Grade 10 Maths · Algebra

Change the subject of a formula

Rearrange a formula to make a different letter the subject (for example from A = πr², make r the subject: r = √(A ÷ π)).

past paper questions use it: 42 past paper questions use it
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Literal Equations Grade 10 Maths Equations PART 1Miss Martins Maths and Science

Literal Equations Grade 10 Maths Equations PART 2 EXAM QUESTIONSMiss Martins Maths and Science

3 Gr10 Mathematics - Equations - Literal EquationsJuniorTukkie at the University of Pretoria

The Maths Prof: Changing Subject of FormulaThe Maths Prof

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Question 1.4 · March 2022 · Provincial · 2 marks

Four options are provided as possible answers to the following questions. Choose the correct option.

1.4 The formula for the volume of a cone is

V = \frac{1}{3} π r^{2} h

. The radius,

r

, of the cone may be expressed as:(2)

A $\frac{3 V}{πh}$
B $\frac{V}{3 πh}$
C $3 \frac{V}{πh}$
D $\frac{1}{3} \frac{V}{πh}$

Work it out on paper first. Then mark yourself with the official memo, one tick at a time.

More past paper questions: change the subject of a formula

Work each one out first, then open the memo and check every tick.

3. Question 2.1.3 · March 2021 · Provincial · 3 marks
2.1 Solve for x in each of the following equations:
2.1.3 $g = \frac{1 + 2 x}{x}$ (3)
Show the memo (3 ticks)Memo
1. ✓
  $gx$ on the left-hand side $gx = 1 + 2 x$
  1 mark · Change the subject of a formula
2. ✓
  Factorisation $gx - 2 x = 1$
  $x (g - 2) = 1$
  1 mark · Change the subject of a formula
3. ✓
  Solve for x $x = \frac{1}{g - 2}$
  1 mark · Change the subject of a formula
4. Question 2.1.4 · March 2020 · Provincial · 3 marks
2.1 Solve for x:
2.1.4 $x = y + x y$ (Make x the subject)(3)
Show the memo (3 ticks)Memo
1. ✓
  Isolate x terms $x - x y = y$
  1 mark · Change the subject of a formula
2. ✓
  Factorise x $x (1 - y) = y$
  1 mark · Change the subject of a formula
3. ✓
  Final expression $x = \frac{y}{1 - y}$
  1 mark · Change the subject of a formula
5. Question 1.2 · November 2024 · Paper 1 · National (DBE) · 5 marks
1.2 Solve for $x$ and $y$ simultaneously:
$2 x + y = 3$ and $y^{2} + x y = 2$ (5)
Show the memo (5 ticks)Memo
1. ✓
  Make y the subject of the first equation $y = 3 - 2 x$
  1 mark · Change the subject of a formula
2. ✓
  Substitute into the second equation $(3 - 2 x)^{2} + x (3 - 2 x) = 2$
  1 mark · Solve linear and non-linear simultaneous equations
3. ✓
  Simplify to standard form $4 x^{2} - 12 x + 9 + 3 x - 2 x^{2} - 2 = 0$
  $2 x^{2} - 9 x + 7 = 0$
  1 mark · Write a quadratic in standard form
4. ✓
  Factorise and solve for x $(2 x - 7) (x - 1) = 0$
  $x = \frac{7}{2}$ or $x = 1$
  1 mark · Solve a quadratic by factorising
5. ✓
  Solve for yIf $x = \frac{7}{2}$ : $y = 3 - 2 (\frac{7}{2}) = - 4$
  If $x = 1$ : $y = 3 - 2 (1) = 1$
  1 mark · Solve linear and non-linear simultaneous equations
6. Question 2.4 · March 2019 · Provincial · 2 marks
Determine, without the use of a calculator, the value of $x$ in each of the following:
2.4 $\overset{p}{˙} i x^{2} h = V$ (2)
Show the memo (2 ticks)Memo
1. ✓
  Isolate x squared $x^{2} = \frac{V}{πh}$
  1 mark · Change the subject of a formula
2. ✓
  Solve for x $x = \frac{V}{πh}$
  1 mark · Change the subject of a formula

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