Edexcel maths revision notes

This is everything i didn't understand in edexcel maths. Hope it helps!

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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 the end of each branch as a list of numbers times together.
NB: Put repeats into powers eg 2*2*3 = 2 squared *3
INDEX LAWS FOR FRACTIONAL, INTEGER AND NEGATIVE POWERS
Anything to the power of a negative is 1 divided by the number to the original power
Anything to the power of a fraction is the root of the number
CONVERT BETWEEN RECURRING DECIMALS AND FRACTIONS
1. Times the decimal by a power of 10 to make the repeating number(s) to the left of the
decimal point.
2. This is 10x.
3. Take 1x away from 10x to get 9x(which should be an integer)
4. Divide this number by 9 to get a fraction.
COMPOUND INTEREST
1. Write down the interest and the number of years.
2. Times the initial money by the interest to the power of the number of years.
3. If reverse, times by the root of the number of years.
REPEATED PROPORTIONAL CHANGE
The same as compound interest
RECIPROCAL AND INVERSE CALCULATION
Reciprocal: 1 over
Inverse: opposite
SURDS AND PI
Rationalising the denominator:
If just a surd on the bottom times by a fraction with that surd on the top and bottom
If an expression(4+root3) times by a fraction with the expression on top and bottom but
reverse the sign in the middle.

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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 of describing a letter
Equation: 1 letter & an equals
SOLVE QUADRATICS
Completing the square:
Solve equation with + and ­ive root:
(x+3)² - 2=0
(x+3)²=2
X+3=+or-2
X=(+or-2)-3
SOLVE INEQUALITIES
1.…read more

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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. Expand and simplify
4. Factorise
5. Sub y into linear(both values) to get x.…read more

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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.…read more

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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 of equal length. Opposite
sides are parallel. Diagonals bisect each other at 90°.
Parallelogram: Diagonally opposite angles are equal. Opposite sides are of equal length.
Opposite sides are parallel. The diagonals bisect each other.…read more

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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.…read more

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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 scale factor is n, volume scale factor is n³
BEARINGS
Bearings are measured from the north line, always in a clockwise direction.
Always described using 3 figures.…read more

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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 quartile,
median and upper quartile from the horizontal axis, and calculate the interquartile range.
Remember to use the total frequency, not the maximum value, on the vertical axis.…read more

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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 x vertical height)
MIDPOINT OF 2 POINTS
EQUATIONS OF CIRCLES
x²+ y²=r²
INTERSECTION OF LINE AND CIRCLE
Same as quadratic simultaneous equations.…read more

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