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Starter
Rearrange each of these formulae to make ‘x’ the subject (ie – get the x term
on its own!)
Factorise these expressions
𝑦 = 𝑥 + 5 𝑦 = 3𝑥 + 1 𝑦 =
𝑥 − 5
4
Subtract 5
𝑦 − 5 = 𝑥
Subtract 1
𝑦 − 1 = 3𝑥
𝑦 − 1
3
= 𝑥
Divide by 3
4𝑦 = 𝑥 − 5
4𝑦 + 5 = 𝑥
Multiply
by 4
Add 5
4𝑥 + 8 𝑥2 + 9𝑥 4𝑥2 + 12𝑥
4(𝑥 + 2) 𝑥(𝑥 + 9) 4𝑥(𝑥 + 3)
4 is a
common
factor
x is a
common
factor
4x is a
common
factor
Changing the subject (2)
• We saw earlier in the year how to change the
subject of a formula
• Remember that this follows the same kind of
process as solving an equation, in that you
move terms across from one side to the other
• Today we will extend this process to
questions with a few more steps in
Changing the subject (2)
• Rearrange the following equation to make a the
subject.
6a2 =
÷ 6
12b
√
a2 = 2b
a = 2b
(Square root)
Changing the subject (2)
• Rearrange the following equation to make r the
subject.
x 3
÷ 4π
3√
𝑉 =
4
3
𝜋𝑟3
3𝑉 = 4𝜋𝑟3
3𝑉
4𝜋
= 𝑟3
3 3𝑉
4𝜋
= 𝑟
(Cube root)
Changing the subject (2)
• Rearrange the following equation to make π the
subject.
x 3
÷ 4r3
𝑉 =
4
3
𝜋𝑟3
3𝑉 = 4𝜋𝑟3
3𝑉
4𝑟3
= 𝜋
y( +
a
Changing the subject (2)
• Rearrange the following equation to make y the
subject.
x = ay + by
x = b)
x = y
(a + b)
Factorise
Divide by (a + b)
You cannot make a letter the
subject if it appears in
multiple terms
 In this type of question
you will need to factorise at
some point!
Changing the subject (2)
• Rearrange the following equation to make b the
subject.
4a + 2b =
- ab
ab + 6
4a + 2b - ab = 6
- 4a
2b - ab = 6 – 4a
Factorise
b(2 – a) = 6 – 4a
Divide by (2 – a)
b = 6 – 4a
(2 – a)
Try to collect
all terms with
the intended
subject on the
same side
first
Changing the subject (2)
• Rearrange the following equation to make d the
subject.
c =
3d
Multiply by (d + 2)
Expand the bracket
d + 2
c(d + 2) = 3d
cd + 2c = 3d
2c = 3d – cd
- cd
2c = d(3 – c)
Factorise
2c = d
3 - c
Divide by (3 – c)
Plenary
Summary
• We have continued re-arranging
equations
• We have used factorising and
square/cube rooting in this

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2) Changing the Subject - Harder.pptx

  • 1.
  • 2. Starter Rearrange each of these formulae to make ‘x’ the subject (ie – get the x term on its own!) Factorise these expressions 𝑦 = 𝑥 + 5 𝑦 = 3𝑥 + 1 𝑦 = 𝑥 − 5 4 Subtract 5 𝑦 − 5 = 𝑥 Subtract 1 𝑦 − 1 = 3𝑥 𝑦 − 1 3 = 𝑥 Divide by 3 4𝑦 = 𝑥 − 5 4𝑦 + 5 = 𝑥 Multiply by 4 Add 5 4𝑥 + 8 𝑥2 + 9𝑥 4𝑥2 + 12𝑥 4(𝑥 + 2) 𝑥(𝑥 + 9) 4𝑥(𝑥 + 3) 4 is a common factor x is a common factor 4x is a common factor
  • 3. Changing the subject (2) • We saw earlier in the year how to change the subject of a formula • Remember that this follows the same kind of process as solving an equation, in that you move terms across from one side to the other • Today we will extend this process to questions with a few more steps in
  • 4. Changing the subject (2) • Rearrange the following equation to make a the subject. 6a2 = ÷ 6 12b √ a2 = 2b a = 2b (Square root)
  • 5. Changing the subject (2) • Rearrange the following equation to make r the subject. x 3 ÷ 4π 3√ 𝑉 = 4 3 𝜋𝑟3 3𝑉 = 4𝜋𝑟3 3𝑉 4𝜋 = 𝑟3 3 3𝑉 4𝜋 = 𝑟 (Cube root)
  • 6. Changing the subject (2) • Rearrange the following equation to make π the subject. x 3 ÷ 4r3 𝑉 = 4 3 𝜋𝑟3 3𝑉 = 4𝜋𝑟3 3𝑉 4𝑟3 = 𝜋
  • 7. y( + a Changing the subject (2) • Rearrange the following equation to make y the subject. x = ay + by x = b) x = y (a + b) Factorise Divide by (a + b) You cannot make a letter the subject if it appears in multiple terms  In this type of question you will need to factorise at some point!
  • 8. Changing the subject (2) • Rearrange the following equation to make b the subject. 4a + 2b = - ab ab + 6 4a + 2b - ab = 6 - 4a 2b - ab = 6 – 4a Factorise b(2 – a) = 6 – 4a Divide by (2 – a) b = 6 – 4a (2 – a) Try to collect all terms with the intended subject on the same side first
  • 9. Changing the subject (2) • Rearrange the following equation to make d the subject. c = 3d Multiply by (d + 2) Expand the bracket d + 2 c(d + 2) = 3d cd + 2c = 3d 2c = 3d – cd - cd 2c = d(3 – c) Factorise 2c = d 3 - c Divide by (3 – c)
  • 11. Summary • We have continued re-arranging equations • We have used factorising and square/cube rooting in this