GCSE NON CALC TOPICS

BIDMAS

  • Brackets
  • Indices (powers)
  • Divide
  • Multiply
  • Add
  • Subtract
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Fractions

Simplest Form- When you find the smallest number that goes into both the top and bottom,

Example: 6/9 divided by 3 is 2/3.

Adding Fractions- If both the bottom numbers are the same, you just add the top numbers.

Example: 2/3 + 1/3 = 3/3 = 1

If the bottom numbers are different, you need to find a number that both the numbers go into.

Example: 2/3 +1/4. 3 and 4 both go into 12. So you will have 8/12 + 3/12 = 11/12

Subtracting Fractions- Same method as adding fractions.

Example: 2/3 - 1/4. 3 and 4 both go into 12. so you will have 8/12 - 3/12 = 5/12

Multiplying Fractions- Times across. Top x Top. Bottom x Bottom.

Divide Fractions- Flip the Second Number Upsidedown and Times across.

2/3 divided by 1/4. 2/3 x 4/1.    2 x 4 = 8. 3 x1 =3.   =8/3 = 2 and 2/3.

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Area and Circumference of Circles

To work out the Circumference= Pi x Diameter   or (2xRadius) x Pi.

To work out the Area of Circle = (Pi x Radius) x (Pi x Radius)

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Area of Compound Shapes

(http://3.bp.blogspot.com/-HbbTiM0ILFw/Tq54yOLpOXI/AAAAAAAAABM/T2zE6lGiUdo/s1600/CompoundArea.jpg)

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Rotation of Shapes

(http://www.11plusforparents.co.uk/Maths/images/data/rot1.gif) You just need to rotate from centre of rotation.

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Reflection of Shapes.

(http://slideplayer.com/5754835/19/images/23/Reflecting+shapes+Use+this+activity+to+dynamically+prove+the+result+on+the+previous+slide..jpg)

Just flip (mirror image) it over the mirror line given.

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Conversions

1 metre =1,000 millimetres

1\text{ metre} = 100\textbf{ centi}\text{metres}1 metre=100 centimetres

1,000\text{ metres} = 1\textbf{ kilo}\text{metres}1,000 metres=1 kilometre

Centimetres = 10 Millimetres

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Data

  • Discrete data (or discrete variables) can only take certain values, e.g. shoe sizes increase in increments of a half: 7, 7.5, 8, 8.5, and so on. You can’t buy size 7.65 shoes.
  • Continuous data (or continuous variables) can take any value, e.g. the height of a person can be any number of centimetres: 182cm, 173.4cm, 167.892cm, and so on.
  • Primary data is data that you collect first-hand.
  • Secondary data is data that was collected in the past by other people.
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Density Mass Volume

Density = Mass Divided by Volume

Mass= Density x Volume

Volume = Density x Mass

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Mean, Mode, Median and Range

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Percentages

To find a percentage always divide the original number by 100. then times by the amount.

Example: Find 20% of 150.

150 divided by 100 = 1.5

1.5 x 20 =30. 

To make a percentage decimal is simple.

20 % -0.20

35% - 0.35 etc.

To make a percentage a fraction. just put the number over a 100.

20% = 20/100 =2/10 = 1/.

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Ratio Question

Example: Liv and Laura win a lottery of £350,000 and decide to split their winnings according to the ratio 3:43:4. Work out how much each person receives.

In total, this ratio is made up of 

3+4=73+4=7 parts. This means that Liv receives \dfrac{3}{7}73 of the total winnings, and Laura receives \dfrac{4}{7}74 of the total. So, we get

\text{Liv’s winnings }=\dfrac{3}{7}\times350,000=\pounds150,000Liv’s winnings =73×350,000=£150,000

\text{Laura’s winnings }=\dfrac{4}{7}\times350,000=\pounds200,000Laura’s winnings =74×350,000=£200,000

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