Grade 10 Maths · Algebra

Find undefined or non-real values

Find values that make an expression undefined or non-real (for example 1/(x − 2) is undefined when x = 2, and √−4 is non-real).

past paper questions use it: 14 past paper questions use it
videos: 3 videos

Learn it: find undefined or non-real values

Pick one and watch it, then try the questions below. Videos load only when you tap play.

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

10 Undefined and non realWiskunde_Mathematics_SUM

Rational, Irrational, Non-real, and Undefined NumbersMathology

Now try it on a real exam question

No sign-up. Takes 3 minutes.

Question 1.2 · March 2023 · Provincial · 3 marks

1.2 The roots of a quadratic equation, in terms of

p

, are given as:

x = \frac{4 \pm 8 - p ^{3}}{p}

. Determine the value(s) of

p

for the roots to be real.(3)

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

More past paper questions: find undefined or non-real values

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

3. 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
4. Question 1.3 · June 2025 · Paper 1 · Provincial · 1 mark
Consider the expression:

$K = \frac{3 n}{n + 5}$

Write down the value(s) of $n$ for which:
1.3 $K$ is non-real.(1)
Show the memo (1 tick)Memo
1. ✓
  Determine n for which the expression is non-real $n + 5 < 0$
  $n < - 5$
  1 mark · Find undefined or non-real values
5. Question 1.1.3 · March 2025 · Provincial · 1 mark
1.1 If $x \in {0; 7; 9}$ , choose the value of $x$ from the given set that will make the expression $x - 5$ be:
1.1.3 Non-real(1)
Show the memo (1 tick)Memo
1. ✓
  Select valueFor $x = 0$ : $0 - 5 = - 5$ (Non-real)
  Answer: $0$
  1 mark · Find undefined or non-real values
6. Question 1.1 · June 2024 · Paper 1 · Provincial · 1 mark
If $x \in {0; 1; 2; 3; 4}$ , write down a value of $x$ such that $K = \frac{9}{4 - x}$ is:
1.1 Undefined(1)
Show the memo (1 tick)Memo
1. ✓
  Identify value where denominator is zero $4 - x = 0 ⟹ x = 4$
  1 mark · Find undefined or non-real values

Free on Android

Know exactly which skill is costing you marks.

Mark past papers tick by tick in the NavyBlue app. It remembers every mark you lose, shows you the skills to fix first, and picks your next questions.

The NavyBlue app showing a learner's weak skills