Cambridge IGCSE / A-Level
IGCSE Maths 0580 Paper 4: The Extended Calculator Paper, With Practice Questions
Paper 4 is the Extended calculator paper for IGCSE Maths 0580: 2 hours, 100 marks, half the qualification, sat alongside the non-calculator Paper 2. Since 2025 both Extended papers carry equal weight. Expect multi-part structured questions across number, algebra, geometry, mensuration, trigonometry, probability and statistics, with method marks for shown working.
I sit the Extended papers for 0580, and Paper 4 is the one where preparation pays off most directly, because the question types repeat so reliably that you can rehearse almost the entire paper in advance. The syllabus changed for 2025 exams onwards: Paper 4 is now 2 hours for 100 marks with a calculator, paired with a non-calculator Paper 2 of equal weight, so the old 130 mark marathon is gone. Below is how the paper is built, what examiners look for in working, and four original exam-style questions solved step by step, written to match the current format.
The current Paper 4 format (2025 onwards)
Paper 4 Calculator (Extended) is 2 hours long, worth 100 marks, and counts for 50 percent of the IGCSE. The other half is Paper 2 Non-calculator (Extended), also 2 hours and 100 marks. This structure started with the 2025 examinations, replacing the old pairing of a 70 mark short paper and a 130 mark long paper, so be careful with past papers: anything from 2024 or earlier follows the old format, and the old Paper 2s were short-answer papers. Cambridge has published specimen papers in the new format, and real sessions in the new style now exist too. You need a scientific calculator and geometry instruments, and tracing paper is allowed. Questions are structured and grow as the paper progresses: early questions spread 4 to 8 marks across parts, later ones can carry 10 or more, often built around one scenario such as a journey, a container or a sequence. A mark every 72 seconds sounds generous, but the late algebra and trigonometry questions absorb time, so banking the early number work quickly matters.
What comes up and how marks are given
The whole Extended syllabus can appear, but certain question families are close to permanent residents of Paper 4. Percentages with compound interest or exponential growth. Simultaneous and quadratic equations, including forming the equation yourself from a wordy setup. The sine rule, cosine rule and the area formula 1/2 ab sin C, often wrapped in a bearings diagram. Mensuration with cylinders, cones and spheres, including similar shapes where areas scale with the square and volumes with the cube of the length ratio. Cumulative frequency, histograms and averages from grouped data. Tree diagrams and conditional probability. Functions, sequences and graphs fill the gaps. Marking is method plus accuracy: method marks for a correct approach even with wrong numbers, accuracy marks for correct values, and independent marks for statements like a correct reason. That is why working is never optional. Give non-exact answers to 3 significant figures unless the question says otherwise, give angles to 1 decimal place, and never round in the middle of a calculation, because accuracy marks die at the rounding step more than anywhere else.
Technique for a 2 hour calculator paper
My routine: a first pass through the paper doing everything that yields, flagging anything that stalls, then a second pass with the remaining time. Write down more than you think you need: the formula before the substitution, the substitution before the answer, because method marks attach to visible method. Use the calculator properly: store intermediate values in memory instead of retyping rounded versions, bracket the numerator and denominator of every fraction, and work in degrees mode, checking the mode symbol whenever a trig answer looks alien. When a question says show that, the target value is a gift for the next part, but your working must derive it rather than assume it, and you can still use the given value in later parts even if you could not derive it. Draw on the diagram: mark given lengths and angles, and for bearings sketch the north line at every point before calculating anything. Finally, sanity-check magnitudes: a ladder is not 400 m long, a probability never exceeds 1, and a percentage profit of 3000 usually means a factor slip.
Worked questions, step by step
Amira invests 5000 dollars in an account paying 3.2 percent per year compound interest. (a) Calculate the value of the investment at the end of 6 years. (b) Find the least number of complete years for the investment to be worth more than 7000 dollars. [5]
- (a) Compound interest formula: value = 5000 x 1.032^6.
- 1.032^6 = 1.20803..., so value = 5000 x 1.20803 = 6040.16 dollars, to the nearest cent.
- (b) You need 5000 x 1.032^n > 7000, which simplifies to 1.032^n > 1.4.
- Test values on the calculator: 1.032^10 = 1.370 and 1.032^11 = 1.414, so 11 years is the first time the value passes 1.4.
- Answer the actual question asked: the least number of complete years is 11.
Answer: (a) 6040.16 dollars. (b) 11 years.
Where marks slip: In part (b), show the trial values either side: 1.032^10 = 1.370 and 1.032^11 = 1.414. That comparison is the method mark, and an unsupported 11 can lose it.
Try one yourself: Same account, but now the value after 6 years is given as 6040.16 dollars and the rate is unknown: find it. Reverse percentage setups reuse the identical formula, rearranged.
A rectangular garden has length 3 m greater than its width, w m. The area of the garden is 40 m2. (a) Show that w^2 + 3w - 40 = 0. (b) Solve the equation to find the dimensions of the garden. [5]
- (a) The length is w + 3, so the area gives w(w + 3) = 40.
- Expand: w^2 + 3w = 40, then bring everything to one side: w^2 + 3w - 40 = 0, as required.
- (b) Factorise: two numbers multiplying to -40 and adding to 3 are 8 and -5, so (w + 8)(w - 5) = 0.
- w = -8 or w = 5. A width cannot be negative, so w = 5.
- State the dimensions asked for: width 5 m and length 5 + 3 = 8 m.
Answer: (a) Area = w(w + 3) = 40 leads directly to w^2 + 3w - 40 = 0. (b) Width 5 m, length 8 m.
Where marks slip: In show that parts, every algebraic line must appear; jumping from w(w + 3) = 40 straight to the target equation can drop a mark. Always reject the negative root in words.
Try one yourself: Rebuild it with a border: a path of width x m surrounds a 6 m by 4 m pond, and the area of the path is 39 m2. Form and solve the quadratic in x.
Ship A leaves port P and sails 12 km on a bearing of 070 degrees to point Q. Ship B leaves P and sails 15 km on a bearing of 130 degrees to point R. (a) Show that angle QPR = 60 degrees. (b) Calculate the distance QR. (c) Calculate the bearing of R from Q, correct to the nearest degree. [7]
- (a) Both bearings are measured clockwise from north at P, so angle QPR = 130 - 70 = 60 degrees.
- (b) Cosine rule: QR^2 = 12^2 + 15^2 - 2 x 12 x 15 x cos 60 = 144 + 225 - 180 = 189.
- QR = sqrt(189) = 13.7 km to 3 significant figures. Keep the full value 13.7477... for part (c).
- (c) Sine rule for angle PQR: sin Q / 15 = sin 60 / 13.7477, so sin Q = 0.9449 and angle PQR = 70.9 degrees.
- From Q, the bearing of P is the back bearing of 070, which is 070 + 180 = 250 degrees.
- Draw the north line at Q. Bearing of R from Q = 250 - 70.9 = 179.1, so 179 degrees to the nearest degree. A sketch confirms R is almost due south of Q.
Answer: (a) 130 - 70 = 60 degrees. (b) 13.7 km. (c) 179 degrees.
Where marks slip: Part (c) separates the grades: draw a north line at Q, use the back bearing of 250, and keep the unrounded 13.7477 in the sine rule. Using the rounded 13.7 can shift the final bearing.
Try one yourself: Change ship B to 10 km on a bearing of 200 degrees, then find QR and the bearing of Q from R. Working the reverse direction is the best rehearsal for bearings.
A bag contains 5 red and 3 blue counters. Two counters are taken at random without replacement. (a) Find the probability that both counters are red. (b) Find the probability that the two counters are different colours. (c) Given that at least one counter is red, find the probability that both are red. [7]
- (a) First pick: P(red) = 5/8. Second pick changes because there is no replacement: after a red, P(red) = 4/7.
- P(both red) = 5/8 x 4/7 = 20/56 = 5/14.
- (b) Different colours happens two ways: red then blue = 5/8 x 3/7 = 15/56, and blue then red = 3/8 x 5/7 = 15/56.
- Add the two routes: 15/56 + 15/56 = 30/56 = 15/28.
- (c) P(at least one red) = 1 - P(both blue) = 1 - (3/8 x 2/7) = 1 - 6/56 = 50/56.
- Conditional probability: P(both red given at least one red) = (20/56) / (50/56) = 20/50 = 2/5.
Answer: (a) 5/14. (b) 15/28. (c) 2/5.
Where marks slip: Multiply along branches, add between branches, and keep fractions unsimplified until the end: 20/56 over 50/56 cancels far more safely than decimals. The denominator dropping from 8 to 7 is the without replacement mark.
Try one yourself: Same bag, three counters drawn: find the probability of exactly two reds. Then redo part (c) with the condition that the first counter is red, and notice why the answer changes.
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Solve my question →Quiz me on this topicQuestions students ask
Is IGCSE Maths 0580 Paper 4 still 130 marks?
Not any more. From the 2025 examinations, Paper 4 is 2 hours and 100 marks with a calculator, paired with a 2 hour, 100 mark non-calculator Paper 2. Papers from 2024 and earlier use the old format, so treat them as topic practice rather than timing practice.
What calculator should I use for Paper 4?
A scientific calculator; check the current syllabus and your school's guidance for what is permitted. Fluency matters more than the model: memory keys for intermediate values, fraction display, degrees mode and disciplined brackets are what actually save marks.
Do I lose marks if my final answer is wrong but my method is right?
You keep the method marks if the method is visible. That is the whole argument for writing the formula, the substitution and each stage: an arithmetic slip then costs one accuracy mark instead of the whole question.
Are old past papers still worth doing after the format change?
Yes, for content. The mathematics itself barely changed, so old Paper 4 questions remain excellent practice. Add the 2025 onward specimen and recent papers for timing, and remember old short-answer Paper 2s do not represent the new non-calculator paper.