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Investigate / Determine Whether

Afrikaans: Ondersoek / Bepaal of

Show full working AND state a clear concluding sentence that directly answers the yes/no question asked. Both the working and the conclusion earn separate marks in the mark scheme. Correct working with no concluding statement, or a conclusion with no supporting working, will both lose marks.

Common mistake

Showing correct working but forgetting to write the concluding sentence. The conclusion must be an explicit statement in words, for example, 'Therefore the series converges' or 'Therefore the triangle is NOT equilateral'. Writing only the calculation without a conclusion is one of the most common reasons students lose a mark they otherwise earned. The conclusion must also match the working, do not write 'therefore it converges' if your working shows a divergent series.

Signal phrases

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

  • Investigate whether...: working alone is not enough; a written conclusion stating 'therefore yes' or 'therefore no' is a separate mark.
  • Determine whether the sequence converges, calculate the common ratio r and test |r| < 1; then conclude in words: 'therefore the series converges' or 'therefore the series diverges'.
  • Determine whether the triangle is right-angled, apply the converse of the Theorem of Pythagoras to the side lengths; your concluding statement must say whether it is or is not right-angled.
  • Investigate whether A, B and C are collinear, calculate the gradients of AB and BC; if they are equal, conclude in words that the points are collinear.
  • Determine whether the roots are real, calculate the discriminant Δ = b² − 4ac; then state the conclusion in words based on the sign of Δ (positive: two real roots; zero: equal real roots; negative: no real roots).
  • Determine whether the function is increasing or decreasing, find f'(x) and test its sign at the given x-value; conclude in a sentence that states the direction and references the derivative.

Past paper examples

Determine whether the series converges. Justify your answer.

Source: DBE Mathematics Paper 1, November 2021, Question 4.4

Test yourself

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

Given the sequence: 4 ; 12 ; 36 ; 108 ; ... Determine whether the series formed by the terms of this sequence converges.

Practice question: not from a past paper

Where this comes up