IGCSE Mathematics — Core: Number, Algebra, Shape and Data
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Lesson overview
Everything the Core papers can ask, and the marks that are lost to method rather than to knowledge.
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Pacing
~1 minute per mark; match answer depth strictly to `[1]`, `[2]`, `[3]`, or `[4]` mark allocations.
How IGCSE marks this
Command words govern mark schemes: 'State' = 1 concise fact; 'Describe' = what happens; 'Explain' = why/how using scientific terminology.
Watch out for
Vague everyday wording ('it gets bigger') fails Cambridge mark schemes where exact terms ('rate of collisions increases') are required.
Lesson content
What Core actually tests
Core is not a short syllabus; it is a narrower one, and almost every mark on papers 1 and 3 comes from doing ordinary arithmetic reliably under time pressure. The number block is the largest single lever: addition and subtraction of negatives, the order of operations, factors, multiples, primes, HCF and LCM, fractions and decimals of quantities, standard form for large and small numbers, and the four families of percent work — increase and decrease, reverse percentages, compound interest over a whole number of years, and profit and loss as a percentage of cost. Marks are then taken in algebra that is entirely mechanical once the habits are set: collecting like terms, expanding a single bracket and a product of two brackets, factorising, substituting into a formula with negative values, solving linear equations with the variable on both sides, simultaneous equations by elimination, and simple inequalities on a number line. Geometry and measures are worth roughly a third of the paper and are the section most often answered in prose instead of arithmetic: perimeter and area of rectangles, triangles and parallelograms, volume and surface area of a cuboid and a prism, the circumference and area of a circle, the sum of angles in a triangle and round a point, angles in parallel lines, and the three similarities that matter at this tier: line, rotational and reflection symmetry, plus enlargement with a positive scale factor. Bearings are drawn, measured and stated as three digits. Statistics is the cheapest section on the paper — mean, median, mode and range from a list, the modal class from grouped data, and reading a bar chart, pie chart or scatter graph — and probability is a single idea: favourable outcomes over total outcomes, with the complement used to save work. Presentation carries the rest. Core papers award method marks even when the final answer is wrong, which means a line of working is never wasted; the multiple-choice paper (30% of the total) punishes the reverse, because there is nothing to show, so answers must be checked by substitution or by estimating the size of the result. Two habits fix most Core grades: write the formula before substituting, and re-read the question at the end to answer what was asked — the exact value, to the stated degree of accuracy, with units.
The vocabulary the papers use against you
STANDARD FORM: a number written as A × 10ⁿ with 1 ≤ A < 10 — used for very large and very small quantities. REVERSE PERCENTAGE: finding the original amount when a percentage change has already been applied. SIMULTANEOUS EQUATIONS: two equations solved together, by making one coefficient match and eliminating. BEARING: an angle measured clockwise from north, always stated with three digits. MODAL CLASS: the interval with the greatest frequency in grouped data. ENLARGEMENT: a shape scaled from a centre by a scale factor; lengths multiply by k, areas by k².
A price that rises, then falls — and what the net change really is
A phone costs ₦120,000. Its price rises by 15%, then falls by 15% in a sale. Many candidates answer 'no change'. The multipliers settle it: 120,000 × 1.15 = 138,000, then 138,000 × 0.85 = 117,300 — a net fall of 2,700, which is 2,700 ÷ 120,000 = 2.25% of the original price. Two rules follow, and both are examinable: a rise of p% followed by a fall of p% always returns below the starting value (the multipliers multiply to 1 − p²/10,000), and the net percentage is measured against the value you started from, not against the higher one. Write it as one line of working, 120,000 × 1.15 × 0.85, and the answer cannot be mis-stated.
Simultaneous equations, and the trap in the signs
Solve 3x + 2y = 16 and 5x − 2y = 0. The y coefficients already match, so add: 8x = 16, hence x = 2; substitute into the first equation, 6 + 2y = 16, so y = 5. Check in the second: 5(2) − 2(5) = 10 − 10 = 0 ✓. If instead the equations were 3x + 2y = 16 and 5x + 2y = 24, you would subtract, and the sign of the right-hand side is where marks are lost: 16 − 24 = −8, not 8. When no coefficient matches, multiply one line first — always both sides — and never multiply the equation you are about to subtract from without writing the new line out.
Lesson summary
Core is a reliability exam: number, percent multipliers, algebraic mechanics and the standard area and volume formulas carry roughly four fifths of the marks. Papers 1 and 3 (multiple choice then short answer, 80 marks total) allow no method credit, so estimate the size of an answer before selecting it. Answer the question asked: the stated degree of accuracy, the correct units, and the original quantity rather than the intermediate one.
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