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How to Score Higher in Cambridge IGCSE International Mathematics (0607)

Evidence-based International Mathematics 0607 exam guide built from official examiner reports and mark schemes. Specialised and comprehensive study tips — specific, cited insights so you can achieve top grades.

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Evidence-BasedBuilt from 1 official examiner reports & mark schemes (2025–2025)

What Are Assessment Objectives (AOs)?

Before we dive in, you need to understand how Cambridge actually marks your answers.

AO stands for Assessment Objective. Think of AOs as the different “skills” Cambridge tests you on in every single question. When an examiner marks your paper, they don't just give you a mark out of 12 based on how “good” your answer feels — they allocate specific marks to each AO separately.

For example, a 12-mark question might be split as: AO1 (2 marks) + AO2 (2 marks) + AO3 (2 marks) + AO4 (6 marks). If you write a perfect textbook answer but don't evaluate, you can only score 6 out of 12 — because the other 6 marks are specifically reserved for evaluation.

This is why understanding AOs matters: they tell you exactly what the examiner is looking for and how many marks each skill is worth. Here are the 2 AOs for this subject:

AO1

Mathematical Techniques

~40%

Organise, interpret, and present information in written, graphical, and diagrammatic forms. Perform calculations using a graphic display calculator (Papers 3, 4, 5, 6) or non-calculator methods (Papers 1, 2). Use mathematical instruments and graphic display calculator functions listed in the syllabus.

AO2

Applying and Problem Solving

~60%

Apply combinations of mathematical skills and techniques, including investigation and modelling tasks (Papers 5, 6). Communicate solutions clearly with each step shown, especially in 'show that' and modelling questions where every line of working must be visible.

The key takeaway: Most students lose marks not because they lack knowledge (AO1), but because they skip the higher-order skills — building chains of reasoning (AO2) and making supported judgements (AO3). Everything below shows you exactly how to hit each AO based on what examiners have written in their reports.

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Top Mistakes in IGCSE International Mathematics 0607

The most common reasons students lose marks in IGCSE International Mathematics 0607, cited directly from official examiner reports across multiple sessions.

Describing two transformations when 'single transformation' is asked

Every paper that includes transformations (1, 2, 3, 4) · Affects: Paper 1, Paper 2, Paper 3, Paper 4

What examiners say

“For questions on single transformations, candidates must use the correct term i.e. reflection, translation, rotation or enlargement. Translocation is not a transformation name. Candidates must only give one transformation as the question says single transformation. A good indication to what transformation is required, is that one piece of information is needed for each mark.”
— 0607 Paper 1, May/June 2025

“This part was answered less well with many candidates not giving a single transformation but combining an enlargement with either a translation or a rotation. These candidates were not awarded any marks.”
— 0607 Paper 2, May/June 2025

How to fix this

Give exactly ONE transformation. Use the precise word: reflection, translation, rotation, enlargement — never 'translocation', 'flip', 'mirror', 'shift', 'magnify', 'shrink', 'reduction'. Then provide every required detail (one detail per mark): translation = column vector; reflection = equation of mirror line; rotation = centre + angle + direction; enlargement = centre + scale factor (which can be a fraction or negative for a smaller/inverted image).

Premature rounding — losing accuracy by rounding intermediate values

Every calculator paper (3, 4, 6) · Affects: Paper 3, Paper 4, Paper 6

What examiners say

“Working should be to sufficient degree of accuracy to give a final answer to at least 3 significant figures. Usually that means working to 4 significant figure accuracy. When asked to show a numerical result is accurate to e.g. 3 significant figures, it is necessary to initially show that result to a greater degree of accuracy.”
— 0607 Paper 4, May/June 2025

“Candidates are strongly advised not to round off during their working but to work at a minimum of 4 significant figures to avoid losing accuracy marks.”
— 0607 Paper 4, May/June 2025

How to fix this

Work to at least 4 significant figures throughout. Only round the FINAL answer to 3 sf (or whatever the question asks). Use the Ans key on the GDC to chain calculations exactly — typing approximations like 0.82 instead of 0.821917… loses the accuracy mark. For 'show that' questions, write the unrounded value first, then round.

Working backwards from the given answer in 'show that' questions

Every paper with 'show that' questions · Affects: Paper 2, Paper 3, Paper 4, Paper 6

What examiners say

“A few candidates used the given answer in their Pythagoras equation in order to show the two sides of the equation were equal. This is not acceptable.”
— 0607 Paper 4, May/June 2025

“A small number of candidates tried to use the given value of x = 20 and substitute it into their volume expressions to show that the total was 32 000. Candidates need to remember that they should not use the information they are meant to be showing.”
— 0607 Paper 2, May/June 2025

How to fix this

Work TOWARDS the printed result, never FROM it. Start with given data only, build the algebra/arithmetic step by step, and finish at a value showing more accuracy than the printed answer (e.g. show 224.83 to prove the result rounds to 224.8). Substituting the given answer back to check it works scores zero.

Using non-mathematical vocabulary for circle theorems and reasons

Multiple papers, especially Paper 2 · Affects: Paper 2, Paper 4

What examiners say

“Candidates should state the geometrical wording from the syllabus: namely, 'angle at the centre is twice the angle at the circumference' and not describe the theorem using non-mathematical words such as middle and edge and nor should they refer to points on the diagram.”
— 0607 Paper 2, May/June 2025

“Words and phrases such as perimeter, edge, top of the circle, middle, origin or triangle were not accepted for circumference, centre or angle.”
— 0607 Paper 2, May/June 2025

How to fix this

Memorise exact theorem language: 'angle at the centre is twice the angle at the circumference', 'angle in a semicircle is 90°', 'opposite angles of a cyclic quadrilateral sum to 180°', 'tangent is perpendicular to the radius'. Never use 'middle' for centre, 'edge' or 'top' for circumference, or refer to letters on the diagram instead of stating the property.

Not using the graphic display calculator's graphing mode to solve equations

Every paper requiring a GDC (3, 4, 5, 6) · Affects: Paper 3, Paper 4, Paper 5, Paper 6

What examiners say

“It would be very useful for candidates to understand and be able to use the square root, as well as not only how to draw graphs on their calculator but that this will give them solutions very quickly and a labelled sketch is all that is necessary for communication.”
— 0607 Paper 5, May/June 2025

“Statements such as 'Solved using GDC' are not acceptable for communication marks… candidates are reminded that using an in-built solver receives no credit.”
— 0607 Paper 6, May/June 2025

How to fix this

When asked to solve an equation graphically, sketch the relevant graph(s) on paper from the GDC display, mark the point of intersection or x-intercept clearly, and label scales/intercepts. Never write 'solved using GDC' or rely on the built-in equation solver — neither earns communication marks. Show the graph as evidence.

Non-calculator papers — using calculator-style long arithmetic

Every Paper 1 and Paper 2 report · Affects: Paper 1, Paper 2

What examiners say

“Calculators are not permitted on this paper, so candidates need to be familiar with a range of non-calculator methods and strategies. Candidates are advised to check their working carefully for arithmetical errors.”
— 0607 Paper 1, May/June 2025

“This led to the common error that 0.6 + 0.15 = 0.21. Some performed the addition correctly then omitted to subtract their answer from 1.”
— 0607 Paper 1, May/June 2025

How to fix this

Set out additions and subtractions with decimals as column sums (line up the decimal point) so that 0.6 + 0.15 doesn't collapse to 0.21. Use efficient mental shortcuts: factor before multiplying, simplify fractions before combining, and check that probabilities sum to 1 (not 40 or 100%).

Standard form errors — wrong leading coefficient or missing power of 10

Multiple papers · Affects: Paper 1, Paper 2, Paper 4

What examiners say

“Many candidates were unsure of how a standard form number is written with many changing the place of the decimal point to have no digit in front or more than one and omitting to multiplying by a power of 10. Some wrote, 278 × 10¹, which although it does multiply to give 2780 it is not in standard form.”
— 0607 Paper 1, May/June 2025

“Some candidates included superfluous extra zeros, but these zeros were not significant and so were not penalised.”
— 0607 Paper 4, May/June 2025

How to fix this

Standard form requires EXACTLY one non-zero digit before the decimal point and a power of 10. So 2780 = 2.78 × 10³ (not 27.8 × 10² and not 278 × 10¹). When rounding to a different accuracy, recheck the leading digit — 13205.2 rounded becomes 1.32 × 10⁴, not 13.205 × 10³.

Investigation and modelling — answers without communication of method

Papers 5 and 6 — communication marks lost across nearly every question · Affects: Paper 5, Paper 6

What examiners say

“Candidates need to understand that every step of working must be shown to gain communication marks.”
— 0607 Paper 5, May/June 2025

“When candidates are asked to 'show that' a result is valid, they should produce a clear, accurate and complete mathematical justification leading to the given answer. All method steps should be shown. Candidates should know that selecting parts of the given expression, or formula, and trying to describe their origin is not a valid method.”
— 0607 Paper 6, May/June 2025

How to fix this

On the investigation/modelling papers, communication marks reward the visible process. Show: substitutions, calculations, sequence terms, common differences, sketch graphs with intercepts/scales labelled, and the formula being used. Don't delete working — crossed-out work cannot be credited. State models as equations with the subject (H = …, not just an expression).

Apply what you've learned

Practice identifying these mistakes in real papers. Try a recent paper and mark yourself — you'll spot these patterns immediately.

Try 2025 Oct-Nov All 0607 Papers

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What IGCSE International Mathematics 0607 Examiners Reward

Patterns that consistently earn high marks in IGCSE International Mathematics 0607, based on examiner report commentary on top-scoring answers.

Showing method line by line — even on calculator papers

Across all six papers, the strongest scripts set every step on a separate line: formula → substitution → calculation → answer. Candidates who wrote only the answer scored zero when the answer was wrong, while those with visible method earned method marks via follow-through.

Source: 0607 Paper 4, May/June 2025

Using the GDC's graphing functions for sketching, intersections, regression, and quadratic solutions

'Many candidates demonstrated good use of their graphic display calculators and showed a sketch of a straight line and an exponential curve intersecting in the second quadrant.' Candidates who drew sketches from the GDC found intersections quickly and earned communication marks; those who did algebra by hand often lost time and accuracy.

Source: 0607 Paper 4, May/June 2025

Working at 4+ significant figures and rounding only at the end

'Candidates are strongly advised not to round off during their working but to work at a minimum of 4 significant figures to avoid losing accuracy marks.' Top scripts kept exact values via the Ans key, then rounded the final answer to 3 sf.

Source: 0607 Paper 4, May/June 2025

Using precise transformation and circle-theorem vocabulary

Successful scripts wrote 'reflection in the line x = 5', 'rotation, centre (1, 1), 90° anticlockwise', 'enlargement, centre origin, scale factor 1/3'. Words like 'flip', 'mirror', 'shrink', 'translocation', 'magnify' earned zero.

Source: 0607 Paper 2, May/June 2025

Drawing labelled sketches with intercepts and asymptotes marked

'As usual, the best ones often had the asymptotes drawn in first, in order to ensure that the branches of the graph did not overlap. Most candidates realised that it was important to show on the sketch that the central branch passed through the origin.' Sketches with axes scales and key points labelled earned full marks.

Source: 0607 Paper 4, May/June 2025

Checking answers are sensible for the context

'Candidates should always keep the context in mind in this paper: in this case they might have realised that such a distance was far too small for a hammer throw.' Strong candidates re-read the question and asked whether their answer was a plausible length, time, probability, or speed.

Source: 0607 Paper 6, May/June 2025

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IGCSE International Mathematics 0607 Answer Frameworks

Structured approaches for each IGCSE International Mathematics 0607 question type, derived from mark scheme requirements.

'Show that' questions (2–5 marks)

3–6 minutes

Structure

Start from given information → state the formula being used → substitute values → arrive at a value with more accuracy than the printed answer → state the rounded result.

•Work TOWARDS the printed answer, never FROM it
•Show every algebraic step — gaps lose communication marks even if the answer is right
•When 'show that' includes a square root, draw the vinculum long enough to cover the whole expression
•If your answer is given correct to 1 dp, show 2+ dp first; if to 3 sf, show 4+ sf first
•Substituting the given answer back to verify scores zero

Single transformation description (2–4 marks)

1–2 minutes

Structure

State the type → give every required detail (one detail per mark).

•Translation: column vector — never coordinates and never a fraction
•Reflection: equation of mirror line (e.g. x = 5, y = -1)
•Rotation: centre as coordinates + angle + direction (clockwise/anticlockwise)
•Enlargement: centre + scale factor (can be 1/3, -3, etc.) — still called 'enlargement' even when image is smaller
•Two transformations = 0 marks. Words like 'flip', 'translocation', 'magnify', 'shrink' = 0 marks

Solve graphically with the GDC (3–5 marks)

3–5 minutes

Structure

Enter equation(s) into GDC → sketch onto paper → mark the point of intersection or x-intercept → read coordinates to required accuracy.

•Draw asymptotes first to keep curve branches in the right place
•Mark and label scale on both axes — at minimum, label intercepts
•If the question gives 'graphical method', sketches alone (without algebra) earn full marks
•Never write 'solved using GDC' — show the sketch with intersection marked
•Read coordinates to at least 3 sf; the in-built solver earns zero

Investigation algebraic generalisation (3–5 marks)

5–8 minutes

Structure

Spot the pattern in the table → write the algebraic expression → check by substituting one term → use it to predict a further value.

•Quadratic sequences have a constant SECOND difference — divide by 2 to get the coefficient of n²
•'Show algebraically' means use letters, not numbers — one numerical example does not prove the result
•Show every multiplication step when expanding, e.g. a(a + 33) = a² + 33a
•Watch signs: −a(a + 3) = −a² − 3a, not −a² + 3a
•Don't delete trial sequences — cross outs lose communication marks

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IGCSE International Mathematics 0607 Command Words Decoded

Each command word in IGCSE International Mathematics 0607 is a scoring instruction. Understanding what examiners expect is critical to earning full marks.

calculate1–4 marks

Work out the numerical value, showing the operation. Method must be visible.

Common mistake

Writing only the answer. With no working, an incorrect answer scores zero — even if a partial method would have earned method marks.

find1–4 marks

Determine the value, expression, equation, or coordinates requested. Working must support the answer.

Common mistake

Skipping the working — 'a few gave incorrect answers, such as 24, but did not show any working at all, so it was not possible to give any credit'.

show that2–5 marks

Prove the printed result. Start from given data, work line by line, finish with more accuracy than the given answer.

Common mistake

Substituting the given result back to verify both sides are equal — examiners reject this. Also: writing 'square root of an expression' without a long enough vinculum to cover the whole expression.

work out1–3 marks

Equivalent to 'calculate' — perform the arithmetic step by step.

Common mistake

On calculator papers, doing pencil-and-paper arithmetic when the GDC is faster and more reliable; on non-calculator papers, attempting calculator-style long methods that introduce slips.

sketch2–4 marks

Draw the general shape from the GDC with key features labelled (intercepts, asymptotes, turning points). Not a precise plot.

Common mistake

Tabulating values and joining points (which gives ruled segments) instead of a smooth GDC-shaped curve. Drawing branches that overlap their asymptotes or leave large gaps.

solve2–5 marks

Find the value(s) of the unknown that satisfy the equation or inequality.

Common mistake

On the GDC papers, using the in-built equation solver — not credited. Solve graphically with a labelled sketch, or algebraically with visible steps.

explain1–2 marks

Give a reason in clear mathematical language. Quote a property or theorem rather than describe with calculations.

Common mistake

Restating the question or giving everyday-language descriptions ('the line is straight') instead of naming the property ('alternate angles', 'tangent perpendicular to radius').

write down1 mark

State the answer directly — no working needed because the value can be read from a diagram, table, or formula sheet.

Common mistake

Treating it as 'measure' or 'calculate' — e.g. 'the most common error was to measure the angle using a protractor' when the question said 'write down'.

simplify1–3 marks

Reduce to the simplest form. Cancel factors, collect like terms, rationalise denominators where appropriate.

Common mistake

Leaving fractions inside fractions, or not cancelling fully (e.g. leaving 18/4 instead of 9/2). 'Candidates need to realise that a fraction within a fraction is not a suitable form for a final answer.'

expand1–3 marks

Multiply out brackets, then collect like terms unless the question says otherwise.

Common mistake

Multiplying only the first term of each bracket (giving e.g. 10x + 6x = 16x) and missing the constant terms; or sign errors when expanding (a − b)².

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IGCSE International Mathematics 0607 Diagram Checklist

Incorrect diagrams in IGCSE International Mathematics 0607 are flagged in every examiner report. Use this checklist before every practice and in the exam.

Reciprocal / hyperbola sketch from GDC

Axes: x × y

Two smooth branches approaching but never touching the asymptotes. Mark and label both asymptote equations (e.g. x = -0.5, y = 2). Label x- and y-intercepts as coordinates.

Common error: Branches overlapping the asymptote, large gaps between branch and asymptote, joining the two branches with a straight line, or writing intercepts as bare numbers instead of equations.

Single-transformation grid (rotation / reflection / enlargement)

Axes: x × y

Use a pencil and ruler. Translation preserves size and orientation. Rotation: mark the centre clearly. Reflection: draw the mirror line. Enlargement: image and centre must be consistent with the stated scale factor.

Common error: Drawing transformations freehand, changing the size during a translation, rotating about the wrong centre (origin instead of (1,1)), drawing a reflection when a rotation was asked, or combining two transformations.

Quadratic / cubic curve from GDC

Axes: x × y

Smooth curve with the correct GDC shape. Mark turning points (local max/min) with coordinates. Mark x-intercepts. For cubics, show both turning points if visible in the domain.

Common error: Plotting points by hand and joining with straight segments, missing the second turning point on a cubic, omitting scale on the axes, or rounding turning-point coordinates to fewer than 3 sf.

Trig graph (sin, cos, tan) for solving equations in 0° ≤ x ≤ 360°

Axes: x (degrees) × y

Sketch the standard sine, cosine, or tangent curve over the required domain. Mark the line y = k and identify both intersections. Use the symmetry of the curve to find the second solution.

Common error: Drawing sin x when cos x was required (or vice versa), giving only the principal value (e.g. 60° but missing 240°), giving more than two solutions, or using the wrong principal value (45° instead of 60° for tan x = √3).

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Topics Students Struggle With Most In IGCSE International Mathematics 0607

These IGCSE International Mathematics 0607 topics consistently produce the lowest scores. Prioritise these in your revision.

Single-transformation descriptions (especially enlargement with fractional/negative scale factor)

'The transformation is still called an enlargement even though the image is smaller than the original shape. Some called this a reduction, delargement or disenlargement or used shrink. The second area of misunderstanding was that the scale factor is not 3 but rather 1/3 as the lengths in the image are a third the length of the original's lengths.'

Affects: Paper 1, Paper 2, Paper 4

Standard form — leading digit, power of 10, and rounding

'Many candidates were unsure of how a standard form number is written with many changing the place of the decimal point to have no digit in front or more than one and omitting to multiplying by a power of 10.' Errors include 27.8 × 10² and 278 × 10¹.

Affects: Paper 1, Paper 2, Paper 4

Circle-theorem language (centre, circumference, reflex angles)

'Words and phrases such as perimeter, edge, top of the circle, middle, origin or triangle were not accepted for circumference, centre or angle.' On the reflex-angle question only a minority gave 210°; most gave 150°.

Affects: Paper 2, Paper 4

Solving equations using the GDC graphing mode

'Most candidates instead preferred to write a quadratic equation… A few explained that they had used their graphic display calculator but did not draw the relevant graph to gain credit for communication. Candidates are reminded that using an in-built solver receives no credit.'

Affects: Paper 5, Paper 6

Quadratic-sequence nth term (constant second difference)

'This part was challenging, with only a few candidates reaching the correct answer. Most did not realise the sequence was quadratic, and most of those who offered an nth term wrote a linear expression. Some had realised the second difference was 2 and gave answers of n + 2 or in the form 2n + k.'

Affects: Paper 1, Paper 2, Paper 5, Paper 6

Reverse percentage (compound depreciation, original price)

'Many candidates reduced the given value by 10% and then by 6%, multiplying by 0.9 and then 0.94 instead of dividing by 1.10 and then by 1.06. Some of the weaker candidates added the two percentages and treated the question as an increase of 16%.'

Affects: Paper 4

Surds — simplifying √a × √b and rationalising denominators

'A minority of candidates were able to completely simplify the surds. The most common errors came from candidates using incorrect rules of surds. The most common examples included incorrectly simplifying √(a²b) to b√a or √(cd) to c√d.'

Affects: Paper 2

Modelling — units, accuracy, and stating models as equations

'The model is not precise. So an answer in milliseconds for the time it takes for the hammer to hit the ground is inappropriate and was not credited.' Many candidates also wrote expressions instead of full models with H = … or V = ….

Affects: Paper 6

Target your weak areas

The topics above are where most marks are lost. Use past papers and mark schemes to practice these specific areas until they become second nature.

Past Papers & Mark Schemes

Frequently Asked Questions

What papers make up Cambridge IGCSE International Mathematics 0607?

Six papers grouped by tier. Core: Paper 1 (non-calculator, 1h), Paper 3 (calculator, 1h 30m), and Paper 5 (investigation with calculator, 1h). Extended: Paper 2 (non-calculator, 1h 30m), Paper 4 (calculator, 2h 15m), and Paper 6 (investigation & modelling with calculator, 1h 30m). Each candidate sits one paper from each pair (1 or 2, 3 or 4, 5 or 6).

Do I need a graphic display calculator for 0607?

Yes. Papers 3, 4, 5 and 6 require a graphic display calculator (GDC), and the syllabus lists the specific functions you must be able to use. The examiner reports note that some candidates clearly did not have a GDC and were unable to answer questions on hyperbolas, cubics, regression, or graphical equation-solving. A scientific calculator is not sufficient for these papers.

Is a graphics calculator required?

Yes — a graphics display calculator (GDC) is required for the calculator papers (3, 4, 5, 6). Familiarity with graphing functions, table-of-values mode, and equation solvers is essential. Cambridge approves common models such as Casio fx-CG50 and TI-Nspire CX. Confirm your model is on the permitted list before the exam.

How long is each International Mathematics 0607 paper?

Paper 1 (Core Non-Calculator) is 45 minutes. Paper 2 (Extended Non-Calculator) is 45 minutes. Paper 3 (Core Calculator) is 1h 30m. Paper 4 (Extended Calculator) is 2h 15m. Paper 5/6 are Investigation papers — Core 1h 15m, Extended 1h 30m. Choose Core or Extended at registration.

Put It All Into Practice

You now know exactly what examiners reward and penalise. The next step is deliberate practice with real papers. We have 21 exam sessions available for IGCSE International Mathematics 0607 — question papers, mark schemes, and examiner reports.

View All Past Papers Latest Session: 2025 Oct-Nov