General Maths revision

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  • Created on: 15-05-14 18:50
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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
1

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Algebra
- Directly proportional to x means y = kx
- Directly proportional to x² means y = kx²
- Inversely proportional to x means y = k/x
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- If the equation contains fractions, multiply by the LCM
- Linear inequalities: solid black circle means <= or >=, whereas an empty circle just means < or >
- To work out nth term in sequence:
- If sequence is 5, 10, 15
- N = 5, 2n = 10, 3n = 15 (where…read more

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The exterior angle is equal to the sum of the two opposite interior
angles (in the case to the right, d = a + b)
- pentagon = 5 sides, hexagon = six sides
Rhombus Parallelogram- difference between it Trapezium
and a rhombus is only opposite sides of
equal length (in rhombus all sides are)
- Sum of interior angles of polygons of polygon:
180 (n - 2)
- Sum of exterior angles of polygon: always 360º
- Rotation symmetry: if it has no rotation…read more

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Constructing an angle bisector
Constructing a triangle with a compass
- Ratio of lengths = a:b or
- Ratio of areas = a2:b2 or
- Ratio of volumes = a3:b3 or
Statistics
- If p(a) is the probability of an event happening and p(b)
the probability of it not happening, p(b) = 1 - p(a) Constructing a perpendicular bisector
- The probability of independent events a and c
happening is p(a) x p(c)
-The probability of mutually
exclusive events a or d happening
is p(a)…read more

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