
2
30
faces
31
TRIANGLE
UNIT
Cubic millimetre
Cubic centimetres
Cubic metre
mm3
cm3
m3
You hold a
PENcil with
5 fingers
PENTAGON (5)
SQUARE
HEXAGON (6)
There is
an X in
six
height
width
OCTAGON (8)
length
An Octopus
has 8 legs
VOLUME= Length x width x height
RHOMBUS
SQUARE
4 equal sides
4 right angles
RECTANGLE (4)
(squashed square)
4 sides equal
Opposite angles equal
32
33
KITE
2 sets of
lines next
each other
(adjacent)
equal
Reflection
Rotation
Enlargement
Translation
PARALLELOGRAM
PARALLELOGRAM
Opposite sides
sides parallel
parallel and equal
Opposite
and equal
RECTANGLE
Opposite sides equal
4 right angles
Think of a
quad bike with
4 wheels
TRAPEZIUM
2 sides parallel
34
35
Isosceles Triangle
2 sides equal, 2 angles equal
ACUTE less than 90º
Equilateral Triangle
3 sides equal, 3 angles equal (60º)
OBTUSE between 90º and 180º
Scalene triangle
REFLEX more than 180º
All sides/angles different
Right angled triangle
RIGHT ANGLE 90º
One angle of 90º
37
36
POLYGONS
Angles in a triangle add up to 180º
Sum of EXTERIOR angles = 360º
Angles on a straight line add up to 180º
Sum of INTERIOR angles = (n-2) X 180º
where n is the number of sides in the polygon
Alternate Angles are equal
6 Sides
Angles in a circle add up to 360º
(n – 2) x 180º
(6– 2) x 180º
Sum of interior angles=
38
As this is a regular
hexagon each angle is
540º ÷ 6 = 120º
4 x 180 = 540º
40
Z Angles equal
x
F Angles equal
x
x
x
This applies to regular and irregular
shapes
C Angles add up
to 180º
41
x
x
39
∏ = 3.14 approx
AREA of a circle
∏ X r²
(radius ²)
CIRCUMFERENCE of a circle ∏ X D (diameter)
The Pied (Πd)
Piper walks
round the town
4a
Circumference
+
b
42
-
2a
+
+
A
3b
4a - 2a + b + 3b
EXAMPLE
2a + 4b
6y + 3 - 2y - 6
6y - 2y + 3 - 6
4y - 3
Diameter
Radius
-
+
O
R
44
R
Fraction
.
Divide top
by bottom
1 whole
Fraction
Decimal
Multiply by
100
Percentage
1.0
100%
½
0.5
50%
¼
0.25
25%
/3
0.33
33%
⅛
0.125
12.5%
Over 10/ 100/
1000 & cancel
down
Decimal
Divide by
100
We are on the hunt for common
factors in both numbers and letters
7a +28
59
(7 is the only common factor)
7(a + 4)
10b + 15bc ( 5 and b are common factors) 5b(2 + 3c)
Percentage
4b² + 5b
(b is the only common factor)
Favourite Football team
Supporters
b(4b + 5)
Degrees
Arsenal
15
15 x 10 = 150º
Man United
12
12 X 10 = 120º
Liverpool
8
8 x 10 = 80 º
Burton Albion
1
1 x 10 = 10 º
Construct a pie chart to shown this information.
A full circle is 360º
36 people have been surveyed (15 + 12 + 8 + 1). If they shared
the Pie chart equally each supporter would get 360º = 10º
36
27
49