Revision Topic 5: Rearranging Formulae Changing the suject of simple formulae Introductory example When cooking a roast, the formula that links cooking time (T) ith eight (W) can e ritten as T = 30W + 0. T is called the suject of this formula (as this formula tells you ho to calculate T). If e ished to calculate W for a value of T, e could rearrange the formula to make W the suject. There are to methods of doing this: Method 1: Flochart method We first dra a flochart for the formula (e start ith the letter that e ant to make the suject): W 30 +0 T Reverse the flochart to rearrange the formula: W 30-0 T So the rearranged formula is T 0 W = 30 Method : Algeraic method We can rearrange a formula in the same ay as e ould solve an equation: T = 30W + 0 T 0 = 30W (sutracting 0 from oth sides) T 0 = W (dividing oth sides y 30) So W = T 0 30 30 Example: When a metal rail of length metres is increased in temperature y t C it increases in length. The ne length x metres is given y the formula x = + kt. Make t the suject of the formula. Method 1: Dra a flochart t k + x Reverse the flochart: t k - x x So the rearranged formula is: t or t k x k Dr Duncome Christmas 003 1
Method : x = + kt x = kt x t k (sutracting from oth sides) (dividing oth sides y k) So: t x k Examination Question 1: The heat setting of a gas oven is called its Gas Mark. A Gas Mark, G, may e converted to a temperature F, in degrees Fahrenheit, using the formula: F = 5G + 50. a) Factorise completely 5G + 50. A Gas Mark, G, may e converted to a temperature C, in degrees Celsius, using the formula C = 14G + 11. ) Make G the suject of the formula C = 14G + 11. Examination Question : C = 180R + 000 The formula gives the capacity, C litres, of a tank needed to supply ater to R hotel rooms. Make R the suject of the formula C = 180R + 000. Dr Duncome Christmas 003
Changing the suject of formulae that involve fractions Example 1: The formula for the area A of a triangle is Method 1: Flochart h A. Make h the suject of the formula. h A Reverse h A So the rearranged formula is A h or h A Method : Algeraic method h A First remove the fraction y multiplying y : A h No divide y h: A A h or h Example : Make the suject of the formula: x 5a. Method 1: x -5a x +5a So ( 5a) x or x( 5a) Method : Start y adding 5a to oth sides to isolate the fractional term that contains : 5a x Then multiply oth sides y x to remove the fraction and to get on its on. x( 5a) Dr Duncome Christmas 003 3
Examination Question 3: This formula can e used to convert temperatures from degrees Celsius, C, to degrees Fahrenheit, F: 9 160 F C. 5 a) Use the formula -7 C to degrees Fahrenheit. ) Use the formula to find out at hat temperature F = C. c) Rearrange the formula to give C in terms of F. Examination Question 4: Make p the suject of the formula: 4( p 3) r. 7 Examination Style Question 5: Make y the suject of the formula: k 4 ( y h ). 7 Dr Duncome Christmas 003 4
Rearranging formulae ith squares and square roots Example: A formula is k Rearrange to make the suject. y Method 1: Flochart y Square root π k y square π k So the rearranged formula is k y or k y Method : Algeraic method k y First divide y π to isolate the square root term: k y Square oth sides to remove the square root: k y Multiply y y to get : k y Examination Question 6: The cost C of joining a Sports Clu is given y the formula: 1 C 5 y, 3 here y is the age of the person joining. Express y in terms of C. Dr Duncome Christmas 003 5
Examination Style Question 7: Rearrange the formula y 1 x to make the suject. Harder rearranging equations- algeraic method Example: Make the suject of the formula a t. This is a harder style question as the letter e ish to make the suject of the formula appears on the ottom of the fraction. First multiply oth sides y to remove the fraction: t( ) a Expand rackets: t t a Add t to oth sides to isolate the term involving : t t a Divide y t to get as the suject: t a. t Example Make the suject of the formula: 3y x a. This is a harder example as the term containing the is preceded y a negative sign. Add a to oth sides. This ensures that the term containing the is positive: a 3y x Sutract 3y from oth sides to isolate the term containing the : a x 3y Divide oth sides y a: x 3y a Square root to get : x 3y. a Dr Duncome Christmas 003 6
Examination Question 8: A formula is v a) Calculate the value of v hen x = 14.8, u =.8, and t = 5.. Give your anser correct to 1 decimal place. ) Write don a simple calculation hich could e used to check that your anser to (a) is sensile. c) Make t the suject of the formula. x ut Examination Question 9: Make x the suject of the formula: 4 y x. 5 Examination Style Question 10: Rearrange the formula v u as to make u the suject. Dr Duncome Christmas 003 7