gcse: changing the subject dr j frost ([email protected]) last modified: 30 th august...
TRANSCRIPT
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GCSE: Changing the Subject
Dr J Frost ([email protected])www.drfrostmaths.com
Last modified: 30th August 2015
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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?
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Motivation
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Basic Skill #1: βUndoingβ to UnlockMake the subject of the formula. Undo the last thing done to the subject each time
by doing the opposite.
π¦=π₯β2 π₯=π¦+2
π¦=3 π₯+2 π₯=π¦β23
π¦=βπ₯+1 π₯=(π¦β1 )2
π¦= π₯2βπ4
π₯=Β±β4 π¦+π
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Bro Tip: It doesnβt matter what side the subject is on, provided itβs on its own!
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Basic Skill #2: Subject trapped in a negative term
When the subject is within the first argument of a subtraction, itβs easy to βreleaseβ.
π¦=2 πβ3 2 π=π¦ +3?
However, itβs a tiny bit harder if the subject is in the term being subtracted.
π¦=3β2π₯ π¦+2π₯=32 π₯=3β π¦
When the subject is inside a negative term, just add it to both sides.
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Doing it in one step⦠(if you like)
How could you rearrange the numbers in to get another subtraction?
This suggests you can swap the thing youβre subtracting with the result. (i.e. Only the thing to the left of the subtraction stays put)
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Examples:
πβ π₯=π??
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Exercise 1In each case make the subject of the formula. (Set 1 & 2: Only do odd questions)
1
2
3
4
5
6
78910
15
16
17
N
N
18
?
??
?
?
?11
12
13
14
????
??????
????
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π₯=ππ¦β1
Basic Skill #3: Subject trapped in a denominatorWhen the subject is in the numerator of a fraction, itβs easy to βreleaseβ the subject from the fraction.
π¦=π₯π π₯=ππ¦?
But itβs a bit harder if the subject is in the denominatorβ¦
π¦=ππ₯+1 π¦ (π₯+1 )=π
π₯+1=ππ¦
In general, whenever you have a fraction in an equation, your instinct should be to multiply both sides by the denominator.
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Basic Skill #3: Subject trapped in a denominator
! Isolate the fraction on one side of the equation, then multiply by denominator.
π=πβππ₯
ππ₯
+π=π
π=πβππ₯
1 2
3
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+2 first as was last thing done to
Doing it in one step⦠(if you like)
How would you rearrange the numbers in to get another division?
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Examples:
π=π
4β2 π₯4β2 π₯=
ππ
π=ππ₯
πβπ2
π₯+1=π π¦= π¦ 2
π₯+π¦β2
E1 E2E3
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Thus we can swap the thing weβre dividing by and the result. The numerator is left unchanged.
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Skill #3b: βCross multiplyingβ
If you have just a fraction on each side of the equation, you can βcross multiplyβ.
ππ
ππΒΏ Click for
Bromanimation
Examples:Make the subject:
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E1E2
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Exercise 2In each case make the subject of the formula. (Sets 1 & 2: Odd numbered questions)
1
2
3
4
5
6
7
8
12
13
14
N
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??
?
?
?
?
?
?
?
?
?
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9
11
N
?
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(4 marks)
What does it mean to make the βsubject of the formulaβ?
Can we think of generic tips that will help us solve these kinds of questions?
A* Question
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Tip Why? When?
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.
Once we weβve eliminated fractions.
Factorise out new subject. Now only one occurrence of new subject in equation.
When terms involving subject all on one side of equation.
Collect terms involving new subject on one side of equation.
So that we can then factorise.
When new subject is free from fractions and brackets.
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Using your solution to the previous questionβ¦
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(Note: According to the Examinerβs Report, only 5% of students got full marks to this question)
Make a the subject of the formula:
Answer: ?
Another A* Question
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Challenges
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EdExcel Mock Paper
Q4
Q5
EdExcel Mar 2012:
Q3
EdExcel Nov 2012:
Q6
EdExcel May 2009:
Q2EdExcel Nov 2009:
Q7
Q8
EdExcel Nov 2009:
EdExcel Jun 2011:
Q9EdExcel Nov 2002:
O Level 1957:
Q10
Q1 ?
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Questions
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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:
Final Tips?
π¦β2π2=π₯
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π₯=π+1πβ1
Make x the subject
π₯=πβ1π+1
π₯=2πβ12π+1
π₯=1βπ1+π
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π₯=(πβππ )2
π₯=Β±β1βπππ₯=Β±β πβπππ₯=Β±β πβππ
Make x the subject
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x = (a β b)/2a X = (ab β b)/2a X = (2a β b)/abX = (b β 2a)/b
Make x the subject
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X = (b β a)/(ab β b2) X = (b2 + a)/(ab β a) X = (a β b)/(ab + b2)X = (b2 β a)/(ab β a)
Make x the subject
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X = ba/c X = ac/b X = abcX = bc/a
Make x the subject
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Further ExercisesIn all cases make the subject.
Q4
Q5
Q3
Q2
Q1
Q6
Q7
Q8
Q9
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