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If / Given That

Afrikaans: As / Gegee dat

Use the stated condition as a constraint or substitution in your working, it is not optional context. The condition restricts the problem to a specific case, and your answer must apply only within that restriction. Ignoring the given condition and solving the general problem will produce a wrong or incomplete answer.

Common mistake

Ignoring the given condition and solving the problem in general, without applying the stated restriction. For example, if the question says 'given that x = 2 is a root', you must use that fact, typically by substituting x = 2 to find an unknown constant, or by using polynomial division with (x − 2). Students who miss the 'given that' clause often solve a harder, different problem and lose all the marks.

Signal phrases

These are the words that tell you this instruction is being used.

  • If x > 0, solve for...
  • Given that f(2) = 0, determine...
  • Given that x = 2 is a root of f(x) = 0, determine the other roots
  • If P(A) = 0,3 and A and B are independent...

Past paper examples

Given that x = 2 is a root of f(x) = 0, determine the other roots.

Source: DBE Mathematics Paper 1, November 2022, Question 3.1

Test yourself

Before you read the answer, what is this question asking you to do?

f(x) = x³ + bx² − x − 6. Given that f(2) = 0, determine the value of b.

Practice question: not from a past paper

Where this comes up