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461520
Maths - Formulae and Equations
Description
Mind Map on Maths - Formulae and Equations, created by pondcott on 03/01/2014.
Mind Map by
pondcott
, updated more than 1 year ago
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Created by
pondcott
over 10 years ago
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Resource summary
Maths - Formulae and Equations
Using Formula
A taxi firm charges £0.50 per miles plus a fixed rate of £2.00
It costs £2 + £0.50 to travel 1 mile, It costs £2 + 2 x £0.50 to travel 2 miles ...
So travelling 'n' miles will cost £2 + n x £0.50
The formula is COST = £2 + (n x £0.50)
Substitution
What is the cost of hiring the taxi for 16 miles?
C = £2 + (16 x £0.50)
C = £2 + £8
C = £10
A rectangle has a width of x and a length of 2x
Perimeter = x + x + 2x + 2x
P = 6x
Re-arranging Symbols
Collecting like terms
To simplify an expression, we collect like terms
4x + 5x - 2 - 2x + 7
The x terms can be collected together and the numbers can be collected together
So 4x + 5x - 2x = 7x and 7 - 2 = 5
This simplifies to 7x + 5
x + 5 + 3x - 7 + 9x + 3 - 4x
So x + 3x + 9x -4x = 9x and 5 + 3 - 7 =1
This simplifies to 9x + 1
Different Terms
You may have to simplify an equation with many different terms and letters
5a + 3b - 3a - 5c + 4b
Collect like terms
5a - 3a +3b +4b - 5c
Simplify all terms
2a + 7b - 5c
Multiplying out brackets
3(4x - 7)
First Multiply: 3 x 4x = 12x
Then multiply: 3 x -7 = -21
Therefore: 3(4x - 7) = 12x - 21
Remember whether the numbers are negative or positive
Multiplying out two brackets
(x+4)(x+3)
FOIL
x2 + 7x + 12
Brackets and Powers
(a-5) squared
(a-5)(a-5)
a2 - 10a + 25
Changing the subject of a formula
Arrange the formula C=2pi r to make r the subject
Divide both sides by 2pi
r = C/ 2pi
Rearrange the formula V = 4/3 pi r (3)
Multiply by 3
3V = 4pi r (3)
Divide by 4 pi
3V/ 4 pi = r(3)
Take the cube root of both sides
r = cube root of 3V / 4pi
Simultaneous Equations
2x + y = 7
3x - y = 8
Add the equations
5x = 15 so...
x = 3
Substitute in...
(2 x 3) + y = 7
y = 7-6
x = 3, y = 1
If the item you want to remove is two positives or two negatives you subtract, if they are one positive and one negative you add
Equations with Fractions
x/2 - 4 = 3
+4 so x/2 = 7
x2 so x = 14
Trial and Improvement
Always see to how many d.p the answer needs to be
Remember to get as close to the final answer
Index Notation
Powers
a squared = a x a
b cubed = b x b x b
4d squared = 4 x d x d
Index Laws
When multiplying you add the indices, when subtracting you divide the indices
p3 x p7 = p10
4s3 x 3s2 = 12s5
Solving Equations
Using inverses
x - 6 = 9
x = 9+6
x = 15
Unknowns on both side
3b + 4 = b + 12
-b so 2b + 4 = 12
-4 so 2b = 8
/2 so b = 4
Equations with brackets
3(b+2) = 15
3 x b + 3 x 2 = 15
3b +6 = 15
3b = 9
b = 3
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