# Maths - Formulae and Equations

Mind Map by , created almost 6 years ago

## Mind Map on Maths - Formulae and Equations, created by pondcott on 01/03/2014.

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Maths - Formulae and Equations
1 Using Formula
1.1 A taxi firm charges £0.50 per miles plus a fixed rate of £2.00
1.1.1 It costs £2 + £0.50 to travel 1 mile, It costs £2 + 2 x £0.50 to travel 2 miles ...
1.1.1.1 So travelling 'n' miles will cost £2 + n x £0.50
1.1.1.1.1 The formula is COST = £2 + (n x £0.50)
1.1.1.1.1.1 Substitution
1.1.1.1.1.1.1 What is the cost of hiring the taxi for 16 miles?
1.1.1.1.1.1.1.1 C = £2 + (16 x £0.50)
1.1.1.1.1.1.1.1.1 C = £2 + £8
1.1.1.1.1.1.1.1.1.1 C = £10
1.2 A rectangle has a width of x and a length of 2x
1.2.1 Perimeter = x + x + 2x + 2x
1.2.1.1 P = 6x
2 Re-arranging Symbols
2.1 Collecting like terms
2.1.1 To simplify an expression, we collect like terms
2.1.1.1 4x + 5x - 2 - 2x + 7
2.1.1.1.1 The x terms can be collected together and the numbers can be collected together
2.1.1.1.1.1 So 4x + 5x - 2x = 7x and 7 - 2 = 5
2.1.1.1.1.1.1 This simplifies to 7x + 5
2.1.1.2 x + 5 + 3x - 7 + 9x + 3 - 4x
2.1.1.2.1 So x + 3x + 9x -4x = 9x and 5 + 3 - 7 =1
2.1.1.2.1.1 This simplifies to 9x + 1
2.2 Different Terms
2.2.1 You may have to simplify an equation with many different terms and letters
2.2.1.1 5a + 3b - 3a - 5c + 4b
2.2.1.1.1 Collect like terms
2.2.1.1.1.1 5a - 3a +3b +4b - 5c
2.2.1.1.1.1.1 Simplify all terms
2.2.1.1.1.1.1.1 2a + 7b - 5c
2.3 Multiplying out brackets
2.3.1 3(4x - 7)
2.3.1.1 First Multiply: 3 x 4x = 12x
2.3.1.1.1 Then multiply: 3 x -7 = -21
2.3.1.1.1.1 Therefore: 3(4x - 7) = 12x - 21
2.3.2 Remember whether the numbers are negative or positive
2.3.3 Multiplying out two brackets
2.3.3.1 (x+4)(x+3)
2.3.3.1.1 FOIL
2.3.3.1.1.1 x2 + 7x + 12
2.3.3.2 Brackets and Powers
2.3.3.2.1 (a-5) squared
2.3.3.2.1.1 (a-5)(a-5)
2.3.3.2.1.1.1 a2 - 10a + 25
3 Changing the subject of a formula
3.1 Arrange the formula C=2pi r to make r the subject
3.1.1 Divide both sides by 2pi
3.1.1.1 r = C/ 2pi
3.2 Rearrange the formula V = 4/3 pi r (3)
3.2.1 Multiply by 3
3.2.1.1 3V = 4pi r (3)
3.2.1.1.1 Divide by 4 pi
3.2.1.1.1.1 3V/ 4 pi = r(3)
3.2.1.1.1.1.1 Take the cube root of both sides
3.2.1.1.1.1.1.1 r = cube root of 3V / 4pi
4 Simultaneous Equations
4.1 2x + y = 7
4.1.1 3x - y = 8
4.1.1.1.1 5x = 15 so...
4.1.1.1.1.1 x = 3
4.1.1.1.1.1.1 Substitute in...
4.1.1.1.1.1.1.1 (2 x 3) + y = 7
4.1.1.1.1.1.1.1.1 y = 7-6
4.1.1.1.1.1.1.1.1.1 x = 3, y = 1
4.2 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
5 Equations with Fractions
5.1 x/2 - 4 = 3
5.1.1 +4 so x/2 = 7
5.1.1.1 x2 so x = 14
6 Trial and Improvement
6.1 Always see to how many d.p the answer needs to be
6.1.1 Remember to get as close to the final answer
7 Index Notation
7.1 Powers
7.1.1 a squared = a x a
7.1.1.1 b cubed = b x b x b
7.1.1.1.1 4d squared = 4 x d x d
7.2 Index Laws
7.2.1 When multiplying you add the indices, when subtracting you divide the indices
7.2.1.1 p3 x p7 = p10
7.2.1.1.1 4s3 x 3s2 = 12s5
8 Solving Equations
8.1 Using inverses
8.1.1 x - 6 = 9
8.1.1.1 x = 9+6
8.1.1.1.1 x = 15
8.2 Unknowns on both side
8.2.1 3b + 4 = b + 12
8.2.1.1 -b so 2b + 4 = 12
8.2.1.1.1 -4 so 2b = 8
8.2.1.1.1.1 /2 so b = 4
8.3 Equations with brackets
8.3.1 3(b+2) = 15
8.3.1.1 3 x b + 3 x 2 = 15
8.3.1.1.1 3b +6 = 15
8.3.1.1.1.1 3b = 9
8.3.1.1.1.1.1 b = 3