GCSE Changing the Subject Dr J Frost jfrosttiffin

GCSE: Changing the Subject Dr J Frost (jfrost@tiffin. kingston. sch. uk) www. drfrostmaths. com Last modified: 30 th August 2015

Motivation The formula to calculate a temperature in Fahrenheit if we have the temperature in Celsius: How could we find a new formula that allows us to determine the temperature in Celsius given the temperature in Fahrenheit? ?

Basic Skill #1: ‘Undoing’ to Unlock Bro Tip: It doesn’t matter what side the subject is on, provided it’s on its own! ? ?

Basic Skill #2: Subject trapped in a negative term When the subject is within the first argument of a subtraction, it’s easy to ‘release’. ? However, it’s a tiny bit harder if the subject is in the term being subtracted. When the subject is inside a negative term, just add it to both sides. ? ?

Doing it in one step… (if you like) ? This suggests you can swap the thing you’re subtracting with the result. (i. e. Only the thing to the left of the subtraction stays put) Examples: ? ? ?

Exercise 1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 ? ? 15 ? 16 ? ? ? ? ? 17 18 N ?

Basic Skill #3: Subject trapped in a denominator When the subject is in the numerator of a fraction, it’s easy to ‘release’ the subject from the fraction. ? But it’s a bit harder if the subject is in the denominator… In general, whenever you have a fraction in an equation, your instinct should be to multiply both sides by the denominator. ? ? ?

Basic Skill #3: Subject trapped in a denominator ! Isolate the fraction on one side of the equation, then multiply by denominator. 1 2 ? ? 3 ?

Doing it in one step… (if you like) Thus we can swap the thing we’re dividing by and the result. The numerator is left unchanged. ? Examples: ? E 3 E 2 E 1 ? ? ?

Skill #3 b: ‘Cross multiplying’ If you have just a fraction on each side of the equation, you can ‘cross multiply’. Click for Bromanimation Examples: E 1 E 2 ? ?

Exercise 2 1 ? 11 ? 2 3 ? 4 ? 5 ? 6 7 8 9 ? ? 12 13 ? ? ? ? 14 ? N N ?

A* Question (4 marks) Can we think of generic tips that will help us solve these kinds of questions?

Using your solution to the previous question… Tip Why? When fractions present, multiply both sides of the equation by the denominators. Allows us to collect like terms more easily. Immediately! Expand out any brackets. Allows us to collect like terms more easily. ? Collect terms involving new subject on one side of equation. So that we can then factorise. Factorise out new subject. ? ? ? Once we we’ve eliminated fractions. ? When new subject is free from fractions and ? brackets. Now only one occurrence of When terms involving new subject in equation. subject all on one side ? ? of equation.

Another A* Question Make a the subject of the formula: Answer: (Note: According to the Examiner’s Report, only 5% of students got full marks to this question) ?

Challenges ? ? ?

Questions ? Q 1 Q 2 Ed. Excel Nov 2009: ? Ed. Excel Mock Paper ? Q 3 Ed. Excel May 2009: ? Q 6 Ed. Excel Nov 2009: ? Q 7 Ed. Excel Jun 2011: ? Q 8 Ed. Excel Nov 2012: ? Q 4 Ed. Excel Nov 2002: Q 9 Ed. Excel Mar 2012: Q 5 ? O Level 1957: ? Q 10 ?

Final Tips? What tips would you give to someone answering the following questions? Make a the subject of the formula: Make x the subject of the formula:

X = bc/a X = ba/c X = ac/b X = abc

Further Exercises Q 1 ? Q 2 ? Q 3 ? Q 4 ? Q 5 ? Q 6 ? Q 7 ? Q 8 ? Q 9 ?