Search

Search instruction words and topic guides

Calculate / Determine

Afrikaans: Bereken / Bepaal

Show full working that leads to a numerical or algebraic answer. Every intermediate step earns marks, a correct answer with no working will not receive full marks in an NSC exam. The examiners award marks for the method, not just the result, so your working must be clear, logical, and show every step from the given information to the final answer.

Common mistake

The most common error is writing only the final answer with no working shown. Some students show partial working and then jump to the result, this also loses marks for the steps in between. In a question worth 3 or more marks, each mark corresponds to a specific step in your working. A correct answer with zero working is usually capped at 0 or 1 mark depending on the mark scheme. If you run out of time, it is better to write incomplete correct working than a bare answer.

Signal phrases

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

  • Calculate the value of x, show every algebraic step from the equation to the final answer; a bare answer with no working earns 0 marks regardless of whether it is correct.
  • Determine the value of x, 'calculate' and 'determine' are interchangeable in NSC papers and carry identical expectations; both require full, step-by-step working shown.
  • Determine the length of AB, set up the relevant formula (distance, Pythagoras, or trigonometric ratio as appropriate), substitute the given values in a visible step, then simplify to the final length.
  • Calculate the gradient of the line, state the gradient formula m = (y₂ − y₁)/(x₂ − x₁), substitute the coordinates explicitly, and simplify; do not write only the final number.
  • Determine the equation of f, this signals that you must reach a specific algebraic form such as y = mx + c or y = a(x − p)² + q; you must show the substitution of known values and the simplification to that form.
  • Calculate the area of the region bounded by..., set up the integral or geometric formula first, then evaluate each step; the setup earns marks even if the arithmetic goes wrong.
  • Determine the coordinates of the turning point, show the differentiation or completing-the-square steps that lead to the x-value, then substitute to find y; both coordinates must be stated.
  • Calculate, correct to TWO decimal places..., the rounding instruction is a separate mark; round only at the final step (not mid-calculation), and check that you have exactly two digits after the decimal point.
  • Determine the nature of the roots, this signals a discriminant question, not a solving question; compute Δ = b² − 4ac and then interpret the sign in a concluding sentence (Δ > 0: two real unequal roots; Δ = 0: two equal real roots; Δ < 0: no real roots).

Past paper examples

Determine the value(s) of x for which 2x² − 5x − 3 = 0.

Source: DBE Mathematics Paper 1, November 2023, Question 2.1

Calculate the length of QR, correct to two decimal places.

Source: DBE Mathematics Paper 2, November 2022, Question 4.2

Test yourself

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

Given: f(x) = 3x² − x + 2. Determine f(−2).

Practice question: not from a past paper

Where this comes up