Maths Unit 2 revision cards - NUMBER

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 - 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

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

• 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

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)

• 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 

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)

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.

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

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

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