Module 12 & 13 revision Flashcards
What is the rule for angles in a semi-circle?
they equal 90°
What is the rule for angles in the same segment?
they are equal
What is the rule for angles at a centre?
they are twice the angle on the edge
What is a cyclic quadrilateral?
What is the rule?
all four corners are on the edge of the circle
diagonally opposite angles add to 180°
What is the rule for alternate segments?
diagonally opposite angles are equal
What is the rule for the radius and a tangent?
the radius and tangent make a right angle
What is the rule for a triangle formed by two radii?
it is isosceles
How do you calculate the upper and lower bounds?
0.5 more and 0.5 less
e.g. 2.5
UB = 2.55
LB = 2.45
How do you calculate the HCF and LCM?
1) draw a frequency tree for both numbers
2) write down all of the numbers circled multiplied together
HCF is the numbers that appear in both (use lowest index)
LCM is all the numbers (use highest index)
e.g. 150 and 250
150 = 5² x 2 x 3
250 = 5³ x 2
HCF = 5² x2 = 50
LCM = 5³ x 2 x 3 = 750
What are the three rules of indicies?
when x, + the indicies
when /, - the indicies
when there are (), multiply indicies
e.g. (2³)³ = 2 to the power of 9
What is the rule of indicies when it is to the power of 0?
it equals 1
What is the rule of indicies when it is to a negative power?
it becomes 1/x to the power of x
e.g. 2-³ = 1/2³
What is the rule of indicies when the power is a fraction? (fractional indicies)
a number to the power of a fraction is the square root of that number
the denominator is the root
the numerator is the power
e.g. 27 to the 2/3 = (the cube root of 27)² = 3² = 9
What is the rule of indicies when there is a fraction to the power of -1?
you just flip the fraction
e.g. (2/3) to the -1 = 3/2
What is the rule of indicies when there is a fraction to the power of x?
you add the power to both numbers in the fraction
e.g. (2/5)² = 2²/5² = 4/25
remember to simplify if possible!!
What is the rule for negative fractional indicies? (a number to the power of a negative fraction)
the same as fractional indicies but you just add 1/x
e.g. 27 to the -1/3 = 1/ the cube root of 27 = 1/3
How do you simplify surds?
find two factors of the number - one must be a square number
e.g. √75 = √25√3 = 5√3
How do you add or subtract surds?
the surds must be the same
it’s like collecting ‘like terms’
e.g. 3√2 + 5√2 = 8√2
2√27 - 3√3 = 6√3 - 3√3 = 3√3
simplify = 2 x√9√3 = 2x3√3 = 6√3
What is the rule for multiplying surds that are the same?
they equal the normal number
e.g. √3 x √3 = √9 = √
√5 x √5 = 5
√2 x √2 = 2 etc
How do you expand double brackets with surds?
expand brackets like normal except :
multiplying the same surd equals the normal number
if you are multiplying two different surds you just multiply the two numbers and add the √
e.g. √3 x √3 = 3
√3 x √2 = √6
you then collect the like terms
e.g. (3 + √2) (5 - √2) = 15 - 3√2 + 5√2 - 2 = 13 + 2√2
(3 - √5) (4 - √2) = 12 - 3√2 - 4√5 + √10
How do you rationalise surds?
it is just multiplying out the surd in the denominator - so multiple the numerator and denominator by the denominator
e.g. 7/√2 = 7/√2 x √2/√2 = 7√2/2
How do you find a percentage of a number without a calculator?
- find 10% of the number (divide by 10)
- find 1% of the number (divide by 100)
- multiply the 10% by the amount of tens in the number
- multiple the 1% by the amount of ones in the number
e.g. find 56% of 8200
10% = 820
1% = 82
820 x 5 = 4100
82 x 6 = 492
4100 + 492 = 4592
How do you find a percentage of a number with a calculator?
% means out of 100 so…
- divide percentage by 100 to get a decimal
- multiply the decimal by the number
e.g. find 56% of 8200
0.56 x 8200 = 4592
How do you calculate percentage increase?
- the original number is 100%
- add the percentage increase onto 100%
- divide by 100 to get a decimal
- multiply the original number by the decimal
e.g. £1552 increasing by 20%
100% + 20% = 120% = 1.2
1552 x 1.2 = £1862.4
How do you calculate percentage decrease?
- the original number is 100%
- minus the percentage decrease from 100%
- divide by 100 to get a decimal
- multiply the original number by the decimal
e.g. £250 decreasing by 15%
100% - 15% = 85% = 0.85
250 x 0.85 = 212.5
How do you write a number out of a number as a percentage?
smaller number/ larger number x 100
e.g. 94 out of 200
94/200 x 100 = 47%
How do you calculate percentage change? (same for increase and decrease)
percentage change = actual change/ original number x 100
e.g. 40 increases to 56, what is the percentage increase
actual increase = 56 - 40 = 16
percentage increase = 16/ 56 x 100 = 40%
How do you calculate compound interest?
total = original amount x multiplier (percentage (as decimal) inc/dec) to the power of the number of years
e.g. £3000 in a bank for 3 years, earns 2% compound interest
total = 3000 x 1.02³ = £3183.62
How do you calculate reverse percentages?
(they are to find the original amount and are usually in sale questions, asks for the cost before)
- write down the answer
- write a ? to represent the original amount
- next to ? x by the percentage multiplier
- rearrange so that you have the answer over the multiplier
- solve
e.g. on sale for £22.05 reduced by 10%, what was the price before?
? x 0.9 = 22.05
22.05/0.9 = £24.50
How do you calculate reverse percentages?
(they are to find the original amount and are usually in sale questions, asks for the cost before)
- write down the answer
- write a ? to represent the original amount
- next to ? x by the percentage multiplier
- rearrange so that you have the answer over the multiplier
- solve
e.g. on sale for £22.05 reduced by 10%, what was the price before?
? x 0.9 = 22.05
22.05/0.9 = £24.50
