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Additional Mathematics — IGCSE

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Syllabus code 0606 · no verification date claimed yet · 6 questions available on this subject's topics (12 marks)

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Topic map

Simplifying, expanding and factorisingFactorising is marked on the fully factorised form; a single common factor taken out is not finished.
Linear and simultaneous equationsOne mark usually belongs to the method, so write the elimination or substitution step.
Sequences and the nth termThe coefficient of n is the common difference; test your rule on the first two terms before writing it down.
Graphs, gradients and curve sketchingA coordinate is a pair — both values are needed for the mark.
Pythagoras and right-angled trigonometryIdentify opposite, adjacent and hypotenuse before choosing sine, cosine or tangent.

Practice available now (6 questions)

Expand and simplify (2x − 3)(x + 5).

1 mark · Expand and simplify · Simplifying, expanding and factorising

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Answer: 2x² + 7x − 15

Four products: 2x·x, 2x·5, −3·x, −3·5
2x² + 10x − 3x − 15
Collect: 2x² + 7x − 15

Write all four products before collecting. Skipping a term is the single most common error in this question type, and it costs the whole mark rather than part of it.

Solve 3(2x − 1) = 2(x + 4) + 5.

3 marks · Solve · Linear and simultaneous equations

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Answer: x = 4

Expand both sides: 6x − 3 = 2x + 8 + 5
Simplify the right: 6x − 3 = 2x + 13
Collect: 4x = 16, so x = 4

Expand both sides first, then collect. Collecting before expanding is where sign errors are born.

Find the nth term of the sequence 5, 8, 11, 14, …

1 mark · Find · Sequences and the nth term

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Answer: 3n + 2

Common difference = 3, so the rule starts 3n
n = 1 gives 3, but the first term is 5, so add 2

One mark, five seconds of checking: substitute n = 1 and n = 2 into your own rule. It is the cheapest verification in the whole paper.

In a right-angled triangle the hypotenuse is 9.6 m. One of the sides next to an angle is 7.2 m. Work out that angle, giving your answer to one decimal place.

3 marks · Work out · Pythagoras and right-angled trigonometry

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Answer: 41.4°

The two sides involved are the adjacent (7.2 m) and the hypotenuse (9.6 m), so use cosine
cos θ = 7.2 ÷ 9.6 = 0.75
θ = 41.4°

Label opposite, adjacent and hypotenuse on the diagram before choosing a ratio. Most marks lost here are lost to using sine because it was written first on the formula sheet.

A rectangle measures 9 cm by 12 cm. Work out the length of a diagonal.

1 mark · Work out · Pythagoras and right-angled trigonometry

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Answer: 15 cm

Pythagoras: diagonal² = 9² + 12²
= 225
Diagonal = 15 cm

The 9-12-15 triangle is a scaled 3-4-5, which appears in papers again and again. Recognising it saves a minute you can spend on a harder question.

A straight line passes through the points (2, 5) and (6, 13). Find the equation of the line in the form y = mx + c.

3 marks · Find · Graphs, gradients and curve sketching

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Answer: y = 2x + 1

Gradient m = (13 − 5) ÷ (6 − 2) = 8 ÷ 4 = 2
Substitute (2, 5): 5 = 2(2) + c, so c = 1
Equation: y = 2x + 1

One mark for the gradient, one for substituting a point, one for the finished equation. Show each of the three lines — a bare correct equation can score one mark, not three.