Transcript Foundation Revision

Revision: The Bare essentials
Factors: Numbers that divide into other numbers.
Look for pairs of numbers e.g. Factors of 12 are 1x12
2x6
3x4
= 1,2,3,4,6,12
Multiples: Answers to the times tables.
First 5 multiples of 5 are 5,10,15,20,25.
Square Numbers: Times a number by itself to give a square number.
Can also form a square from it. Square numbers: 1,4,9,16,25,36,49,64,81,100
3x3=9 so 9 is a square number. 4x4=16 so 16 is a square number.
Shown as 42 =16
Cube Numbers: Times a number by itself and then itself again.
Cube numbers are: 1,8,27,64,125,216
3x3x3=27 so 27 is a cube number.
Square Root: Opposite of squaring. Means what number times itself?
4
= 2 (as 2x2=4)
25 = 5 (as 5x5=25)
64 = 8 (as 8x8=64)
Prime Numbers: Only has 2 factors (numbers that go into them). Numbers that
go in are only 1 and the number itself.
Factors of 7 are only 1 and 7 so it’s a prime number so are 2,3,5,7,11,13,17,19…
Even numbers can’t be prime as 2 goes into them. 1 is not a prime number.
Rotational Symmetry: Order is how many times it looks the same in one
complete rotation.
Start
1
2
3
4
Order = 4 as looks the same 4 times.
Triangles:
Equilateral
Same sides
2 sides same
Same angles
Scalene
All different
2 angles same
60
60
Rounding Off:
Isosceles
60
1 Significant figure = one number then zeros
234 to 1 sig fig = 200 ( 1 number then 0s)
48752 to 1 sig fig = 40000
Estimating: Round to 1 sig fig then do calculation.
234 x 65 = 200 x 70 = 14000
Make the numbers easy to use first even if you are allowed to use a calculator.
Fractions of amounts: Divide amount by bottom number then times by top.
2
1
2
of
£150
=
150
÷
5
=
£30
(
that’s
5
5 of £150) then £30 x 2 = £60 ( 5 )
If ½ or ¼ or ¾, then ÷ 2 for a half and ÷ 2 again for ¼.
Percentage of Amounts: Always out of 100.
Find 1% by dividing by 100, then multiply up.
Find 12% of £150,
Do £150 ÷ 100 = £1.50 ( 1%) then times up by 12
e.g £1.50 x 12 = £18.
Remember ÷ 100 to give 1% then multiply it up.
Remember to add amount on if it asks for the new price not just the increase.
Top ÷ bottom
Fractions
e.g.
2
16
9
40
X 100
Decimals
2 ÷ 16
9 ÷ 40
Percentages
0.125
X 100
12.5%
0.225
X 100
22.5%
Probability: Always out of 1.
Usually write as a fraction but also as a decimal or percentage.
List outcomes to see how many there are.
Flick a coin and role a dice: 1H 2H 3H 4H 5H 6H
1T 2T 3T 4T 5T 6T
(12 outcomes)
Coordinates:
along first, then up or down. (x,y)
5
-3,2
4
3
-5 –4 –3 –2 –1
-2
-3
-5,-4
3,4
2
1
1 2 3 4 5
3,-3
-4
-5
Angles
acute
obtuse
reflex
180º
Angles add
up to 360 º
Angles
add up to
180 º
360°
Congruent: Same shape, same size
90°
Powers: Shows how many numbers to times together.
22 means 2 x 2 = 4
23means 2 x 2 x 2 = 8
24means 2 x 2 x 2 x 2 = 16 Not 2 x 4
Ratio: Shows how to share out things.
Method 1
Method 2
Find how many shares there are.
Count out the quantity in the ratio
Divide amount by this total to find
given until all used up then add up.
the amount in one share then multiply out.
Example: 20 sweets in the ratio 4:1 between Tom and Daniel
4 + 1 = 5 ( total number of shares)
Tom
Daniel
16 sweets
4 sweets
20 sweets ÷ 5 = 4 sweets ( number of
sweets in one share)
Tom gets 4 x 4 sweets = 16 sweets
Daniel gets 1 x 4 sweets = 4 sweets
Example
Range = biggest – smallest
2,8,3,5,9,3
range=9-2=7
Mode = Most often or common one
mode=3
Mean = Total of all numbers ÷ How many numbers you have
mean=30÷6=5
Median = middle number (put in order first then cross off from each end)
(If 2 middle numbers take the mean e.g. the number that would be between
them) Can’t have 2 numbers for the median.2 3 3 5 8 9
median = 4
4
Common Conversions to Learn
Fraction
1
2
1
4
3
4
1
5
1
3
1
10
Decimal
Percentage
0.5
50%
0.25
25%
0.75
75%
0.20
20%
0.33
33.3%
0.10
10%
Perimeter: Distance round the outside. Imagine you are walking around it,
how far have you gone all the way round?
Area = ½ x base x height
height
width
Area = length x width
length
Volume:
Space inside.
Volume = length x width x height
base