The subject of the formula always appears on the Left hand side of the equals sign and is a single term.
For example, in formula of area of a trapezium:
\[A = \frac{a + b}{2} h\]
A is known as the Subject of a formula and it appears on the left side of the equation as a single term.
Here are 5 must-know methods for solving equations to make the subject of the formula.
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1. Making the Subject Involving Add or Subtract
Important tips to make the subject of the formula:
– When you bring over positive, you get negative.
– When you bring over negative, you get positive.
By using inverse operations, you can shift the figures around and receive your answer.
Example
Make b the subject of the formula.
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(a) b + 2 = c b = c – 2 |
(c) 2 – b = c b = 2 – c |
|
(b) c = b + 4 b = c – 4 |
(d) c = 3 – b b = 3 – c |
2. Making the Subject involving Multiply or Divide
Important tips:
– When you bring over multiplication, you get division.
– When you bring over division, you get multiplication.
Make use of inverse operation to equalise the figures and find your Subject.
Example
Make h the subject of the formula.
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(a) 3h = k h = 3/k |
(c) –hk = 2 h = –2/k |
|
(b) k/h = 5 h = k/5 |
(d) 5/k = 4/h 5h = 4k h = 4k/5 |
3. Making the Subject involving Square Root or Cube Root
Important tips:
– To remove square root, you need to square both sides.
– To remove cube root, you need to cube both sides.
Example
Make w the subject of the formula.
|
(a) √2w = x (√2w)2 = x2 2w = x2 w = x2/2 |
(c) 3√(y/w) = z + 2 (3√(y/w) )3 = ( z + 2)3 y/w = ( z + 2)3 w = y/( z + 2)3 |
|
(b) 5(√(w – x) ) = y √(w – x) = y/5 (√(w – x))2 = y2/52 w = y2/25 + x |
(d) 3√w + 1 = z 3√w = z – 1 (3√w)3 = (z – 1)3 w = (z – 1)3
|
4. Making the Subject involving Square or Cube
Important tips:
– To remove square, you need to square root both sides, and you need to include ± on the right hand side.
– To remove cube, you need to cube root both sides, and you do not need to include ±.
Example
Make p the subject of the formula.
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(a) p2 = q + r p = ± 2√( q + r) |
(c) r = p3 – q p3 = r – q p = 3√(r – q) |
|
(b) 5p2 = r p2 = r/5 p = ±2√(r/5) |
(d) p2/5 = q p2 = 5q p = ±2√(5q)
|
5. Making the Subject involving Common Factors/ Remove Brackets
Important tips:
– To remove the common factor, you need to factorise the expression.
– To remove the bracket, you need to expand the expression.
Example
Make c the subject of the formula.
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(a) c + ac = b c(1 + a) = b c = b/(1+a) |
(d) a(c – b) = b ac – ab = b ac = b + ab c = (b + ab)/a |
|
(b) ac + b = bc + d ac – bc = d – b c (a – b ) = d – b c = (d – b)/(a –b) |
(e) bc = d(c –d) bc = dc – d2 dc – bc = d2 c(d – b ) = d2 c = d2/(d – b) |
|
(c) (a + c )/ c = d a + c = dc a = dc – c a = c (d – 1) c = a/(d – 1) |
(f) 1 = (cd + c)/3 3 = c (d + 1) c = 3/(d + 1) |
Master these 5 methods to become proficient in solving questions involving making the subject of the formula.
Last Minute Revision for O Level Math?
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