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Learn why formulas are crucial in mathematics and how to use them effectively. Explore formulas for area of a disc, speed, distance, time, and the famous equation E=mc2. Understand the process of changing the subject in formulas.
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Why have formulas? Area of disc Speed, Distance, Time E = mc2 Changing the subject
Why have formulas? • Formulas are designed to make maths easy. • When presented with a new formula, learn what each letter stands for. Once this is known, the formula can be used. • The important thing about formulas is to use them without worrying about where the formulas come from. This is what they are produced for.
Area of disc = r2 r r
Distance Time Speed = 10 5 D S T = Walk 10 metres (m) across the room in 5 seconds. = 2 m/sec
E = mc2 E = energy measured in joules (J) m = mass measured in kilogrammes (kg) c = speed of light measured in metres per second (m/s) Light moves at about 300,000 km/sec!
Changing the subject of a formula –– E = m c2 (m) Divide both sides by c2
Changing the subject of a formula –– E = m c 2 (c) Divide both sides by m Take the square root of both sides
Changing the subject of a formula e 2 + 2f – ––––– (e) ( ) a + d = u Multiply both sides by u Take 2f from both sides Take the square root of both sides
s = ut + at2 1 2 – Changing the subject of a formula (a) Take ut from both sides
s – ut = at2 1 2 – Changing the subject of a formula (a) Multiply both sides by 2
Changing the subject of a formula (a) 2(s – ut)= at2 Divide both sides by t2
2(s – ut) ––––––– = a t2 Changing the subject of a formula (a) Multiply out top line
2s –2ut ––––––– = a t2 Changing the subject of a formula (a) Simplify
2s 2u –– – –– = a t2 t Changing the subject of a formula (a)