Cambridge IGCSE International Mathematics 0607 | Syllabus, Modelling and Preparation

Cambridge IGCSE International Mathematics 0607 | Core, Extended, GDC, Investigation and Modelling

Cambridge IGCSE International Mathematics 0607 is not simply Cambridge IGCSE Mathematics 0580 with a graphic display calculator added. It is a distinct qualification built around mathematical techniques, technology, investigation, modelling and communication. The current 2025–2027 assessment structure uses three papers at each tier. Core candidates take Paper 1 Non-calculator, Paper 3 Calculator and Paper 5 Investigation. Extended candidates take Paper 2 Non-calculator, Paper 4 Calculator and Paper 6 Investigation and Modelling.

For the current 2025–2027 syllabus, Core Paper 1 and Paper 3 are each 1 hour 15 minutes and 60 marks, each worth 40%. Core Paper 5 is 1 hour 15 minutes and 40 marks, worth 20%. Extended Paper 2 and Paper 4 are each 1 hour 30 minutes and 75 marks, each worth 40%. Extended Paper 6 is 1 hour 30 minutes and 50 marks, worth 20%. A graphic display calculator is required on Papers 3, 4, 5 and 6; calculators are not allowed on Papers 1 and 2. The 2028–2030 syllabus preserves the broad three-component Core/Extended architecture, but examination-year resources should always use the syllabus for the candidate’s actual series.

1. What makes 0607 different

0607 gives explicit ownership to two mathematical jobs that ordinary examination preparation can neglect:

• using technology as a mathematical tool rather than as a button sequence;
• investigating and modelling unfamiliar situations rather than only executing a named technique.

This means a strong learner needs more than reliable algebra and geometry. They need representation choice, conjecture, validation, interpretation and mathematical communication.

2. Core and Extended remain distinct routes

Core candidates work within Core content and are eligible for the Core grade range. Extended candidates work through the wider Extended content and higher grade route. Tier decisions should be made from sustained evidence rather than one mock or one difficult topic.

Useful tier evidence includes:

• accuracy across number and algebra;
• graph and function control;
• geometry and trigonometry;
• probability/statistics interpretation;
• GDC fluency;
• investigation independence;
• ability to explain a model.

3. Paper 1 and Paper 2: non-calculator control

The non-calculator paper reveals whether the learner owns exact Mathematics. Preparation should include:

• fractions;
• percentage and ratio structure;
• factorisation;
• algebraic manipulation;
• exact geometry;
• graph interpretation;
• probability;
• statistics;
• recognition of shortcuts and identities.

The goal is not fast mental arithmetic for its own sake. It is seeing structure before arithmetic becomes large.

4. Original non-calculator task: difference of squares

Evaluate:

[ rac{103^2-97^2}{12}. ]

Use:

[ 103^2-97^2=(103-97)(103+97)=6(200)=1200. ]

Therefore:

[ 1200/12=100. ]

Recognition is the efficient method.

5. Original non-calculator task: reverse percentage

A value after a 20% decrease is 96.

Let the original value be (x):

[ 0.8x=96. ]

[ x=120. ]

The learner should understand that 96 represents 80% of the original value.

6. Original non-calculator task: algebraic fractions

Simplify:

[ rac{x^2-16}{x^2-x-12}. ]

Factor:

[ rac{(x-4)(x+4)}{(x-4)(x+3)} = rac{x+4}{x+3}, ]

with original restrictions (x e4,-3).

7. Original non-calculator task: coordinate geometry

A line passes through ((1,4)) and ((5,16)).

Gradient:

[ m=rac{16-4}{5-1}=3. ]

Equation:

[ y=3x+1. ]

8. Paper 3 and Paper 4: GDC-supported Mathematics

A graphic display calculator should support:

• graphing;
• solving equations numerically;
• statistical summaries;
• regression;
• numerical checking;
• exploring parameter changes;
• testing conjectures.

But technology does not decide what mathematical model is valid.

9. GDC habit: predict before plotting

Before graphing:

[ y=x^2-6x+5, ]

factor:

[ (x-1)(x-5). ]

Predict x-intercepts at 1 and 5. Complete the square:

[ (x-3)^2-4. ]

Predict turning point ((3,-4)). The GDC should confirm the structure rather than reveal it for the first time.

10. GDC habit: window choice matters

A graphing window can hide:

• a second root;
• a distant turning point;
• an asymptote;
• a different long-run trend.

When a graph appears to show “no solution”, change the window or use algebraic evidence before concluding.

11. Original GDC task: intersections

Find intersections of:

[ y=x^2 ]

and:

[ y=2x+3. ]

Algebra:

[ x^2-2x-3=0 ]

[ (x-3)(x+1)=0. ]

So (x=-1,3). The GDC graph should show two intersections.

12. Original GDC task: regression

Suppose a small dataset relates hours studied (x) to score (y). A regression line may be useful, but the learner should ask:

• Is the relationship approximately linear?
• Are there outliers?
• Is extrapolation justified?
• Does association imply causation?

Regression is a model, not a verdict.

13. Paper 5: Investigation

Core Paper 5 focuses on open-ended investigation. The student may need to:

• generate values;
• notice patterns;
• form a conjecture;
• test cases;
• generalise;
• communicate reasoning.

A strong investigation is more than a list of calculator outputs.

14. Original investigation: square numbers

Consider consecutive square differences:

[ 2^2-1^2=3, ]

[ 3^2-2^2=5, ]

[ 4^2-3^2=7. ]

Conjecture:

[ (n+1)^2-n^2=2n+1. ]

Justify algebraically:

[ n^2+2n+1-n^2=2n+1. ]

The investigation moves from pattern to proof.

15. Original investigation: matchstick model

A row of joined squares uses:

[ 4,7,10,13,ldots ]

matchsticks.

General rule:

[ M(n)=3n+1. ]

The learner should explain why each new square adds three sticks after the first.

16. Paper 6: Investigation and Modelling

Extended Paper 6 contains both investigation and modelling. This asks the learner to move between pure mathematical structure and a context-based model.

The modelling cycle is:

define variables → choose assumptions → build relationship → calculate/explore → interpret → validate → refine.

17. Original modelling task: water tank

A tank contains 200 L. Water enters at 14 L/min and leaves at 2 L/min.

Net rate:

[ 12 ext{ L/min}. ]

Model:

[ V(t)=200+12t. ]

If capacity is 800 L:

[ 800=200+12t ]

[ t=50. ]

The model should not be extrapolated beyond capacity without modification.

18. Modelling requires assumptions

For the tank model, assumptions include:

• constant inflow;
• constant outflow;
• no overflow before capacity;
• accurate starting volume.

A correct equation can still be a poor model if assumptions are false.

19. Original modelling task: population

A population starts at 1200 and grows by 3% per year:

[ P(n)=1200(1.03)^n. ]

Ask when it exceeds 1500, then ask whether a constant percentage growth model remains plausible indefinitely.

20. Investigation and modelling are different

Investigation asks:

What mathematical pattern or relationship can I discover and justify?

Modelling asks:

What mathematical relationship represents this real situation, under what assumptions, and how well does it work?

Paper 6 can require both ways of thinking.

21. Communication is assessed throughout

Students should define variables, label graphs, show equations and write conclusions that answer the problem.

A page of GDC screenshots without explanation is not strong mathematical communication.

22. Accuracy discipline

For calculator papers, Cambridge instructs candidates to avoid premature rounding. Keep internal precision and round final non-exact results according to the question or syllabus conventions.

23. Original rounding task

Suppose an intermediate calculation gives 7.846193.

If this feeds into a later step, store the full value. Do not replace it with 7.85 too early unless the problem explicitly requires that rounding.

24. The content should be integrated

Useful mixed relationships include:

• ratio + algebra;
• functions + graphs;
• geometry + trigonometry;
• statistics + modelling;
• probability + simulation;
• sequences + investigation.

25. Original mixed task: ratio and geometry

A rectangle has length:width ratio 5:3 and area 240 cm².

Let sides be (5k), (3k).

[ 15k^2=240. ]

[ k=4. ]

Dimensions are 20 cm by 12 cm.

26. Original mixed task: graph and percentage

A quantity rises linearly from 80 to 100 over 4 periods.

Absolute rate:

[ (100-80)/4=5. ]

Overall percentage increase:

[ 20/80=25%. ]

Linear rate and percentage change answer different questions.

27. Core preparation should include investigation early

Do not postpone Paper 5 until the end of the course. Use short investigations throughout teaching so conjecture and communication become normal.

28. Extended preparation should include modelling early

Do not treat Paper 6 as a special examination trick. Use modelling tasks with functions, statistics and geometry across the course.

29. Technology should be used during learning

Because 0607 expects GDC fluency, students should use technology during learning to:

• test conjectures;
• compare graphs;
• explore parameters;
• analyse data;
• check calculations.

But they should still be able to explain the Mathematics without referring to button sequences alone.

30. Original parameter exploration

Investigate:

[ y=x^2+kx+4 ]

for different (k).

Use GDC graphs to conjecture when there are two, one or no real roots. Then verify with discriminant:

[ Delta=k^2-16. ]

31. Original data investigation

Given two numerical variables, the learner can:

• plot scatter graph;
• calculate regression;
• identify outliers;
• interpret correlation;
• challenge extrapolation.

32. Error categories for 0607

33. First-error feedback

If a modelling answer fails because the variable was defined incorrectly, later arithmetic is not the main issue. Repair the representation first.

34. Fresh transfer after feedback

If a student fixes a linear tank model, retest with a taxi fare, exchange-rate or temperature context so the model-selection rule has to transfer.

35. Six-week Core cycle

Week 1: number/algebra diagnostic.

Week 2: graphs/geometry.

Week 3: probability/statistics.

Week 4: GDC fluency + investigation.

Week 5: Papers 1, 3 and 5 sections.

Week 6: full three-paper simulation and transfer.

36. Six-week Extended cycle

Week 1: algebra/functions.

Week 2: geometry/trig/vectors.

Week 3: probability/statistics.

Week 4: GDC modelling/investigation.

Week 5: Papers 2, 4 and 6 sections.

Week 6: full route simulation and fresh transfer.

37. Full assessment pacing

Current Core:

• Paper 1 — 1h15, 60 marks, 40%;
• Paper 3 — 1h15, 60 marks, 40%;
• Paper 5 — 1h15, 40 marks, 20%.

Current Extended:

• Paper 2 — 1h30, 75 marks, 40%;
• Paper 4 — 1h30, 75 marks, 40%;
• Paper 6 — 1h30, 50 marks, 20%.

38. 0607 and 0580 should remain separate

0580 uses two papers per tier and a scientific calculator on the calculator paper. 0607 uses three papers per tier, requires a graphic display calculator on calculator/investigation components, and explicitly assesses investigation/modelling.

Do not merge the owners.

39. 2028 version control

Cambridge publishes a 2028–2030 0607 syllabus. Candidates sitting in 2028 should use that syllabus and current specimen materials. Stable mathematical content can be reused, but paper-specific practice must match the examination year.

40. Parent check

• Core or Extended?
• 0607 or 0580?
• Which exam year?
• Does the student have appropriate GDC fluency?
• Can they investigate and model, not just calculate?

41. Tutor check

A tutor should plan separately for:

• non-calculator mathematics;
• GDC-supported mathematics;
• investigation;
• modelling;
• communication.

42. Official-source control

Use Cambridge International’s 0607 qualification page and the syllabus for the examination year. The 2025–2027 syllabus confirms the current Core and Extended three-component structures and the GDC requirement on calculator/investigation papers. Cambridge also publishes a 2028–2030 syllabus.

43. Final learner checklist

• I can work without a calculator.
• I can use a GDC to support, not replace, Mathematics.
• I can investigate a pattern and justify a rule.
• I can build and evaluate a model.
• I can communicate variables, graphs and conclusions clearly.
• I preserve accuracy until the final answer.
• I know my tier and syllabus year.

44. The durable 0607 model

The complete route is:

foundation Mathematics → exact non-calculator control → GDC representation → investigation → modelling → communication → timed three-paper practice → first-error repair → fresh transfer.

This is what makes International Mathematics 0607 distinct.

Cambridge 0607 Mastery Clinic: GDC Fluency, Investigation, Modelling and Three-Paper Transfer

The difference between a learner who has studied International Mathematics 0607 and a learner who can perform reliably in it is not the number of topics completed. It is whether the student can move among exact non-calculator Mathematics, graphic-display-calculator representations, open investigation and model evaluation without losing the underlying mathematical object.

1. Build one mathematical system across all three components

A useful weekly mixed set should contain:

• one exact number or algebra problem;
• one graph/function problem;
• one geometry/trigonometry problem;
• one probability/statistics problem;
• one GDC representation task;
• one short investigation or modelling prompt.

The learner should not know the required method from the worksheet heading.

2. The non-calculator paper should expose structure

For Paper 1 or Paper 2, efficiency comes from recognition:

• factor before expanding;
• keep fractions exact;
• use identities;
• use ratio relationships;
• read graph structure;
• use known geometry.

3. Original exact-algebra task

Solve:

[ rac{x+1}{3}+rac{x-2}{4}=5. ]

Multiply by 12:

[ 4(x+1)+3(x-2)=60. ]

[ 4x+4+3x-6=60. ]

[ 7x=62. ]

[ x=rac{62}{7}. ]

The exact fraction is the correct endpoint unless the question asks for approximation.

4. Original exact-ratio task

A recipe uses flour:sugar in ratio 7:3. There are 280 g of flour.

One part = 40 g. Sugar = 120 g.

Now increase the recipe by scale factor 1.5. Flour becomes 420 g and sugar 180 g. The ratio remains 7:3.

5. GDC competence begins before the device

Before graphing a function, predict:

• intercepts;
• turning points if possible;
• sign;
• long-run behaviour;
• reasonable window.

The GDC should test the mathematical picture, not manufacture it.

6. Original GDC task: cubic behaviour

Consider:

[ f(x)=x^3-4x. ]

Factor:

[ x(x-2)(x+2). ]

Predict roots (-2,0,2). Then graph and inspect turning points.

Differentiate if appropriate for an Extended transfer:

[ f'(x)=3x^2-4. ]

The GDC graph, algebraic roots and derivative structure should agree.

7. GDC solution checking

If a numerical solver returns a root, substitute it into the original equation or compare it with a graph. A solver result should be treated as a candidate until it is interpreted.

8. Original GDC equation task

Solve numerically:

[ e^x=4-x. ]

A GDC can locate intersections of (y=e^x) and (y=4-x). The student should first consider approximate location from simple values, then verify that the graph window contains all relevant intersections.

9. GDC statistics should remain contextual

A regression coefficient, correlation coefficient or summary statistic should be interpreted according to the data context. Strong students ask:

• What does the slope mean?
• Is the model valid outside the data range?
• Are there outliers?
• Does the relationship appear linear?
• Is causation justified?

10. Investigation should produce a general claim

Paper 5 and Paper 6 investigation preparation should repeatedly use:

generate → organise → conjecture → generalise → test → justify.

11. Investigation lab: polygon diagonals

Number of diagonals in a polygon:

• triangle: 0;
• quadrilateral: 2;
• pentagon: 5;
• hexagon: 9.

A useful conjecture is:

[ D(n)=rac{n(n-3)}2. ]

Justification: each of (n) vertices connects to (n-3) non-adjacent vertices, giving (n(n-3)) directed counts; every diagonal is counted twice.

12. Investigation lab: sums of consecutive integers

Explore sums of three consecutive integers:

[ 1+2+3=6, ]

[ 4+5+6=15, ]

[ 10+11+12=33. ]

Let the integers be:

[ n-1,n,n+1. ]

The sum is:

[ 3n. ]

Therefore every sum of three consecutive integers is divisible by 3.

13. Investigation lab: parameter graphs

Use a GDC to explore:

[ y=x^2+kx+4. ]

Record the number of x-intercepts for several (k). Conjecture the boundary between 0, 1 and 2 real roots. Then verify:

[ Delta=k^2-16. ]

The investigation should end in exact algebra, not remain a visual pattern.

14. Modelling should identify the reader job

Before building a model, ask:

• What must be predicted or decided?
• Which variables matter?
• What units?
• What assumptions?
• What range of inputs is valid?

15. Modelling lab: taxi fare

Taxi A:

[ A=5+2.4d. ]

Taxi B:

[ B=9+1.8d. ]

Break-even:

[ 5+2.4d=9+1.8d. ]

[ 0.6d=4. ]

[ d=rac{20}{3}. ]

Then interpret which fare is lower before and after the break-even distance.

16. Modelling lab: cooling

A simple model:

[ T(t)=20+60(0.9)^t. ]

Ask:

• What is ambient temperature?
• What is initial temperature?
• What does 0.9 mean?
• Does the model ever reach exactly 20?
• When is the model practically close enough?

The Mathematics and the interpretation should remain connected.

17. Modelling lab: data fit

Given data points, compare linear and quadratic models. Use GDC regression if available. Do not choose the model only because it has the higher fit statistic. Ask whether the model makes sense outside the observed interval and whether the mechanism supports its shape.

18. A model can calculate correctly and still be poor

If a linear population model predicts negative population at a later time, the arithmetic may be correct while the model has exceeded its useful domain.

Validation is part of modelling.

19. Communication should explain GDC use

Instead of writing “calculator gives (x=2.37),” write:

“Solving the intersection of (y=f(x)) and (y=g(x)) numerically gives (xapprox2.37); substitution confirms the two values agree to the required accuracy.”

20. Diagrams and graphs should be labelled

A strong 0607 response should use:

• variable names;
• units;
• axes;
• scale;
• key coordinates;
• clear conclusions.

21. Core mastery lab

A Core learner should solve one task that combines:

• percentage;
• linear modelling;
• graph interpretation;
• data summary.

The student should use GDC tools only where appropriate and still explain the mathematical relationships.

22. Extended mastery lab

An Extended learner should solve a task combining:

• quadratic/exponential functions;
• trigonometry or vectors;
• GDC exploration;
• modelling validity;
• generalisation.

23. Original Extended modelling task: projectile-style curve

Suppose:

[ h(t)=-5t^2+20t+2. ]

The GDC can find maximum height and zeros. Algebra can verify the turning point:

[ t=-rac{b}{2a}=2. ]

Maximum height:

[ h(2)=22. ]

A negative time root should be interpreted according to the physical context.

24. Investigation marking habit

After an investigation, ask:

• Did I identify a pattern?
• Did I write a general rule?
• Did I test edge cases?
• Did I justify it?
• Did I communicate it clearly?

25. Modelling marking habit

After a model, ask:

• variables defined?
• units included?
• assumptions stated?
• model chosen?
• result interpreted?
• limitation evaluated?

26. First-error atlas

27. GDC practice should include reset skills

Students should know how to:

• clear old graphs;
• reset window;
• check angle mode;
• distinguish exact and approximate output;
• avoid hidden stored data affecting analysis.

28. But exam rules govern permitted functionality

Use the current Cambridge 0607 syllabus and exam guidance for permitted calculators and exam-mode expectations. Device familiarity should never substitute for current-rule checking.

29. Three-paper simulation

Core:

• one Paper 1 non-calculator simulation;
• one Paper 3 calculator simulation;
• one Paper 5 investigation simulation.

Extended:

• one Paper 2 non-calculator simulation;
• one Paper 4 calculator simulation;
• one Paper 6 investigation/modelling simulation.

Review the three together so the learner sees common mathematical weaknesses across environments.

30. Delayed transfer matters

After feedback, wait several days and give a new investigation or model with a different context. If the learner can still generate, generalise, model and evaluate independently, the skill is more durable.

31. A final investigation challenge

Investigate:

[ n^2-n ]

for integer (n). Numerical examples suggest the value is always even. Prove:

[ n^2-n=n(n-1), ]

a product of consecutive integers, hence even.

32. A final modelling challenge

A reservoir begins with 1000 m³ and changes according to:

[ V(t)=1000+40t-0.5t^2. ]

Use algebra/GDC to investigate maximum volume, relevant time interval and whether the model remains physically plausible for large (t).

33. Progression beyond 0607

Strong Extended learners can progress toward:

• Cambridge International AS & A Level Mathematics 9709;
• IB Diploma Mathematics;
• other advanced upper-secondary Mathematics routes.

The strongest bridge skills are algebra, functions, trigonometry, vectors, statistics, GDC judgement and modelling.

34. Final Core checklist

• exact non-calculator Mathematics secure;
• GDC calculator work checked;
• investigation can reach a justified rule;
• graphs and data communicated clearly;
• fresh transfer successful.

35. Final Extended checklist

• Core foundations secure;
• Extended algebra/functions stable;
• GDC used intelligently;
• investigation and modelling distinct;
• assumptions/limitations evaluated;
• progression readiness visible.

36. Final 0607 release standard

International Mathematics 0607 is mastered when the learner can move from exact Mathematics to digital representation to investigation and modelling without losing mathematical meaning.

Release principle: calculate, explore, generalise, model, communicate, validate.

0607 Final Practice Lab: Core and Extended Release Evidence

The final preparation stage for Cambridge IGCSE International Mathematics 0607 should look like the qualification itself: exact Mathematics without a calculator, technology-supported Mathematics with a GDC, open investigation, modelling, interpretation and mathematical communication. A learner should be able to move among these modes without treating them as separate subjects.

1. Final Core mixed set

Use a compact set containing number, algebra, geometry, probability, statistics and an investigation prompt.

Core Task A: reverse percentage

A jacket is reduced by 25% and now costs 72.

[ 0.75P=72. ]

[ P=96. ]

The student should identify the original base before calculating.

Core Task B: ratio and equation

The ratio of red to blue counters is 3:5. After 6 red counters are added, the ratio becomes 1:1.

Let original numbers be (3k) and (5k).

[ 3k+6=5k. ]

[ k=3. ]

Original numbers: 9 red and 15 blue.

Core Task C: graph interpretation

A line passes through ((0,4)) and ((6,16)).

Gradient:

[ m=rac{16-4}{6}=2. ]

Equation:

[ y=2x+4. ]

Ask the learner to interpret 2 and 4 in a practical context such as cost or distance.

Core Task D: data interpretation

Values:

[ 5,6,6,7,31. ]

Mean:

[ 55/5=11. ]

Median = 6.

Ask which summary best represents a typical value and why.

Core Task E: investigation

Explore:

[ 1+2=3, ]

[ 2+3=5, ]

[ 3+4=7. ]

Conjecture a formula for the sum of two consecutive integers:

[ n+(n+1)=2n+1. ]

The result is always odd. The student should justify the claim algebraically.

2. Final Extended mixed set

An Extended set should require deeper functions, trigonometry, GDC use and modelling.

Extended Task A: quadratic model

Let:

[ f(x)=x^2-8x+12. ]

Factor:

[ (x-2)(x-6). ]

Complete the square:

[ (x-4)^2-4. ]

Roots: 2 and 6. Turning point: ((4,-4)).

Graph with GDC and verify.

Extended Task B: exponential model

A value grows according to:

[ V(t)=500(1.04)^t. ]

Ask when it first exceeds 700. The GDC can solve numerically or the student can use logs. Then ask whether 4% growth is likely to continue indefinitely.

Extended Task C: trigonometry

A triangle has sides 8 and 11 with included angle (57^circ).

[ c^2=8^2+11^2-2(8)(11)cos57^circ. ]

Before calculation, use triangle inequality:

[ 3

The numerical answer should fall inside the bound.

Extended Task D: probability

A bag has 5 red, 4 blue and 3 green counters. Two are selected without replacement. Find the probability they are the same colour.

[ P(RR)=rac5{12}rac4{11}, ]

[ P(BB)=rac4{12}rac3{11}, ]

[ P(GG)=rac3{12}rac2{11}. ]

Add the mutually exclusive cases.

Extended Task E: modelling

A reservoir is modelled by:

[ V(t)=1000+60t-2t^2. ]

Use algebra or GDC to find the maximum. Since the quadratic opens downward:

[ t=-rac{60}{2(-2)}=15. ]

Maximum volume:

[ V(15)=1450. ]

Then ask whether the model is physically meaningful for large (t).

3. Paper 5 investigation release

Give a fresh pattern rather than one practised in class.

Example:

[ 2,6,12,20,30,ldots ]

These terms can be written:

[ 1cdot2, 2cdot3, 3cdot4, 4cdot5, 5cdot6. ]

Conjecture:

[ T_n=n(n+1). ]

Ask the learner to:

• verify several terms;
• explain the structure;
• find (T_{20});
• solve (T_n=420);
• justify whether the solution index is valid.

4. Paper 6 investigation-and-modelling release

Use one unfamiliar dataset or physical model. Require:

1. definition of variables;
2. graph or table;
3. conjecture or model;
4. GDC analysis;
5. interpretation;
6. limitation;
7. refinement.

5. Original Paper 6-style data model

Suppose a dataset records advertising spend (x) and sales (y). The GDC suggests a positive linear relationship.

Ask:

• what a regression slope means;
• whether an outlier changes the line;
• whether extrapolation beyond the observed range is sensible;
• whether increased advertising can be claimed to cause increased sales;
• what other variables might matter.

The modelling question is not finished when the regression equation appears.

6. Model sensitivity lab

A taxi model is:

[ C=5+2.2d. ]

If the rate changes from 2.2 to 2.5, how much does a 20 km trip change?

Original:

[ 49. ]

New:

[ 55. ]

The difference is 6. Parameter sensitivity can matter to a decision.

7. Investigation failure: examples only

A student writes five rows of a table and says “the pattern continues”. This is evidence, not a general argument.

Repair: express the (n)-th case symbolically and justify why the structure continues.

8. Modelling failure: no assumptions

A student fits a straight line and reports future values without discussing whether the rate can remain constant.

Repair: state the domain and the assumptions that support extrapolation.

9. GDC failure: graph window

A function appears to have one root in a narrow window. A larger window reveals three.

Repair: use algebraic expectations and zoom/window control before concluding how many solutions exist.

10. GDC failure: regression without plot

A high correlation coefficient can still hide an influential outlier or non-linear structure.

Repair: plot before summarising.

11. Communication failure: undefined variables

A model uses (x) and (y) without units or meaning.

Repair:

“Let (x) be distance in kilometres and (C) be fare in dollars.”

Mathematical communication improves the validity of the model.

12. Accuracy failure: early rounding

A student rounds an intermediate angle to one decimal place, then uses it in a second calculation.

Repair: store the full calculator value and round only the final result unless the question says otherwise.

13. Core paper pacing

Core candidates should practise distributing attention across:

• Paper 1 exact work;
• Paper 3 GDC work;
• Paper 5 investigation.

The investigation paper deserves regular preparation throughout the year rather than a late revision block.

14. Extended paper pacing

Extended candidates should rotate:

• Paper 2 exact work;
• Paper 4 GDC work;
• Paper 6 investigation/modelling.

The third component should be treated as a major assessment mode, not an appendix.

15. A three-week final Core cycle

Week 1: Paper 1 + Paper 3 mixed topic repair.

Week 2: two investigations and one full Paper 5.

Week 3: full Paper 1/Paper 3 pair + delayed investigation transfer.

16. A three-week final Extended cycle

Week 1: algebra/functions/trig and Paper 2/Paper 4 pair.

Week 2: GDC modelling, regression and Paper 6 tasks.

Week 3: full three-component simulation and first-error repair.

17. One delayed Core release task

After several days without notes, ask the learner to solve:

• one reverse percentage problem;
• one linear graph problem;
• one statistics interpretation;
• one fresh numerical pattern.

The student should still generalise and explain.

18. One delayed Extended release task

After several days, ask the learner to:

• analyse a new quadratic/exponential graph;
• build one model from a short context;
• use GDC appropriately;
• state one assumption;
• state one limitation.

19. Progression to 9709

An Extended 0607 student moving to Cambridge International AS & A Level Mathematics should be especially secure in:

• algebra;
• functions;
• trigonometry;
• series;
• vectors;
• probability/statistics;
• technology use;
• modelling.

20. Final route verification

Before the exam series, confirm:

• 0607 rather than 0580;
• Core or Extended;
• examination year;
• permitted GDC;
• three correct components;
• current Cambridge syllabus.

21. Final error evidence

The learner should have no repeated error category left untested. Every recurring error should have:

• a diagnosis;
• a repair;
• a changed example;
• a delayed retest;
• a final paper check.

22. Final standards checklist

• exact Mathematics stable;
• GDC mathematically controlled;
• investigation reaches generalisation;
• model states assumptions and limitations;
• communication is clear;
• rounding is controlled;
• three-paper route is correct;
• fresh transfer is successful.

Final release standard: 0607 is complete when the learner can calculate exactly, explore digitally, discover patterns, construct models, validate conclusions and communicate the Mathematics independently.

0607 Standards Appendix: Final Evidence for Calculation, Investigation and Modelling

A complete 0607 owner should finish with evidence that the learner can perform under all three assessment modes. Topic coverage alone is insufficient because International Mathematics explicitly asks students to operate differently across non-calculator work, GDC-supported work and open investigation/modelling.

1. Non-calculator release evidence

Give five fresh questions:

• fraction or ratio;
• algebraic simplification;
• coordinate geometry;
• geometry/trigonometry structure;
• probability or statistics interpretation.

The learner should work exactly, choose an efficient method and keep domain/units visible.

2. GDC release evidence

Give a function with several features:

[ f(x)=x^3-5x. ]

Before graphing, identify obvious root (x=0), odd symmetry and expected end behaviour. Then use the GDC to locate all roots and turning points. The student should compare the digital graph with the algebraic structure instead of accepting the screen uncritically.

3. Investigation release evidence

Investigate the number of regions formed by joining points on a circle under a stated rule. Require a table, conjecture, test, symbolic or geometric justification and a note about whether hidden conditions affect the pattern. The exact investigation can vary; the process should remain stable.

4. Modelling release evidence

Give a fresh real-life problem such as water use, travel cost, population or cooling. Require the learner to:

1. define variables and units;
2. state assumptions;
3. choose a relationship;
4. calculate or use GDC exploration;
5. interpret;
6. check validity;
7. state one limitation.

5. Example: two competing models

Model A:

[ A(t)=100+8t. ]

Model B:

[ B(t)=100(1.05)^t. ]

Ask which is larger for small (t), when the exponential model overtakes the linear model, and which assumptions distinguish the models. The GDC can locate the intersection, but the learner should explain additive versus multiplicative growth.

6. Example: sensitivity

Suppose:

[ C=20+3.5x. ]

If the rate 3.5 may actually lie between 3.3 and 3.7, ask how much the predicted cost at (x=40) changes. This introduces sensitivity without requiring advanced statistics.

7. Example: data quality

A regression line is built from six points, one of which is far from the rest. Ask the learner to compare the regression with and without the outlier and explain why the model changes. This is stronger evidence than simply knowing how to press the regression command.

8. Paper-specific first-error audit

9. Core final simulation

A Core learner should complete:

• one full non-calculator paper;
• one full GDC paper;
• one full investigation paper;
• one delayed fresh investigation several days later.

The final delayed task is important because it shows whether investigative reasoning survives beyond recent practice.

10. Extended final simulation

An Extended learner should complete:

• one full non-calculator paper;
• one full GDC paper;
• one full investigation/modelling paper;
• one changed-context modelling task after delay.

11. Progression evidence

Before progression to 9709 or another advanced route, the learner should be able to:

• manipulate algebra independently;
• read and transform functions;
• use trigonometry confidently;
• interpret data;
• use a GDC critically;
• build and evaluate models;
• generalise patterns.

12. Version-control evidence

Every mock should carry the syllabus year. A 2025–2027 candidate should not be assessed using later paper assumptions unless the resource is clearly labelled cross-generation practice. A 2028 candidate should use the 2028–2030 syllabus and current specimen materials.

13. Final release record

The learner should have:

• a recent paired non-calculator/GDC evidence set;
• a recent investigation;
• a recent model;
• an error ledger;
• at least one delayed fresh-transfer success;
• confirmed tier and exam year.

Final standard: 0607 is ready when exact Mathematics, GDC representation, investigation, modelling, communication and version control all work as one system.