0580/42 May June 2025 Worked Solutions | IGCSE Maths
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0580/42 May/June 2025 Worked Solutions: IGCSE Maths Paper 4
Step-by-step 0580/42 May/June 2025 worked solutions for six IGCSE Maths Paper 4 questions, covering bounds, compound interest, functions, trigonometry and 3D angles, with how the marks are given and common mistakes.
Teachn.io Team·11 min read
Last updated: 19 October 2026
Short answer: This post gives step-by-step 0580/42 May June 2025 worked solutions for six questions from IGCSE Maths Paper 4 (Extended): a cone's mass, bounds, compound interest, functions, trigonometry with the sine and cosine rules, and a 3D angle in a cube. The key answers are 149 g (Q6), 58 cm (Q12), $742.97 (Q17c), 8 (Q19d), 43.0 m (Q20c) and 35.3° (Q27), and every one has been checked against the official mark scheme.
Want to try one yourself first? Our IGCSE Maths 0580 course has past paper questions with two buttons on every part: Learn this with Nio and Show me the answer. Nio is our built-in AI help, and it works through the answer mark by mark with the official mark scheme behind the scenes. Create a free account and get 50 credits (about 30 minutes).
What is 0580 Paper 42 like?
Paper 42 is one version of Paper 4, the calculator paper for Extended candidates. Here is the format, checked against the front cover of the May/June 2025 paper and the Cambridge 0580 syllabus page (2025–2027 syllabus):
Give non-exact answers to 3 significant figures, and angles to 1 decimal place, unless the question says otherwise. Losing accuracy is one of the easiest ways to drop marks, so keep full calculator values until the end.
How do you solve 0580/42 May/June 2025 Q6 (cone mass)? [3 marks]
The question (paraphrased): A solid wooden cone has base radius 4 cm and height 12 cm. The wood has density 0.74 g/cm³. Find the mass of the cone. (0580/42/M/J/25 Q6)
Solution:
Volume of a cone: V=31πr2h=31×π×42×12=64π
On your calculator, 64π=201.06... cm³. Keep this value.
Mass = density × volume =0.74×201.06...=148.78...
To 3 significant figures: 149 g
How the marks are given: One method mark (M1) for the cone volume calculation, one M1 for multiplying 0.74 by your volume, and the accuracy mark (A1) for 149 (anything from 148.7 to 148.8... also gets it).
Common mistake: Forgetting the 31 and using the cylinder formula, which gives three times the right mass.
Not sure which formula to use? Open a past paper question in our 0580 course and tap Learn this with Nio to go over volume and density before you try it. Sign up free for 50 credits (about 30 minutes).
How do you solve 0580/42 May/June 2025 Q12 (bounds)? [2 marks]
The question (paraphrased): A rectangle has length 16 cm and width 14 cm, both correct to the nearest centimetre. Find the lower bound of the perimeter. (0580/42/M/J/25 Q12)
Solution:
"Nearest centimetre" means the error is half of 1 cm, which is 0.5 cm.
Lower bound of the length: 16−0.5=15.5 cm
Lower bound of the width: 14−0.5=13.5 cm
The smallest perimeter uses both lower bounds: 2×(15.5+13.5)=2×29
Lower bound of the perimeter: 58 cm
How the marks are given: M1 for writing 15.5 or 13.5 (or something equivalent), then A1 for 58. The mark scheme says "nfww", meaning the 58 must not come from wrong working.
Common mistake: Using 15.4 and 13.4, or mixing up lower and upper bounds. The lower bound is exactly 15.5, not 15.4.
Bounds keep coming up. In the IGCSE Maths 0580 course, hit Show me the answer on a past paper bounds question and Nio shows you where each mark comes from. Your chats are saved, so you can come back to them before the exam. Create a free account.
How do you solve 0580/42 May/June 2025 Q17(c) (compound interest)? [4 marks]
The question (paraphrased): Bobbie invests $500 at compound interest. After 17 years it is worth $700.13. Find its value after 20 years. (0580/42/M/J/25 Q17c)
Solution:
Compound interest means 500×r17=700.13, where r is the yearly multiplier.
Divide: r17=500700.13=1.40026
Take the 17th root: r=171.40026=1.0200..., so the rate is 2% per year.
Value after 20 years: 500×1.0220=742.97...
Answer: $742.97
You can also start from year 17 and grow it three more years: 700.13×1.023, which also lands in the accepted range.
How the marks are given: Finding the multiplier 1.02 (or a 2% rate) earns B3 straight away, and the last mark is for an answer from 742.97 to 742.99. Other routes also get credit: M2 for the 17th root of 500700.13, M3 for using it with a power of 20 (from $500) or 3 (from $700.13). If you only set up 500×(…)17=700.13, that is M1, with one more M1 for using your rate with the right power.
Common mistake: Treating it as simple interest by sharing $200.13 equally over 17 years. Compound growth needs a root, not a division.
Compound interest feels tricky? Tap Learn this with Nio on a percentages question in our 0580 course and learn the multiplier method step by step. Get 50 free credits (about 30 minutes) when you sign up.
How do you solve 0580/42 May/June 2025 Q19 (functions)? [6 marks]
The question (paraphrased): You are given f(x)=x+1, g(x)=5−2x and h(x)=2x. The parts ask for f(−3), the range of g for a given domain, x when h(x)=321, and x when h−1(x)=3. (0580/42/M/J/25 Q19)
Solution:
(a) [1 mark] f(−3)=−3+1=−2
(b) [2 marks] The domain is {−3, 0, 2}. Put each value into g: g(−3)=5+6=11, g(0)=5, g(2)=5−4=1. The range is {11, 5, 1}.
(c) [1 mark] 2x=321=2, so .
(d) [2 marks] If h−1(x)=3, then x=h(3). So .
How the marks are given: (a) and (c) are one mark each for the answer. In (b), you get B1 if two of the three values are right. In (d), M1 is for writing x=h(3) or 23, then A1 for 8.
Common mistake: In (d), trying to find the inverse function first. The quickest route is the rule "if h−1(x)=3, then x=h(3)".
Inverse functions not clicking yet? Past paper questions in the IGCSE Maths 0580 course have a Show me the answer button, and Nio talks you through it in plain English. Create your free account and get 50 credits.
How do you solve 0580/42 May/June 2025 Q20 (sine and cosine rule)? [10 marks]
The question (paraphrased): Quadrilateral ABCD is split by the diagonal DB = 12 m. CD = 10 m and angle CDB = 56°, so triangle CDB sits above DB. Triangle DBA sits below it, with angle DBA = 90° and angle ADB = 34°. Find (a) AB, (b) the area of ABCD and (c) its perimeter. (0580/42/M/J/25 Q20)
Solution:
(a) [2 marks] Triangle DBA is right-angled at B, so use tan:
AB=12tan34∘=8.094..., so AB = 8.09 m.
(b) [3 marks] Add up the two triangles.
Triangle CDB: 21×10×12×sin56∘=49.74...
Triangle DBA: 21×12×8.094...=48.56...
Total: 98.30..., so the area is 98.3 m².
(c) [5 marks] You need BC and AD.
Cosine rule for BC: BC2=102+122−2×10×12cos56∘=109.79..., so BC=10.478...
Right-angled triangle for AD: AD=cos34∘12=14.474...
How the marks are given: (a) M1 for tan34∘=12AB, then A1. (b) M1 for 21×10×12sin56∘, M1 for 21×12× your AB, then A1 for 98.3 (98.28 to 98.31 accepted). (c) M2 for the cosine rule worked out to BC (M1 if you only reach BC2), M2 for AD=cos34∘12 (M1 for just writing cos34∘=AD12), and the last mark for an answer from 43.0 to 43.1.
Common mistake: Leaving your calculator in radians. Check it shows "D" or "DEG" before any trig question.
Lots of marks in one question. Tap Show me the answer on trigonometry past paper questions in our 0580 course and Nio goes through them one mark at a time, like a teacher marking your script. Sign up free and get 50 credits (about 30 minutes).
How do you solve 0580/42 May/June 2025 Q27 (3D angle in a cube)? [4 marks]
The question (paraphrased): ABCD is the base of a cube, and P is the top corner directly above C. Find the angle between the diagonal AP and the base ABCD. (0580/42/M/J/25 Q27)
Solution:
The angle you want is angle PAC. It sits in the right-angled triangle PAC, with the right angle at C.
No length is given, so pick a side length. Let each edge be 1.
Base diagonal AC (Pythagoras): AC=12+12=2
Height PC = 1, so tan(∠PAC)=2
∠PAC=tan−1(2
Answer: 35.3°
How the marks are given: M1 for spotting that the angle is PAC, M2 for a correct Pythagoras step (such as AC=k2 for side k), M3 for a full correct trig statement for angle PAC, and A1 for 35.3 (or 35.26...).
Common mistake: Using the edge AB instead of the diagonal AC, which gives 45°.
3D trig is easier once you see it. Open a 3D question in the IGCSE Maths 0580 course and tap Learn this with Nio to work out which right-angled triangle you need. Create a free account for 50 credits (about 30 minutes).
How to use these solutions
Try it first. Cover the solution, time yourself (about 1.2 minutes per mark), then check.
Mark yourself honestly. Use the "How the marks are given" notes. If you got the method but not the answer, you still earned M marks. Know where they came from.
Keep full values. Q17(c) and Q20(c) both punish early rounding. Store values in your calculator memory.
Spot repeats. Bounds, compound interest, functions and trigonometry turn up in Paper 4 again and again. Practise the same type from other years.
Redo mistakes after a week. A question you got wrong is worth more than one you got right.
How can Teachn.io help with 0580 Paper 4?
Teachn.io is a tutoring platform with real teachers in the loop, plus AI help. For IGCSE Maths 0580 you get:
Concise lecture notes for each topic, so you revise what the exam actually tests.
Past papers where every question part has Learn this with Nio and Show me the answer buttons.
A repeat question tracker that shows which question types keep coming back.
Mentors who keep you on track.
It is a web app, so it works in your phone's browser, with nothing to install. If you want to know which topics to focus on next, read our post on IGCSE Maths 0580 most repeated questions.
Cambridge publishes the official mark scheme for May/June 2025, which lists the final answers and mark points. This post gives full worked solutions for six questions, with answers that match that mark scheme.
Where can I get the official 0580/42 May/June 2025 question paper?
Cambridge International publishes it. Registered Cambridge schools can download past papers and mark schemes from the Cambridge School Support Hub, so the easiest route is to ask your school or maths teacher for a copy.
What is Nio?
Nio is the AI help built into Teachn.io. On past paper questions in our courses, Show me the answer gives a mark-by-mark worked answer, with the official mark scheme passed to Nio privately. Learn this with Nio teaches the topic first. Your chats are saved so you can reopen them.
How many marks is 0580 Paper 4?
Paper 4 (Extended) is 100 marks in 2 hours, and it is worth 50% of the IGCSE. A scientific calculator is required.
Does this paper have a histogram or nth term question?
Not in Paper 42 for May/June 2025. Those topics often appear in other 0580 papers, so keep practising them with other years.
