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Page 1

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HCF AND LCM
LCM:

1. Write out the prime factors of both numbers
2. Cross out 1 of each repeat
3. Times the remaining numbers together

HCF:

1. Write out the prime factors
2. Times one of each repeat together.

PRIME FACTOR DECOMPOSITION
1. Do a factor tree
2. Write…

Page 2

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UPPER AND LOWER BOUNDS
If minusing, use upper bound of 1st no. and lower bound of 2nd no
If dividing, do the same.

APPROXIMATION
Round to 1sf/ do what is logical

EQUATION, FORMULA, IDENTITY AND EXPRESSION
Expression: no equals

Formula:has equals & contains more than one letter

Identity: 2 ways…

Page 3

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Quadratic:

1. Write out 1st, 2nd and 3rd difference of sequence
2. a+b+c= 1st difference
3. 3a+b=2nd difference
4. 2a=3rd difference
5. Then write it out in the form an²+bn+c
6. This is the nth term.

SIMULTANEOUS QUADRATIC EQUATIONS
1. Rearrange linear to get x
2. Sub into quadratic
3.…

Page 4

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Sin:




Cos:




LOCI
See maths book 4

DIRECT AND INVERSE PROPORTION
Direct proportion= when 2 quantities increase and decrease in the same ratio.
Inverse proportion= when one quantity increases at the same rate as the other quantity
decreases.

TRANSFORMING GRAPHS AND FUNCTIONS
Y=f(x)

Numbers inside the brackets affect x
Numbers…

Page 5

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Squares: All of its angles are equal (90°). All of its sides are of equal length. Opposite sides
are parallel. The diagonals bisect each other at 90°. The diagonals are equal in length. It has 4
lines of symmetry.
Rhombus: Diagonally opposite angles are equal. All of its sides are…

Page 6

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CIRCLE THEOREMS




And on 7, a line joining the centre of the circle to point R bisects the angle between the tangents.

AREA OF SECTOR AND LENGTH OF ARC

Arc length: /360 x 2r

Sector area: /360 x r²

USE VECTORS




The vector from X to Y may also be…

Page 7

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The magnitude of the vector(i.e. its number value) is expressed as:




Inverse vectors
An inverse vector is a vector of equal magnitude to the original but in the opposite direction.




EFFECT OF ENLARGEMENT ON AREA AND VOLUME
If length scale factor is n, area scale factor is n²
If length…

Page 8

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It looks like this:




CUMULATIVE FREQUENCY GRAPHS
The points are plotted at the upper class boundary.
Finding the median and quartiles:
By drawing horizontal lines to represent 1/4 of the total frequency, 1/2 of the total
frequency and 3/4 of the total frequency, we can read estimates of the lower…

Page 9

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TREE DIAGRAMS
In a tree diagram to find a probability of an outcome we multiply along the branches and add
vertically.
If it is a head or a tail, add
If it is a head then a tail, multiply

VOLUME OF CONE
1/3 x r² x h (1/3 x base…

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