# General Maths revision

- Created by: Sophie
- Created on: 15-05-14 18:50

First 476 words of the document:

GCSE

Number In percentage questions you may

- Converting recurring decimals to fractions: have to:

- Find a given percentage of an

No. of repeating digits Multiply by Divide by amount.

- Work out a percentage when given

1 (e.g. 0.5) 10 (5) 9 (5/9)

2 amounts.

2 (e.g. 0.45) 100 (45) 99 (45/99) - Work backwards from a

percentage increase or decrease

3 (e.g. 0.345) 1000 999 (reverse percentages).

- Find a cumulative change.

- rp x rq = rp+q

- (rq)p = rpq Sets

- More index rules on revision list : "is an element of,": "is not an

- Adding 15% to a price: price x 1.15 element of"

- Taking away the 15% extra tax: taxed price ÷ 1.15 To define: B = {2, 4, 6, 8, 10} or C = {x :

- Taking away 15% of an original price: price ÷ x is an even integer, 1 < x < 11}, n(B) = 5

- Percentage change - new/old OR change/original We can say B=C as they contain the

- Simple interest is interest only on the original amount same numbers

- Compound interest is interest on whatever amount is in the Empty sets: { } or Ø

account at the end of the year : "is a subset of," : "is not a subset

of"

- To rationalise the denominator of : U or E: denotes universal set

- LCM and HCF: Complement (e.g. B'): everything not

- 24's prime factors: (2 x 2 x 2) x (3) in B

- 36's prime factors: (2 x 2) x (3 x 3) Intersection: , Union:

- Highest Common Factor: 2 x 2 x 3 = 12

- Lowest Common Multiple: 24 has the most 2s (3) and 36 has the most 3s (2), so: (2 x 2 x 2)

x (3 x 3) = LCM = 72

- 90's prime factors: (2) x (3 x 3) x (5)

- 175's factors: 1 x 175 = 1 x 5 x 35 = 1 x 5 x 7 x 5

- 175's prime factors: (5 x 5) x (7)

- Highest Common Factor: 5

- Lowest Common Multiple: (2) x (3 x 3) x (5 x 5) x (7) = 3150

- A sack of sand weighs 20 kg measured to the nearest kg. It is used to fill bags that will contain

250 g of sand measured to the nearest 10 g. Work out the maximum number of bags that can

be filled.

UB LB -For maximum number of filled bags, we

want the most sand and the smallest bags

Of sand sack 20.5kg = 20500g 19.5kg = 19500g -Maximum sand weight ÷ smallest bag

weight

Of bags 255g 245g -205000 ÷ 245 = 83.67...

-As it asks for the maximum number of

bags FILLED, we round down to 83

- Standard form:

- r x 10n where 0 < r < 10

- (7.93 x 108) - (4.2 x 106) = (793 x 106) - (4.2 x 106) = (793 - 4.2) x 106 = 7.8... x 106

- (7.93 x 108) ÷ (4.2 x 106) = (7.93 ÷ 4.2) x (108 ÷ 106) = 1.89 x 10²

- If scale factor is 1:5, area factor is 1:5²

- 1m² = (100x100)cm² = 10000cm²

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