Maths Unit 2 revision cards - NUMBER
main points about the number section for maths unit 2 exam (specifically Edexcel modular higher tier paper)
- Created by: Amber
- Created on: 13-11-11 18:32
Prime Numbers
1)Prime numbers DON'T divide by anything EXCEPT 1 and itself
e.g. 11 is a prime no. as its only factors are 1 and 11
2)They end in 1,3,7 or 9 ONLY
BUT - 1 ISN'T a prime number and NOT ALL numbers ending in 1,3,7 or 9 are prime number e.g. 9 - it's not a prime number as a factor of it is 3
3)FINDING PRIME NUMBERS -
- Does it end in 1,3,7,9?
- Find its square root
- List all the primes less than its prime root
- Divide all of these by the number in question
- If none of them dvide cleanly into it the number is a prime number , if they do it ISN'T a prime number
Multiples, Factors and Prime Factors
- MULTIPLES - the times table of a number
e.g. multiples of 4 are: 4,8,12,16,20 etc
- FACTORS - all the numbers that divide into a number
e.g. factors of 10 are: 10, 1, 2, 5
- Finding prime factors - the FACTOR TREE
divide the number by prime numbers until you get prime factors and then express it as a product of its primes
e.g. prime factors of 420 are 2,2,3,5,7 - I would write it as 420=2x2x3x5x7
Lowest Common Multiple(LCM) and Highest Common Fac
LCM - SMALLEST number that will divide by all the numbers in question
- METHOD:
1)List multiples of all the numbers
2)Find the smallest one that is a multiple of all the numbers
HCF - BIGGEST number that will divide into all the numbers in question
- METHOD:
1) List all of the factors of all the number
2) Find tthe biggest in all the lists
Converting fractions, decimals and precentages
- FRACTION to DECIMAL - divide top by bottom
e.g. 1/2 = 1 divided by 2 = 0.5
- DECIMAL to PERCENTAGE - multiply by 100
e.g. 0.5 = 0.5 x 100 = 50%
- PERCENTAGE to DECIMAL - divide by 100
e.g. 25% = 25 divided by 100 = 0.25
Fractions
TYPES...
- RECURRING = have a pattern that repeats for ever e.g. 0.232323232323...
- TERMINTATING = finite decimals e.g. 0.012.
RECURRING DECIMALS to FRACTIONS -
Fraction has the repeating unit on top and the same number of 9's on the bottom
e.g. 0.4444... = 4/9 0.343434... = 34/99 0.124124... = 124/999
(Simplify the fractions if possible)
Fractions
- MULTIPLYING = x top and bottom seperately
e.g. 3/5 x 4/7 = 3x4/5x7 = 12/35
- DIVIDING = turn 2nd fraction UPSIDE DOWN then MULTIPLY
e.g. 3/4 divided by 1/3 = 3/4 x 3/1 = 3x3/4x1 = 9/4
- ADDING and SUBTRACTING = + or - the TOP but only if the bottom is the same
e.g. 1/4 + 2/4 = 3/4 e.g. 3/5 - 2/5 = 1/5
- CANCELLING DOWN - divide top and bottom till they won't go further
- FINDING A FRACTION OF SOMETHING - x by the TOP and DIVIDE by the BOTTOM
- EQUALISING THE DENOMINATOR - find the LCM of the numbers and convert them so that the LCM is the denominator of all the fractions
Ratios
Reducing ratios to thier simplest forms:
divide both numbers by thier highest common factors
e.g. 12:16 - hcf is 4 so its simplest form is - 3:4
Proportional Division:
e.g. share £9100 in the ratio 2:4:7
1) Add up the parts e.g 2:4:7 = 2+4+7 = 13 parts
2) Find the amount of 1 part - divide the amount by the total amount of parts e.g. £9100 divided by 13 = £700
3)Now find the 3 amounts -
2 parts= 2x700=£1400 4 parts = 4x£700 = £2800 7 parts = 7 x 700 = £4900
3) TO CHECK THE ANSWER ADD UP ALL THE PARTS ( £1400 + £2800 + £4900 = £9100)
Percentages
TYPE 1 - "Find x% of y" - e.g. 15% of £46 - 0.15 x 46 = £6.90
TYPE 2 - "Express x as a % of y" - e.g. give 40p as a % of £3.34 -
(40 divided by 334) x 100 = 12%
% CHANGE -
percentage "change" = ("change" divided by original amount) x 100
change could be profit, decrease, increase, error, discount etc.
Rounding Numbers
METHOD -
1) Idenify the position of the LAST DIGIT
2) Then look at the next digit to the RIGHT (decider)
3) If the decider is 5 or more ROUND UP, If the decider is less than 5 ROUND DOWN
SIGNIFICANT FIGURES (S.F.) -
1) The 1st s.f. of any number is simply THE FIRST DIGIT WHICH ISN'T A ZERO.
2) The 2nd,3rd,4th etc s.f.'s follow on immediately after the 1st, REGARDLESS OF BEING 0'S OR NOT.
3) Afrter rounding off the LAST DIGIT, end 0's must be filled up to BUT NOT BEYOND, the decimal point
Bounds and Reciprocals
KEY POINTS...
- UPPER and LOWER bounds - 1/2 the rounded unit up or down
e.g. 2.4cm to the nearest cm UPPER BOUND: 2.45cm LOWER BOUND: 2.35cm
- RECIPROCALS - IS 1 OVER A NUMBER
e.g. reciprocal of 5 = 1/5
- RECIPROCAL of a fraction = turn it upside down
e.g. reciprocal of 3/8 = 8/3
- A number MULTIPLIED by its reciprocal is 1
e.g. 6/7 x7/6 = 1
- 0 has NO RECIPROCAL
Metric to Imperial Conversions
Distance -
8km = 5miles
1 metre = 39 inches
30cm = 1 foot
2.5 cm = 1 inch
Wieght -
1 kg = 2.2 pounds
25 grams = 1 ounce
Volume -
4.5 litres = 1 gallon
1 litre = 1.75 pints
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