IGCSE Maths Extended: Cambridge (CIE) 0580

In short: Cambridge IGCSE Mathematics 0580 Extended is the higher tier of Cambridge IGCSE Maths. You sit Paper 2 (non-calculator) and Paper 4 (calculator), and you can achieve grades A* to E.

Cambridge designs the Extended content for students targeting grades A* to C. It contains all of the Core content plus harder topics such as surds, functions, differentiation, the sine and cosine rules, vectors, conditional probability and histograms.

Cambridge supports schools in 160 countries, and IGCSE Maths is widely used for entry to A Level, IB Diploma and other pre-university courses. A strong 0580 grade is often a requirement for A Level Mathematics.

This FLN Tutors course covers the full Extended syllabus one to one with a verified maths tutor.

Official syllabus page: Cambridge IGCSE Mathematics 0580. For wider support, see maths tutoring, or the Cambridge IGCSE Maths Core course if you are still choosing a tier.

Extended candidates take two written papers. Both are set and marked by Cambridge, and any Extended topic can appear on either paper.

Assessment objectives for Extended:

More than half the marks reward reasoning and problem-solving, not just routine methods. Exams run in the June and November series, and also in March in India.

Cambridge publishes 0580 syllabuses in three-year cycles. Check the exam year on your entry, then use the matching document.

The papers, timings, marks and Extended topic list are the same in both cycles, and textbooks endorsed for the syllabus from 2025 remain suitable. If you start IGCSE now and sit in 2028, you can follow the same plan.

Your tutor checks your exam year at the first lesson and uses the specimen papers and past papers that match it.

The Extended content is organised into nine areas. Each includes the Core content plus Extended-only topics.

Algebra and number carry the widest range of skills, so they get the most time in the plan. Statistics is often left until last by students and then rushed, so your tutor schedules it earlier.

Choose Extended if you are aiming for grade C or above, and especially if you want an A or A*. Core caps your grade at C. Your school usually decides the tier after mocks; if your mock marks are close to the boundary, ask about Extended, because the extra content is learnable with a clear plan.

Comparing 0580 with Cambridge IGCSE International Mathematics (0607)? See our 0607 Core course and check which syllabus your school offers.

Extended is demanding because it rewards reasoning, not just method. The parts students find hardest are usually:

1. Paper 2 without a calculator, especially surds, indices, fractions and exact trigonometric values.
2. Multi-step problems that combine topics, such as similarity with area or vectors with ratio.
3. Functions and differentiation, which feel new compared with earlier school maths.
4. Accuracy rules, because answers to the wrong number of significant figures lose marks.

Students who practise both papers regularly, learn the accuracy rules and review every mistake usually improve steadily. Most of the hard questions use the same methods repeatedly, so practice pays off.

Paper 2 is worth half the qualification and every question must be done by hand.

1. Secure written methods for fractions, decimals, long multiplication and division.
2. Learn square numbers to 15², cubes to 5³ and common powers of 2, 3 and 10.
3. Practise surds and indices until simplifying feels automatic.
4. Know exact values of sin, cos and tan for 30°, 45° and 60°.
5. Estimate first so you can spot a wrong answer quickly.
6. Show every step: method marks are available even if the final answer slips.

Your tutor sets a short non-calculator set every week, timed, and tracks which skills keep costing marks.

Simplify √50 + √18.

Rationalise 6/√3. Multiply top and bottom by √3: 6√3 / 3 = 2√3.

Evaluate 8^(2/3) and 27^(-1/3).

1. 8^(2/3) = (cube root of 8)² = 2² = 4.
2. 27^(-1/3) = 1 ÷ (cube root of 27) = 1/3.

The rule to remember: the denominator of a fractional index is the root, the numerator is the power, and a negative index means the reciprocal.

Solve 2x² - 3x - 7 = 0, giving answers to 2 decimal places.

1. a = 2, b = -3, c = -7.
2. x = [3 ± √(9 + 56)] ÷ 4 = (3 ± √65) ÷ 4.
3. √65 = 8.0623, so x = 2.77 or x = -1.27.

Triangle problem. Two sides are 7 cm and 9 cm with an included angle of 50°. Find the third side and the area.

Keep full calculator values until the last step; rounding cos 50° to 0.64 too early changes the final answer.

Differentiation is part of the Extended syllabus. Find the turning points of y = x³ - 6x² + 9x + 1.

1. Differentiate: dy/dx = 3x² - 12x + 9.
2. Set dy/dx = 0: 3x² - 12x + 9 = 0, so x² - 4x + 3 = 0.
3. Factorise: (x - 1)(x - 3) = 0, so x = 1 or x = 3.
4. Find y: when x = 1, y = 1 - 6 + 9 + 1 = 5; when x = 3, y = 27 - 54 + 27 + 1 = 1.

The turning points are (1, 5) and (3, 1). For a cubic with a positive x³ term, the first turning point is a maximum and the second is a minimum, so (1, 5) is a maximum and (3, 1) is a minimum.

Check with values either side: y(0) = 1, y(2) = 3, y(4) = 5, which matches rising to 5, falling to 1, then rising again.

Limits of accuracy. A square has sides of 12 cm, correct to the nearest centimetre. Find the upper bound of its area.

1. The side lies in the interval 11.5 ≤ L < 12.5.
2. Upper bound of area = 12.5² = 156.25 cm².
3. Lower bound of area = 11.5² = 132.25 cm².

Histogram. In a histogram, the height of each bar is the frequency density.

Frequency density = frequency ÷ class width. A common error is plotting the frequency itself, which makes wide classes look far bigger than they are.

The accuracy rules are stated in the syllabus and apply on every paper:

List of formulas. A list of formulas appears on page 2 of each Extended paper, including areas and volumes of some shapes and the sine and cosine rules. It does not include everything: you still need to know, for example, Pythagoras, basic area formulas and the rules of indices. Your tutor gives you a checklist of what is given and what you must learn.

Most of these are habits. They fall away with regular marked practice and an error log you review every week.

Cambridge sets grade thresholds for each series, so there is no fixed mark for an A*. What consistently moves students up:

1. Cover every topic, including statistics and differentiation, so no question is a write-off.
2. Practise both papers every week: one non-calculator set and one calculator set.
3. Learn the accuracy rules and the given formulas, so you do not lose easy marks.
4. Keep an error log and redo each wrong question a week later.
5. Do full timed papers in the final eight weeks, alternating Paper 2 and Paper 4.
6. Review the hardest questions with your tutor, because the last marks on each paper decide an A*.

Use published thresholds from recent series only as a guide when you mark past papers, and aim comfortably above them.

Past papers are the best practice once the content is secure. A plan for the final term:

Mark each paper with the official mark scheme and read the examiner reports, which explain where candidates lost marks. Use papers from the current syllabus first; older papers are still useful for most topics.

• Year 10 and Year 11 students (or Grades 9 and 10) on the Extended tier.
• Students moving from Core to Extended who need the extra content.
• Students aiming for A Level or IB Maths who want an A or A*.
• International students in the Gulf, India, Malaysia, the UK and elsewhere, with lessons in your time zone.

Prerequisites: confident arithmetic, fractions, percentages and ratio, with basic algebra and geometry.

What you get: live one-to-one video lessons, worked methods for both papers, weekly practice marked with Cambridge mark schemes and a plan built around your exam series. See also Cambridge IGCSE Additional Maths (0606). Book a lesson or ask a question from this page to start.