Find the HCF
Use tree diagram to find the product of prime numbers, (do factors and when prime number circle it) multiply the common ones from each number.
Find the LCM
Use tree diagram to do prime factorisation then multiply all the ones together without repeating from both numbers.
Recurring decimal to fraction

write x = recurring decimal, times both sides by ten. then take away 1x to remove the recurring decimal numbers and be left with the whole number. then simplify.
natural numbers
positive whole numbers, starting from 1.
integers
whole numbers (positive, zero and negative)
rational and irrational numbers
Rational numbers can be expressed as a fraction where both sides are integers, but irrational numbers can't.
reciprocal
a number that is found by dividing 1 by that number
∈
element is in set
∉
element isn't in set
∅
The empty set
A ⊆ B
A is a subset of B
A ⊈ B
A is not a subset of B
A ∪ B
all elements that are in either set A, or set B, or both
A ∩ B
The elements in both sets, intersection of Venn diagram
recall of squares and their corresponding roots from 1 to 15
1 = 12
4 = 22
9 = 32
16 = 42
25 = 52
36 = 62
49 = 72
64 = 82
81 = 92
100 = 102
121 = 112
144 = 122
169 = 132
196 = 142
225 = 152
recall cubes from 1 to 15
1 = 13
8 = 23
27 = 33
64 = 43
125 = 53
216 = 63
343 = 73
512 = 83
729 = 93
1000 = 103
What are the 6 laws of indices? 7
- When multiplying indices with the same base, add the powers.
- When dividing indices with the same base, subtract the powers.
- When there is a power outside the bracket multiply the powers.
- x to the power of 0 = 1
- When the index is negative, put it over 1 and flip (write its reciprocal) to make it positive x-m = 1/xm
- When the index is a fraction, the denominator is the root of the number or letter, then raise the answer to the power of the numerator. xa/b =( b√x)a
- A value raised to the power of ½ means take the square root and a value raised to the power of ⅓ means take the cube root and so on.
Simple interest
PRT/ 100
principal (original amount) x interest rate x time / 100
Compound interest
P(1 + r/100)n
Principal( 1 + rate/100)number of years
Exponential growth and decay
P(1+r)n and. P(1-r)n
Frequency density
Frequency / class width
Acceleration
Speed difference / time
Area of sector of a circle
xo /360 x π x r2
Interior angles of a polygon and number of sides equation

Where n is the number of sides
Circle theorems

How to do differentiation

The original formula only tells you the amount
(height, profit, distance, etc.) at a point.
The rate of change
tells you how fast that amount is increasing or
decreasing at that point.
Different types of curves based off equations

Calculate percentage increase or decrease.

Value change / initial value x 100
Calculate using reverse percentages
- Identify the known value and the percentage it represents: For example, if a sale price is $81, and it represents a 10% discount, then $81 is 90% of the original price.
- Convert the percentage to a decimal or fraction: In the example above, 90% is 0.90 or 9/10.
- Divide the known value by the decimal or fraction: $81 / 0.90 = $90, or $81 / (9/10) = $90.
- The result is the original amount: The original price of the item was $90.
Rationalise the denominator.
You remove any square roots (surds) from the denominator by multiplying the entire fraction (numerator and denominator) by the surd in the denominator.
For denominators with a sum or difference of surds (e.g., a + b√c), you multiply by the same expression with the opposite sign (the conjugate) to use the difference of squares formula (a² - b²) and eliminate the surd.
Example with a rational number and a surd e.g., 1 / (√5 + √2)
- Identify the conjugate: The conjugate of √5 + √2 is √5 - √2.
- Multiply by the conjugate: (1 * (√5 - √2)) / (√5 + √2) * (√5 - √2)).
-
Expand and simplify:
- Numerator: √5 - √2.
- Denominator: (√5)² - (√2)² = 5 - 2 = 3.
- Final answer: (√5 - √2) / 3.
how to solve quadratic simultaneous equations

For y = x + 3
and y = x2 + 5x -2
Then once have x sub and find y. 2 answers for quadratic equation.
how to solve regular simultaneous equations

1. Find x or y
2. sub into other equation
3. solve
rules for linear equality graphs.
Broken lines are used to represent greater or lesser than but not equal (<, >) and straight lines for greater or lesser and equal (⩽, ⩾).
shading is used to represent unwanted regions
How to identify and solve linear, quadratic, cubic and exponential sequences.
Exponential sequences increase by a common ratio from term to term, with the nth term being defined as
a × r(n−1) where a is the first term and r is the value that you multiply by each time.
Patterns in linear sequences are recognized by identifying a constant difference between consecutive terms. The nth term = )difference x n-1) + first term.
For quadratic (nth term = an2 + bn + c ) equal second difference) The coefficient of the n2 term of a quadratic sequence is half of the second difference. Then subtract this from the original sequence and you will have a regular linear equation to solve and make up the rest of the equation.
For cubic (equal third difference) nth term = an3 + bn2 + cn + d first find the third difference. The coefficient for the n3 term is the third difference divided by 6. Take this away and you will be left with a quadratic equation and second difference, solve this for the n2 coefficient and subtract. Then solve the linear and put it together.