Factors
What are the factors of
20?
1, 20 2,10 4,5
Primes
What are prime
numbers between 20
and 30?
23, 29
(they only have 2 factors, 1 and itself)
How do you know 30 is
not a prime
Because 30 is 3 x 10
Multiply negatives
What is -4 x -3 = 12
What is -4 x 3 = -12
Two negatives make a positive
Add / subtract
negatives
3--5=3+5=8
3 - + 5 = 3 – 5 = -2
Negative
temperatures
What temperature is 10
degs below 4 degrees?
4 – 10 = 6
Powers, Cubes
What is 54
What is 104
54 = 5 x 5 x 5 x 5 =625
104 = 10 x 10 x 10 x 10 = 10000
Fractions
What is ¾ of 80
80 ÷ 4 x 3 = 60
Percentages
What is 27% of 87?
0.27 x 87, % means ÷ 100
Percentages
What percentage is 27
of 50?
27 ÷ 50 x 100 = 54%
Equivalencies
Which is bigger 0.22,
24% or 23/100?
0.22 = 22/100 24%=24/100
Rounding / SF
Round 2.3537 to 3 dp
Round 2.3537 to 2 sf
2.354 (4th decimal number is 7 so round up)
2.4 (2 sf means round to 2 significant figures)
Ratio
Split 120 into ratio 1:2:3
1+2+3 = 6 (buckets)
Divide 120 by 6 = 20
1x20 : 2x20 : 3x20 = 20:40:60
Multiply fractions
9 1

10 3
Just multiply the numbers
Multiplication
124 x 707
=9
30
- - becomes +
- + becomes -
100
20
4
70000
14000
2800
0
0
0
0
700
140
28
7
700
Multiply out each pair of numbers than add up all
the bold numbers in the grid
70000+14000+2800+700+140+28 = 87668
0.08 x 400
8 x 400 = 3200
0.8 x 400 = 320
0.08 x 400 = 32
0.8 x 0.5
Division
144 ÷ 8
BIDMAS
Work out 52 – 3x4
Coordinates
#P is (2,4)
Q is (6,0)
R and S have been plotted
on the grid.
8 x 5 = 40
0.8 x 5 = 4.0
0.8 x 0.5 = 0.4
1 8
8 )1 4 64
Brackets, Indices, Division, Mult, Add, Subtract
52 – 3x4 Work out 52 first
25 – 3x4 Now work out 3 x 4
25 – 23 Now subtract
12
Substitute
Y= 4t – 10
t =5
y = 4x5 – 10
y = 20 – 10
y = 10
Solve
4g = 20
g = 20 ÷ 4 (÷4 is opposite of x4)
g=5
Solve
2g – 10 = 4
Undo -10 by adding 10
2g = 14
Undo 2x by dividing by 2
g = 14 ÷ 2
g=7
Solve
3(x+2) = 60
Undo 3x by dividing by 3
x+2 = 20
Undo + 2 by subtracting 2
x = 18
Solve
5x – 6 = 3x + 2
Take 3x from both sides
2x – 6 = 2
Add 6 to both sides
2x = 8
x=4
Simplify
3x + 2y – 2x + y + 5
Collect like terms
3x -2x + 2y + y + 5
x + 3y + 5
Multiply brackets
2a (a+3b)
2a x a = 2a2
2a x 3b = 6ab
So 2a (a+3b) = 2a2 + 6ab
Powers
Simplify t x t x t x t x t
Simplify t5 ÷ t3
Simplify t5 × t3
t x t x t x t x t = t5
t5 ÷ t3 = t2 (subtract the powers)
t5 × t3 = t8 (add the powers)
Create expressions
James has 10 bags of sweets
and 5 loose sweets. There are
T sweets in each bag. How
many sweets has he got?
10 T + 5
Mean
Mean of 10, 12, 5, 7, 6
Add up = 10+12+5+7+6 = 40
Divide by number of numbers = 40 / 5 = 8
Mode /
modal
Mode of 10, 12, 12, 5, 7, 6
Most frequent number = 12
Median
Median of 10, 12, 5, 7, 6, 12
Write in order = 5, 6, 7, 10, 12, 12
Pick middle number or half way between
middle numbers = 8 ½
Range
Range of 10, 12, 12, 5, 7, 6
Biggest – smallest = 12 – 5 = 7
Stem Leaf
0
1
2
3
4
5
9
1
0
1
0
4
3
1
4
2
6
Range = biggest – smallest = 56 – 9 = 47
4
1 2 5 6 7
4 5 6 7 9
2 2 8
Mode = most common = 42
Median = middle number = 34
Probability
0
0.25
0.5
0.75
1
This shows a probability scale
0 is impossible
1 is certain
0.25 is ¼ which is unlikely
0.75 is ¾ which is likely
Probability
This shows the probability of rolling two
four sided dice and adding up the sides
1
2
3
4
The probability that you will get a 7 is
1
2
2 =1
16 8
3
4
Probability
Probabilities are written as fractions
The probability that Rovers will win their
next match is 0.6.
Total probability = 100% = 1
The probability that Rovers will lose their
next match is 0.15.
So probability that they will draw is 0.25
1 – 0.6 – 0.15 = 0.25
Work out the probability that Rovers will
draw their next match.
Probability
The probability that it will be sunny
tomorrow is 0.3. Why is the probability
that it will rain NOT 0.7?
Because it could be cloudy or snowy as well.
____________
____________
Scatter
Graphs
Correlation
____________
____________ then negative weak correlation, then no
These____________
show positive strong correlation,
correlation
Scatter
graphs
12
Line of best
fit
Through the
middle of
the crosses
10
____________
8
German
6
4
2
0
0
2
4
6
8
Speed
A car travels 200 miles in 4 hours
What is its speed?
Speed
A car travels for 1 hour 30 minutes at an
average speed of 34 mph. How far does it
go?
Units
Kilo means
1000
Metric
1 kilo gramme = 1000 grammes
10
12
14
16
18
20
French
Speed = miles per hour
( per means divide )
= 200 miles ÷ 4 hours
= 50 mph
1 hour 30 minutes = 1.5 hours
34 x 1.5 = 51 miles
Imperial
Estimate
2 pounds
Weight of an OJ
carton
1 metre
= 100 centi metres
= 1000 milli metres
About 1 yard
1 big step
1 kilo metre
= 1000 metres
About ½ mile
15 minute walk
1 litre
= 1000 milli litres
2 pints
orange juice carton
Shapes
Parallelogram
...........................................
Trapezium
...........................................
Isosceles triangle
...........................................
Kite
...........................................
(f)
Pentagon
Shapes
Hexagon 6
...................
Pentagon 5
...................
Octagon 8
...................
Shapes
Square based pyramid
Cylinder
8m
Area
4m
6m
5m
Area of a triangle
Split it into two shapes and work out area of each
4 x 8 = 32 cm2
2 x 5 = 10 cm2
10 + 32 = 42 cm2
Width x height
Then Halve it
Area and perimeter
Area = count the squares
Area and perimeter
using algebra
Perimeter = distance around the outside of the shape
What is the area and perimeter of a rectangle whose sides as 2a and a
long?
Area = 2a x a = 2a2
Perimeter = 2a + a + 2a + a = 6a
Volume of a cuboid
3cm
2cm
5cm
3 x 5 x 2 = 30 cm3
Symmetry
Octagon has 5 lines of symmetry
Angle words
Reflex
Acute
Obtuse
Angles on a
NOT TO
SCALE
straight line
p
ADD UP TO 180
55°
180 – 55 – 45 = 90
45°
Angles in a
quadrilateral (four
sided shape)
80°
NOT TO
SCALE
130°
ADD UP TO 360
r
80°
q
r = 360 – 80 – 130 – 80 = 70; q = 180 – 70 = 110
Angles in parallel lines
F
Z
w
X
y = 50 (Z angle)
angles
x = 70 (F angle)
w = 70 (X angle)