IGCSE Maths 0580 command words explained

• Work out: find the answer from the facts given, with or without a calculator. Show the steps, because method marks are awarded even if the final number slips. Example: "Work out 3/4 + 2/5." Write 15/20 + 8/20 = 23/20, not just the answer.
• Calculate: the same as Work out. Your working must be visible. Example: "Calculate the area of a circle of radius 5 cm." Write π × 5² = 78.5 cm².
• Determine: establish the answer with certainty. Give the value and enough working to justify it. Example: "Determine whether (2, 7) lies on y = 3x + 1." Substitute: 3 × 2 + 1 = 7, so yes, it does.

Free lessons: Fractions, decimals and percentages · Circles, arcs and sectors

• Write down: give the answer with no significant working. Usually one mark, so do not spend long on it. Example: "Write down the next term of 3, 7, 11, 15." Answer: 19.
• Write: give the answer in a specific form. Check the form asked for. Example: "Write 0.00062 in standard form." Answer: 6.2 × 10⁻⁴.
• Give: produce an answer from the information or from memory. Watch the accuracy asked for. Example: "Give your answer correct to 2 decimal places."
• State: say it clearly and exactly, with no calculation expected. Example: "State the type of correlation." Answer: negative.

Free lessons: Sequences · Standard form · Scatter diagrams

The answer is printed in the question. All the marks are for the working that leads to it, so a bare answer scores nothing. Show every step and give at least one more figure of accuracy than the printed answer.

Free lesson: Pythagoras theorem

• Explain: give reasons, saying why or how, with evidence. Use the correct maths words. Example: "Explain why angle x = 65°." Say "alternate angles are equal", not "they look the same".
• Describe: state the main features. For a transformation, name it and give every detail. Example: "Rotation, 90° clockwise, centre (1, 2)." Missing the centre loses a mark.

Free lessons: Parallel lines · Angles · Transformations

• Sketch: a simple freehand drawing that shows the key features. It does not need to be to scale, but label intercepts and turning points. Example: sketch y = x² − 4 and mark where it crosses the axes at (−2, 0), (2, 0) and (0, −4).
• Plot: mark points accurately on a graph, using small crosses within half a small square.
• Construct: make an accurate drawing with a ruler and compasses. Leave your construction arcs showing, because they are the evidence. Example: construct the perpendicular bisector of AB.

Free lessons: Sketching curves · Graphs of functions · Geometrical constructions

• Solve: find the value or values that make the equation true. Show each line and finish with x = …. Example: 2x + 3 = 11, so 2x = 8, so x = 4.
• Simplify: write it in the simplest equivalent form. Example: 3a + 5b − a + 2b = 2a + 7b.
• Expand: multiply out the brackets. Every term inside multiplies every term outside. Example: (x + 3)(x − 5) = x² − 5x + 3x − 15 = x² − 2x − 15.
• Factorise: write as a product of factors. Take out the highest common factor first and check by expanding. Example: 6x² + 9x = 3x(2x + 3).

Free lessons: Equations · Algebraic manipulation · Quadratic equations

Round each number to 1 significant figure first, then calculate. Using the exact values, or a calculator, loses the marks.

Free lesson: Estimation

• Non-exact answers: 3 significant figures, or 1 decimal place for angles, unless told otherwise.
• Do not round until the final answer. Carry the full calculator value into later parts.
• Use the π key or 3.142.
• Simplest form always. "Exact value" means leave π or a surd in the answer.
• If asked to show working, a correct answer with no method does not get full marks.
• Never mix fractions and decimals in one answer.