Grade 11 Maths · Algebra · Paper 1

Exponents and Surds Grade 11

Real Exponents and Surds past paper questions and answers from 2024 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: 95 past paper questions
skills: 10 skills
videos: 10 videos

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Question 1.2 · March 2025 · Provincial · 2 marks

1.2 Simplify without using a calculator:

384 + 24

(2)

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

Exponents and Surds skills

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

More Exponents and Surds Grade 11 questions and answers

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4. Question 1.1.4 · May/June 2024 · Paper 1 · National (DBE) · 4 marks
1.1 Solve for x:
1.1.4 $5^{2 x} - 5^{x} = 0$ (4)
Show the memo (3 ticks)Memo
1. ✓
  Common factor $5^{x} (5^{x} - 1) = 0$
  2 marks · Take out a common power
2. ✓
  Rejecting $5^{x} = 0$ $5^{x} \neq = 0$ or $5^{x} = 1$
  1 mark · Solve an exponential equation
3. ✓
  Solve for x $x = 0$
  1 mark · Solve an exponential equation
5. Question 1.2.1 · March 2025 · Provincial · 5 marks
1.2 Given: $x - 3 = \frac{2}{x}$
1.2.1 Solve for $x$ .(5)
Show the memo (5 ticks)Memo
1. ✓
  Squaring both sides $x \cdot x - 3 = 2$
  $x (x - 3) = 2^{2}$
  1 mark · Solve a surd equation
2. ✓
  Standard form $x^{2} - 3 x - 4 = 0$
  1 mark · Write a quadratic in standard form
3. ✓
  Factors $(x - 4) (x + 1) = 0$
  1 mark · Factorise a trinomial
4. ✓
  Valid answer $x = 4$
  1 mark · Solve a quadratic by factorising
5. ✓
  Rejection of x = -1 $x \neq = - 1$ ( $x$ is undefined for $x = - 1$ )
  1 mark · Check solutions of a surd equation
6. Question 2.1.1 · March 2025 · Provincial · 3 marks
2.1 Evaluate the following expressions, without using a calculator:
2.1.1 $\frac{121 x ^{2} - 3 27 x ^{3}}{- 4 ^{0} x}$ (3)
Show the memo (3 ticks)Memo
1. ✓
  Numerator: square root and cube root $121 x^{2} - 3 27 x^{3} = 11 x - 3 x$
  1 mark · Simplify and combine surds
2. ✓
  Denominator $- 4^{0} x = - 1 x$
  1 mark · Use the laws of exponents
3. ✓
  Final simplification $\frac{8 x}{- x} = - 8$
  1 mark · Simplify an algebraic fraction
7. Question 1.1.4 · March 2025 · Paper 1 · Provincial · 5 marks
1.1 Solve for $x$ :
1.1.4 $2 x + x + 1 = 1$ (5)
Show the memo (5 ticks)Memo
1. ✓
  Isolate the surd $x + 1 = 1 - 2 x$
  1 mark · Solve a linear equation
2. ✓
  Square both sides $(x + 1)^{2} = (1 - 2 x)^{2}$
  $x + 1 = 1 - 4 x + 4 x^{2}$
  1 mark · Solve a surd equation
3. ✓
  Standard form $4 x^{2} - 5 x = 0$
  1 mark · Write a quadratic in standard form
4. ✓
  Common factor $x (4 x - 5) = 0$
  1 mark · Take out a common factor
5. ✓
  Rejecting $x = \frac{5}{4}$ $x = 0$ or $x = \frac{5}{4}$
  Check: $x = \frac{5}{4}$ is invalid ( $1, 5 \neq = - 1, 5$ )
  Answer: $x = 0$
  1 mark · Check solutions of a surd equation
8. Question 2.1.1 · March 2025 · Paper 1 · Provincial · 5 marks
2.1 Simplify the following without using a calculator. Your answers must be free of negative exponent and irrational exponents.
2.1.1 $\frac{3 ^{2 n + 2} - 9 ^{n - 1}}{2 \cdot 3 ^{2 n + 1}}$ (5)
Show the memo (4 ticks)Memo
1. ✓
  Convert bases to prime numbers $\frac{3 ^{2 n + 2} - ( 3 ^{2} ) ^{n - 1}}{2 \cdot 3 ^{2 n + 1}}$
  $= \frac{3 ^{2 n + 2} - 3 ^{2 n - 2}}{2 \cdot 3 ^{2 n + 1}}$
  1 mark · Change the base of a power
2. ✓
  Common factor $= \frac{3 ^{2 n} ( 3 ^{2} - 3 ^{- 2} )}{2 \cdot 3 ^{2 n} \cdot 3}$
  1 mark · Take out a common power
3. ✓
  Simplification $= \frac{9 - \frac{1}{9}}{6}$
  $= \frac{\frac{80}{9}}{6}$
  1 mark · Use the laws of exponents
4. ✓
  Answer $= \frac{40}{27}$
  2 marks · Use the laws of exponents
9. Question 1.1.4(b) · November 2025 · Paper 1 · Provincial · 4 marks
1.1 Solve for $x$ :
1.1.4 Given: $f (x) = \frac{x + 14}{x + 2}$
1.1.4(b) Solve for $x$ , if $f (x) = 1$ (4)
Show the memo (4 ticks)Memo
1. ✓
  Isolating the surd $\frac{x + 14}{x + 2} = 1$
  $x + 14 = x + 2$
  1 mark · Solve a linear equation
2. ✓
  Squaring both sides $x + 14 = x^{2} + 4 x + 4$
  1 mark · Solve a surd equation
3. ✓
  Factors $x^{2} + 3 x - 10 = 0$
  $(x + 5) (x - 2) = 0$
  1 mark · Factorise a trinomial
4. ✓
  Answer with choice ( $- 5$ excluded) $x \neq = - 5$ or $x = 2$
  1 mark · Check solutions of a surd equation
10. Question 2.1.1 · June 2024 · Paper 1 · Provincial · 3 marks
2.1 Simplify WITHOUT using a calculator:
2.1.1 $(2^{- 1} + 3^{- 1})^{2}$ (3)
Show the memo (3 ticks)Memo
1. ✓
  Convert exponents $(\frac{1}{2} + \frac{1}{3})^{2}$
  1 mark · Use the laws of exponents
2. ✓
  Add fractions $(\frac{3 + 2}{6})^{2} = (\frac{5}{6})^{2}$
  1 mark · Calculate with common fractions
3. ✓
  Final answer $\frac{25}{36}$
  1 mark · Calculate with common fractions

Exponents and Surds Grade 11 videos

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

Exponents Grade 8 | All Laws CombinedKevinmathscience

Exponents Grade 10: Change to prime numberKevinmathscience

Exponential Equations grade 10Kevinmathscience

Exponents Grade 10: More than One TermKevinmathscience

11) Rational exponent equationsKevinmathscience

Grade 11 Exponents: Rational exponents | Writing roots as powers with rational exponentsMiss Martins Maths and Science

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