# Maths, Edexcel, Whole course

my non-calculator exam was the other day and my calculator is on thursday. So i decided to upload what i wrote in my notebook onto here so hopefully someone will find it useful :D good luck!!!

- Created by: alex
- Created on: 08-06-10 20:23

## Fractions

- Multiplying: Multiply top and bottom separetly

e.g 3/5 X 4/7 = 3X4/5X7 = 12/35

- Dividing: Turn the 2nd fraction upside down, then multiply

e.g 3/7 divided by 9/10 = 3/ 7X 10/9 = 3X10/7X9 = 30/63 = 10/21

- Finding a fraction of something: Multiply the something by the top of the fraction and then divide it by the bottom

e.g 9/20 of $360 = 9X360 divided by 20 = $3240 divided by 20 =$162

- Turning recurring decimals into fractions: the fraction always has the repeating unit on the top and the same number of nines on the bottom

e.g 0.44444 = 4/9, 0.3434 = 34/99, 0.1241 = 124/999 etc.

## Ratios

- Treat ratios like fractions

e.g 3:4 = 3/4

- If ratio isn't a whole number, you need to times both sides equally so they make a whole number

e.g 1 1/4:3 1/2 X both sides by 4 = 5:14

- To reduce a ratio to the form 1:n or n:1, you have to divide both sides by the smallest number

e.g 3:56 divided both sides by 3 = 1:18.7

## Proportional Division

- You have to add up the parts, find the amount for one part (divide total amount by number of parts), then find the three amounts

e.g $9100 is to be split in the ratio 2:4:7

1. 2+4+7=13

2. $9100 divide by 13 = $700

3. 2 parts = $1400, 4 parts = $2800, 7 parts = $4900

## Percentages

- Find x% of y. Multiply!

e.g Find 15% of $46 = 0.15 x 46 = $6.90

- Express x as a percentage of y. Divide and times 100!

e.g Give 40p as a percentage of $3.34 = 40 divided by 334 x 100 = 12%

- Price increase or decrease.

e.g A house increase in value by 20% to $72,000. Find what it was worth before the rise.

$72,000 = 120%

divideby 120: $600 = 1%

x 100: $60,000 = 100%

- Percentage change = change/ original x 100

## The nth term

- Common difference: dn+(a-d)

e.g Nth term? 5,8,11,14

find the difference (d) which is 3

find (a) which is just the first number in the sequence

then add it into the equation - 3n+5-3 = 3n+2

- Changing difference: a+(n-1)d+1/2(n-1)(n-2)c

e.g Nth term? 2,4,9,14

find the difference (d), first number (a) and the change between numbers (c)

2+(n-1)3+1/2(n-1)(n-2)+1 = 2+3n-3+1/2 n²-1/2 n+1

= 1/2n² +1 1/2n = 1/2n (n+3)

## Geometry terms

- Angles on a straight line add up to 180º
- Angles in a 4-sided shape add up to 360º
- Exterior angle of a triangle = sum of opposite interior angles
- Exterior angle = 360º/no. of sides
- Interior angle = 180º - exterior angle
- Whenever one line crosses the two parallel lines the two bunches of angles are the same.
- In a Z shape, alternate angles are equal
- In a C shape supplementary angles add up to 180º
- In a U shape supplementary angles add up to 180º
- In a F shape corresponding angles are equal.

## Circle geometry

- Angle in a semicircle = 90º
- Tangent and radius meet at 90º
- Isosceles triangles are made from two radii
- Chord bisectors are diameters
- Angles in the same segment are equal
- Angle at the centre is twice that at the edge
- Opposite angles of a quadrilateral add up to 180º
- Angle in opposite segments are equal

## Transformations

Remember - TERRY

- Translation
- Enlargement
- Rotation
- Reflection

## Bearings

- Find where you have to go from and draw a north line
- Then draw clockwise the angle

## Trigonometry

- if you want to find an angle use the inverse sign! -1
- Shops Offer Hot Chocolate And Hot Tea On Afternoons - SOHCAHTOA
- Angle of depression is the angle downwards from the horizontal
- Angle of elevation is the angle upwards from the horizontal

## Graphs of Sin, Cos and Tan

- Sin - Looks like a wave and goes from 0º - 360º
- Cos - Looks like a bucket and goes from 0º - 360º
- When sin and cos are stretched they look the same
- Tan - is not limited so it goes to infinity, it is repeated every 180º

## Graphs!

- Gradient = Change in Y / Change in X
- When drawing a straight line graph, first change the order so y is first, then the gradient and then when it reaches (hits the graph) ie. y=mx+x

## Probability

- Always between 0 and 1
- If it is 0 it means it will never happen
- If it is 1 it means it will definitely happen
- Probabilities always add up to 1
- The AND rule - P(A&B) = P(A) X P(B)
- The OR rule - P(AorB) = P(A) + P(B)

## Frequency tables

- The mean is worked out by using : 3rd row total / 2nd row total
- The 3rd row = 1st row x 2nd row
- Probability of an event = Number of times it has happened / number of trials

## Solving equations

- Get rid if the square roots by squaring both sides
- Move the bottom to both the front and the end of the equation
- Multiply out brackets
- Collect subject terms (x/y) from one side of =x and none subject terms on the other side
- Simplify
- Divide B by A ( x = B/A)

The example is impossible to write on here sorry :(

## Simultaneous Equations

- Re-arrange into ax+by = c, label equations 1 & 2
- Then match up either x or y, then re-label 3 & 4
- Add or subtract the two equations (both the same = subtract) (both different = add)
- Simplify
- Substitute back into equation 1 & simplify
- Substitute x & y into equation 2 & simplify

e.g 2x = 6-4y & -3-3y = 4x

- 2x + 4y =6 - label 1 -4x-3y=3 - label 2
- label 1 + label 2 = 4x + 8y = 12 - label 3 -4x-3y=3 - label 4
- 4x + 8y = 12 + -4x - 3y = 3 0x + 5y = 15 y=3
- 2x + 4x3 = 6 2x+12 = 6 2x-6 x= -3
- -4x x -3 -3 x 3 = 3 12-9 = 3

## Related discussions on The Student Room

- 2022 Edexcel Maths GCSE (Higher) Checklist »
- A Level Maths Pearson/edexcel textbook »
- igcse edexcel higher maths- what topics to focus on? »
- Differentiation »
- AS Maths edexcel 2023 »
- What is necessary for me to study to sit for STEP exam? »
- A Level maths »
- here we go againnn........ »
- Maths vs Maths and Physics »
- Further maths or computer science? »

## Comments

Report

Report

Report