Grade 10 Maths · Algebra · Paper 1

Number System Grade 10

Real Number System past paper questions and answers from 2015 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: 40 past paper questions
skills: 5 skills
videos: 5 videos

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Question 1.1 · March 2025 · Provincial · 2 marks

1.1 Indicate between which two consecutive integers

47

lie.(2)

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

Number System skills

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

More Number System Grade 10 questions and answers

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4. Question 1.2 · March 2023 · Provincial · 2 marks
1.2 Between which two consecutive natural numbers does $340$ lie. Show all your working out and do so without the use of a calculator.(2)
Show the memo (2 ticks)Memo
1. ✓
  Find perfect cubes $327 < 340 < 364$
  1 mark · Place a surd between two integers
2. ✓
  Determine integers $3 < 340 < 4$
  1 mark · Place a surd between two integers
5. Question 1.4 · March 2022 · Provincial · 2 marks
1.4 Determine two positive integers between which $33$ lies.(2)
Show the memo (2 ticks)Memo
1. ✓
  Identify perfect squares $25 < 33 < 36$
  1 mark · Place a surd between two integers
2. ✓
  State integers5 and 6
  1 mark · Place a surd between two integers
6. Question 1.1 · March 2022 · Provincial · 2 marks
Four options are provided as possible answers to the following questions. Choose the correct option.
1.1 If $k$ is a negative single digit integer, which of the following is NOT a possible value of $2 - k$ ?(2)
1. A 3
2. B 4
3. C 10
4. D 12
Show the memo (1 tick)Memo
1. ✓
  Analyze rangeSingle digit negative integers are $- 1$ to $- 9$ .
  Max value: $2 - (- 9) = 11$ .
  12 is not possible.
  Answer: D
  2 marks · Calculate with integers
7. Question 3.2.1 · March 2019 · Provincial · 2 marks
3.2 Given: $P = \frac{- 20 x}{1 - 3 x}$ where $x \in R$
3.2.1 For which value(s) of $x$ is $P$ undefined?(2)
Show the memo (2 ticks)Memo
1. ✓
  Identify denominator constraint $1 - 3 x = 0$
  1 mark · Find undefined or non-real values
2. ✓
  Solve for x $3 x = 1$
  $x = \frac{1}{3}$
  1 mark · Find undefined or non-real values
8. Question 1.4 · March 2017 · Provincial · 2 marks
1.4 Without using a calculator, determine between which two consecutive integers $- 13$ lies.(2)
Show the memo (2 ticks)Memo
1. ✓
  Identify perfect squares $9 < 13 < 16$
  $3 < 13 < 4$
  1 mark · Place a surd between two integers
2. ✓
  Apply negative sign $- 4 < - 13 < - 3$
  Integers are -4 and -3
  1 mark · Place a surd between two integers
9. Question 6.1 · March 2016 · Provincial · 2 marks
The area of a square is $45$ cm $^{2}$ .
6.1 Is the length of the side of the square a rational number or an irrational number? Explain your answer.(2)
Show the memo (2 ticks)Memo
1. ✓
  Identify number typeIrrational number
  1 mark · Classify a real number
2. ✓
  Explanation45 is not a perfect square (so $45$ is non-terminating, non-recurring)
  1 mark · Classify a real number
10. Question 1.3.1 · March 2015 · Provincial · 2 marks
1.3 A square frame drawn below encloses an area of $190$ cm $^{2}$ .
1.3.1 Calculate $x$ , the length of the side of the frame, without using a calculator.(2)
Show the memo (2 ticks)Memo
1. ✓
  Set up equation $x^{2} = 190$
  1 mark · Set up an expression or equation
2. ✓
  Solve for x $x = 190$
  1 mark · Solve a quadratic by factorising

Number System Grade 10 videos

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

Integers Grade 9: BODMASKevinmathscience

Add Subtract Fractions Grade 8Kevinmathscience

1) Number Types gr 10 | IntroKevinmathscience

Undefined and Non-Real expressions Grade 11 MathsMiss Martins Maths and Science

Grade 10 Numbers: Surd between integersMaths Monkey

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