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!!!

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  • 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.

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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

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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

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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
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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)

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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.
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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
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Transformations

Remember - TERRY

  • Translation
  • Enlargement
  • Rotation
  • Reflection
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Bearings

  • Find where you have to go from and draw a north line
  • Then draw clockwise the angle
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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
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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
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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
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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)
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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
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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 :(

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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
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Comments

natalie

thanks i did maths on monday.. was so easy! x

alex

yh as you can see i havent really started it yet :P but thanks arwa... and the maths paper was really easy! lets hope its the same on friday x

Amritpal Mundra

where's da y in terry

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