Cambridge IGCSE Mathematics (0580) — Past Papers, Revision Notes & Exam Prep

Averages and range

MistakeYou find the median without putting the list in order, give the highest frequency as the mode instead of its value, or write a range as 17 to 82.

Negative numbers

MistakeYou get signs wrong with negatives: 5 − (−2) becomes 3, −8 + 3 becomes −11, or −3 × (−4) becomes −12.

Standard form

MistakeYou leave the first number outside 1 to 10, like 45.2 × 10⁶, miscount the places, or give a small number a positive power.

Mixed numbers

MistakeYou subtract the whole numbers and the fractions separately, then get stuck when the second fraction is bigger, or you leave the answer in a form not asked for.

Order of operations

MistakeYou work straight from left to right, adding or subtracting before the powers, roots, multiplications and divisions have been done.

Estimation

MistakeYou estimate using the exact values, round to the nearest whole number instead of to 1 significant figure, or round only your final answer.

Factors and primes

MistakeListing factors, you leave out 1 and the number itself, or give only the prime factors. To show a number is not prime, you just restate the definition.

Circles and π

MistakeYou swap the area and circumference formulas, use the diameter as the radius, or change π to a decimal when the answer should be in terms of π.

Diagram assumptions

MistakeYou treat a chord as a diameter, lines as parallel or a triangle as isosceles because the diagram looks that way, then build your answer on it.

Vector routes

MistakeWith OA = a and OB = b, you write AB as a − b, go against an arrow without changing sign, or turn a ratio into the wrong fraction.

Algebraic fractions

MistakeYou cancel single terms, such as x² on the top and bottom, before factorising. When subtracting fractions, you change the sign of only the first term of the second numerator.

Direct and inverse proportion

MistakeYou write the wrong relationship (direct for inverse, square for square root), leave out the constant k, or forget to put k back into the formula.

Dividing fractions

MistakeWhen dividing, you turn the first fraction upside down instead of the second, or stop before your fraction is in its simplest form.

Recurring decimals

MistakeYou treat every digit after the point as repeating when the dots mark only some of them, or you simply write the digits over a power of 10.

Trig equations

MistakeSolving a trig equation for angles from 0° to 360°, you stop after the first angle you find and miss the second solution.

Transformations

MistakeYou describe a transformation in everyday words, give two transformations when one is asked for, or leave out the centre, angle, scale factor or vector.

Inequalities

MistakeYou keep the inequality sign the same after multiplying or dividing by a negative number, or draw a solid boundary line for a strict inequality.

Time calculations

MistakeYou treat time like a decimal (2 h 15 min as 2.15 h, or 18:50 + 25 min as 18:75), or put am or pm on 24-hour times.

Describing transformations

MistakeYou use words like 'turn', 'flip' or 'bigger', give two transformations instead of one, or leave out a centre, an angle's direction or a scale factor.

Expanding and simplifying

MistakeYou lose a minus sign when expanding or collecting, so −2(3x − 4) becomes −6x − 8, or you join unlike terms: 3x + 2y becomes 5xy.

Rounding

MistakeYou round in the middle of a calculation, or mix up significant figures with decimal places, so your final answer is not accurate enough.

Right-angled triangles

MistakeYou add the squares when finding a shorter side, or pick sine, cosine or tangent without checking which sides you actually know.

Interest and discounts

MistakeYou give the interest or discount when the question wants the final amount, or the other way round, or use simple interest when it compounds.

Surface area and volume

MistakeYou work out the volume when the surface area is asked for, miss some faces of a solid, or mix centimetres and metres in one calculation.

Averages from diagrams

MistakeReading a stem-and-leaf diagram, you read a leaf on its own (7 instead of 27), or divide by the wrong count when finding a mean.

Probability without replacement

MistakeYou count only one order (red then blue, but not blue then red), or keep the same denominator for the second pick when the first item is not put back.

Upper and lower bounds

MistakeYou use the wrong half-unit, work out the answer before applying the bounds, or pair upper with upper when dividing or subtracting.

Composite functions

MistakeYou treat fg(x) as f(x) × g(x), work out f first instead of g, or substitute g(x) without brackets.

Inverse functions

MistakeYou write f⁻¹(x) as 1/f(x), or just change the signs, instead of finding the function that undoes f.

Rounding and accuracy

MistakeYou round values partway through, chop off digits instead of rounding, or round an answer that is already exact.

Sine and cosine rules

MistakeYou assume a triangle is right-angled, or accept the calculator's acute angle from the sine rule when the angle is obtuse.

Percentage change

MistakeFor repeated percentage changes you add the percentages, use simple interest when it compounds, or give the total when only the interest is wanted.

Grouped data

MistakeYou draw histogram bars to the frequency instead of the frequency density, or use class boundaries instead of midpoints to estimate a mean.

Similar shapes

MistakeYou use the length scale factor to scale up an area or a volume of similar shapes.