Free Common Mistakes / Misconceptions Lists

Download clean, printable lists of the most common mistakes students make — so you can fix them before they cost marks.

Each sheet is aligned to its exam board and built from recurring student errors highlighted in examiner reports and mark schemes.

Cambridge IGCSEMathematics (0580)CSV + Printable PDFFree download

What you get

A topic-by-topic mistakes list with a “do this instead” fix and a quick self-check.

How to use it

Review before past papers, then use the quick checks to catch errors under timed conditions.

Why it works

Many marks are lost on predictable slips: rounding, sign errors, units, and misreading commands.

Coverage by topic

Algebra20Geometry14Graphs9Mensuration9Number21Probability7Sets4Statistics13Transformations6Trigonometry9Vectors5
Alignment note: This is a practical revision checklist summarising recurring error patterns and mark-scheme expectations. Always verify methods and command words against your official syllabus, mark schemes, and examiner guidance.

Preview (up to 5 per topic)

117 total rows in download

TopicCommon mistake / misconceptionDo this insteadQuick check
NumberRounding too early in multi-step questions (loses accuracy).Keep full calculator value; round only at the end (unless instructed).Did you round intermediate steps?
NumberMixing up significant figures and decimal places.Count from first non-zero digit for s.f.; count digits after decimal for d.p.Does the instruction say s.f. or d.p.?
NumberUsing % as “divide by 100” but forgetting to convert back to a number.Write (p\% = p/100) and keep units consistent.Is your answer a percentage or a value?
NumberConfusing ratio parts with the total (e.g. 2:3 means 5 parts total).Add ratio parts first; scale by the total parts.Did you add the parts before scaling?
NumberIncorrect standard form conversion (wrong power sign).Move decimal: left → positive power; right → negative power.Is (1 \le a < 10) in (a\times10^n)?
AlgebraExpanding brackets incorrectly (sign errors).Distribute each term carefully; check by substituting a simple value.Do your signs match after expanding?
AlgebraFactorising: missing a common factor / incorrect factor pair.Factor out the HCF first; verify by expanding back.Does expanding return the original expression?
AlgebraSolving equations: doing different operations to each side.Keep balance: whatever you do to one side, do to the other.Did you apply the same operation to both sides?
AlgebraInequalities: forgetting to reverse the sign when multiplying/dividing by a negative.Reverse inequality when multiplying/dividing by a negative number.Did you multiply/divide by a negative?
AlgebraSimultaneous equations: substitution errors and sign slips.Substitute carefully; keep brackets; check by plugging back into both equations.Does your solution satisfy both equations?
GraphsGradient mistakes from using (Delta y / Delta x) backwards.Use (m = (y_2 - y_1)/(x_2 - x_1)) consistently.Did you keep the same point order in numerator and denominator?
GraphsReading coordinates inaccurately (not using grid scale).Check axis scale; use half-squares/units carefully.Did you confirm the axis increments?
GraphsMisinterpreting intercepts: mixing x-intercept and y-intercept.x-intercept: where (y=0). y-intercept: where (x=0).Which variable is zero at the intercept asked?
GraphsNot following axis scales correctly (counting squares without checking increments).Check the value per square on both axes before reading or plotting points.Have you confirmed axis increments?
GraphsCoordinates: reading off the wrong axis (mixing x and y values).Always write points as (x, y): across first, then up.Did you read x from the horizontal axis first?
GeometryAngle facts forgotten (alternate/corresponding) leading to wrong reasoning.Write the angle rule used; mark equal angles on diagram.Did you state/mark the angle rule?
GeometryBearings: not measuring from North or not using 3 digits.Bearings are clockwise from North and written as 3 digits (e.g. 045°).Is it clockwise from North with 3 digits?
GeometrySimilarity: mixing up scale factors for lengths and areas/volumes.Length scale factor (k), area (k^2), volume (k^3).Are you using (k) vs (k^2) or (k^3) correctly?
GeometryCircle theorems: applying the right theorem but to the wrong points/angles.Label points; identify the exact angle relationship (same segment, tangent-chord, etc.).Are the angles in the same segment/tangent-chord relation?
GeometryConstructions: not leaving arcs/compass marks (can lose method marks).Use a pencil, ruler and compasses, and leave construction arcs visible.Are your arcs/marks visible?
MensurationMixing units (cm vs m) in area/volume questions.Convert units before calculating; area uses squared units, volume cubed.Are all measurements in the same unit?
MensurationUsing diameter instead of radius in circle formulas.Radius (r = d/2); use (A=\pi r^2), (C=2\pi r).Did you halve the diameter to get radius?
MensurationSectors/arcs: confusing degrees and radians.Use the formula matching the angle unit given (usually degrees in IGCSE).Is your angle in degrees for the formula used?
MensurationUsing diameter where radius is needed in circle formulas.Radius (r=d/2). Use (A=\pi r^2), (C=2\pi r).Did you halve the diameter to get the radius?
MensurationUsing (pi\approx3.14) inconsistently across steps (accuracy loss).Use the calculator (pi) key or keep consistent precision until the final answer.Did you keep consistent accuracy for (pi)?
TrigonometryChoosing the wrong trig ratio (sin/cos/tan) from the triangle.Use SOHCAHTOA and label opposite/adjacent/hypotenuse first.Did you label sides relative to the angle?
TrigonometryCalculator mode errors (degrees vs radians).Use degrees mode for IGCSE trig unless told otherwise.Is your calculator in degrees?
TrigonometrySine/cosine rule: substituting wrong matching side-angle pair.Match each angle with its opposite side; write pairs explicitly.Did you pair each angle with the opposite side?
TrigonometryChoosing the wrong ratio because sides aren’t labelled relative to the angle.Label opposite/adjacent/hypotenuse first, then apply SOHCAHTOA.Did you label sides relative to the angle?
TrigonometryUsing the wrong triangle (not the one containing the required angle/side).Mark the angle/side you need, then choose the triangle that contains them.Did you use the triangle that contains the unknown?
VectorsVector addition/subtraction direction errors.Use head-to-tail method; keep direction consistent with arrows.Does your resultant direction make sense on the diagram?
VectorsTreating vectors like lengths only (dropping direction/notation).Keep vector notation and direction unless the question asks for a magnitude/length.Did you keep direction/notation?
VectorsVector subtraction: adding instead of subtracting (direction error).Subtract by adding the negative: (a-b = a+(-b)). Reverse the vector you subtract.Did you reverse the vector being subtracted?
VectorsUsing scalar multiples incorrectly (e.g. 2a means double length in same direction).Multiply magnitude by the scalar; direction stays the same for positive scalars.Did direction stay consistent for positive scalars?
VectorsNot using a clear diagram for vector journeys (hard to follow and easy to slip).Sketch the journey with arrows; label each vector; then write the equation.Do you have a labelled arrow diagram?
TransformationsEnlargements: using wrong centre or wrong scale factor direction.Mark centre; draw rays through points; multiply distances by scale factor.Did you use the correct centre and scale factor sign?
TransformationsRotation: wrong direction (clockwise/anticlockwise) or wrong centre.State centre + angle + direction clearly; test one point before drawing the full image.Are centre, angle and direction correct?
TransformationsReflection: reflecting in the wrong line (x-axis vs y-axis or a diagonal line).Identify the mirror line first and use perpendicular distances to reflect points.Did you use perpendicular distances to the correct line?
TransformationsTranslation: swapping the vector components (moving x by y and y by x).Translation vector (( + )) means move x then y (horizontal then vertical).Did you move horizontally then vertically by the correct amounts?
TransformationsEnlargement: using the wrong centre or measuring distances from the wrong point.Draw rays from the centre through each point; scale along the rays.Are all new points on rays from the centre?
ProbabilityAdding probabilities of non-mutually exclusive events.Use (P(A\cup B)=P(A)+P(B)-P(A\cap B)) when events overlap.Do events overlap? If yes, subtract the intersection.
ProbabilityTree diagrams: mixing conditional probabilities across branches.Update probabilities after each outcome; multiply along branches, add across paths.Did you multiply for a path and add for combined outcomes?
ProbabilityWithout replacement: not updating probabilities after the first selection.Update totals and counts after each draw; probabilities change without replacement.Did totals change after the first pick?
ProbabilityIndependent events: multiplying when events are mutually exclusive (should add).For OR (either event), add probabilities. For AND (both), multiply (if independent).Is it an OR or an AND situation?
ProbabilityComplement errors: using (1-p) but choosing the wrong (p).Define the event clearly; then (P(\text{not }A)=1-P(A)).Which event is the complement of what you want?
StatisticsMean from grouped data: using class boundaries incorrectly.Use midpoints; compute (\sum fx / \sum f).Did you use the midpoint of each class?
StatisticsScatter graphs: correlation interpreted as causation.State correlation only (positive/negative/no correlation) unless context supports causation.Did you avoid claiming cause without evidence?
StatisticsCumulative frequency / box plots: misreading quartiles from the graph.Q1 at 25%, median at 50%, Q3 at 75%; read carefully from axes.Did you locate 25/50/75% on the CF axis correctly?
StatisticsStem-and-leaf: using full values or decimals as leaves (wrong format).Stem is the leading digit(s); leaf is the final digit. Leaves are single digits and ordered.Are leaves single digits and in order?
StatisticsMedian position: using the middle of the unsorted list or picking the wrong item number.Order the data; median is the ((n+1)/2)th value (or average of two middle values).Did you sort data and use the correct median position?
SetsConfusing (n(A)) (number of elements) with set (A) (the elements).If it asks for (n(A)), give a number (count), not the elements themselves.Does it want the set or the number of elements?
SetsVenn diagrams: putting numbers in the wrong region (overlap vs only A/B).Fill the intersection first, then the exclusive regions, then outside the sets.Did you fill the intersection first?
SetsSet notation symbols confused (∪ vs ∩, complement).Union ∪ means 'OR'; intersection ∩ means 'AND'; complement is 'not in the set'.Are you using ∪ for OR and ∩ for AND?
SetsCounting from a Venn diagram: double-counting the intersection when adding totals.Total in A ∪ B is sum of all distinct regions; don’t add the overlap twice.Have you counted each region once only?
Pair this with the revision checklists and past paper finder for a full study workflow.

FAQ

What is the Cambridge IGCSE Maths (0580) common mistakes list?

It is a downloadable list of frequent mistakes students make in IGCSE Maths (0580), paired with a short fix and a “quick check” so you can catch the error under exam time pressure.

Does this cover the full 0580 syllabus?

Yes — the list includes mistakes across number, algebra, graphs, geometry, mensuration, trigonometry, vectors, probability, statistics and sets/notation.

Is this an official examiner report?

No. It is a practical revision resource summarising recurring error patterns and mark-scheme expectations. Always verify methods and command words against your official syllabus and mark schemes.

How do I use it to improve quickly?

Before a past paper, skim the topics you struggle with. After marking, highlight the mistakes you made and practise 5–10 similar questions using the “quick check” prompts to self-correct.