Grade 10 Maths · Algebra · Paper 1

Exponential Equations Grade 10

Real Exponential Equations past paper questions and answers from 2018 to 2025, with each memo split into the ticks examiners give. Try one, mark yourself, and see exactly which skill cost you marks.

past paper questions: 13 past paper questions
skills: 4 skills
videos: 4 videos

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Question 3.3 · June 2025 · Paper 1 · Provincial · 4 marks

3.3 If

x^{3} + \frac{1}{x ^{3}} = 12

and

x^{2} + \frac{1}{x ^{2}} = 7

.

Determine the value of:

x + \frac{1}{x} + 3

.(4)

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

Exponential Equations skills

Each skill is one thing a memo gives a tick for. Tap one for its own questions, notes and videos.

More Exponential Equations Grade 10 questions and answers

Try each one on paper before you open the memo.

4. Question 2.1.3 · March 2025 · Provincial · 3 marks
2.1 Solve for x:
2.1.3 $3^{5 x - 4} - 729 = 0$ (3)
Show the memo (3 ticks)Memo
1. ✓
  Isolate and convert base $3^{5 x - 4} = 729$
  $3^{5 x - 4} = 3^{6}$
  1 mark · Change the base of a power
2. ✓
  Equate exponents $5 x - 4 = 6$
  1 mark · Solve an exponential equation
3. ✓
  Solve $5 x = 10 ⟹ x = 2$
  1 mark · Solve an exponential equation
5. Question 3.1.3 · June 2024 · Paper 1 · Provincial · 4 marks
3.1 Solve for x:
3.1.3 $16. 2^{x - 1} = (0, 5)^{x - 4}$ (4)
Show the memo (3 ticks)Memo
1. ✓
  Convert to prime bases $2^{4} . 2^{x - 1} = (2^{- 1})^{x - 4}$
  2 marks · Change the base of a power
2. ✓
  Simplify exponents $2^{x + 3} = 2^{- x + 4}$
  1 mark · Use the laws of exponents
3. ✓
  Equate exponents and solve $x + 3 = - x + 4$
  $2 x = 1$
  $x = \frac{1}{2}$
  1 mark · Solve an exponential equation
6. Question 2.1.1 · November 2024 · Paper 1 · Provincial · 4 marks
2.1 Solve for $x$ :
2.1.1 $2. 3^{2 x} = 18$ (4)
Show the memo (2 ticks)Memo
1. ✓
  Isolate the power $3^{2 x} = 9$
  $3^{2 x} = 3^{2}$
  2 marks · Change the base of a power
2. ✓
  Equate exponents and solve $2 x = 2$
  $x = 1$
  2 marks · Solve an exponential equation
7. Question 2.1.2 · March 2023 · Provincial · 3 marks
2.1 Solve for x:
2.1.2 $(\frac{1}{2})^{x - 1} = 128$ (3)
Show the memo (3 ticks)Memo
1. ✓
  Exponential form (base 2) $(2^{- 1})^{x - 1} = 2^{7}$
  1 mark · Change the base of a power
2. ✓
  Simplification $2^{- x + 1} = 2^{7}$
  1 mark · Use the laws of exponents
3. ✓
  Answer $- x + 1 = 7$
  $x = - 6$
  1 mark · Solve an exponential equation
8. Question 3.1.2 · March 2022 · Provincial · 3 marks
3.1 Solve for x in each of the following equations:
3.1.2 $5^{x - 4} + 5^{x} = 626$ (3)
Show the memo (3 ticks)Memo
1. ✓
  Factorise exponent $5^{x} (5^{- 4} + 1) = 626$
  1 mark · Take out a common power
2. ✓
  Solve for base $5^{x} (\frac{1}{625} + 1) = 626$
  $5^{x} (\frac{626}{625}) = 626$
  $5^{x} = 625$
  1 mark · Solve a linear equation
3. ✓
  Solve for x $5^{x} = 5^{4} ⟹ x = 4$
  1 mark · Solve an exponential equation
9. Question 2.1.4 · March 2021 · Provincial · 3 marks
2.1 Solve for x in each of the following equations:
2.1.4 $3 \cdot 7^{x - 1} + 7 = 154$ (3)
Show the memo (3 ticks)Memo
1. ✓
  Isolate the power: $7^{x - 1} = \frac{147}{3}$ $3 \cdot 7^{x - 1} = 147$
  $7^{x - 1} = \frac{147}{3} = 49$
  1 mark · Solve a linear equation
2. ✓
  Prime base $7^{x - 1} = 7^{2}$
  1 mark · Change the base of a power
3. ✓
  Answer $x - 1 = 2 ⟹ x = 3$
  1 mark · Solve an exponential equation
10. Question 2.1.3 · March 2020 · Provincial · 2 marks
2.1 Solve for x:
2.1.3 $5^{2 x - 1} - 1 = 0$ (2)
Show the memo (2 ticks)Memo
1. ✓
  Equate bases $5^{2 x - 1} = 5^{0}$
  1 mark · Change the base of a power
2. ✓
  Solve exponent $2 x - 1 = 0 ⟹ x = \frac{1}{2}$
  1 mark · Solve an exponential equation

Exponential Equations Grade 10 videos

Short lessons from South African teachers first. Videos load only when you tap play, to save your data.

Exponents Grade 10: Change to prime numberKevinmathscience

Exponential Equations grade 10Kevinmathscience

Exponents Grade 10: More than One TermKevinmathscience

11) Rational exponent equationsKevinmathscience

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