🏛️ Misconception Museum
A catalog of the most common mistakes in GCSE Mathematics and how to avoid them
Confusing parallel with collinear H
"The Parallel Pitfall"
Geometry & ShapesIgnoring direction (negative signs)
"The One-Way Street"
Geometry & ShapesWriting column vectors as fractions
"The Fraction Habit"
Geometry & ShapesAdding first term to dn without checking
"The First Term Fumble"
Algebra & GraphsAdding numbers under the root sign H
"The Root Addition Error"
Number & ProportionAdding probabilities when you should multiply
"The AND/OR Mixup"
Probability & StatisticsAdding the percentage instead of multiplying
"The Add-On Error"
Number & ProportionAssuming correlation means causation
"The Causation Confusion"
Probability & StatisticsCalculating gradient with x over y instead of y over x
"The Gradient Flip"
Algebra & GraphsCancelling terms instead of factors
"The Term Terminator"
Algebra & GraphsConfusing "bearing of A from B" with "bearing of B from A"
"The From Confusion"
Geometry & ShapesConfusing HCF and LCM
"The HCF-LCM Swap"
Number & ProportionConfusing opposite and adjacent sides
"The O-A Swap"
Geometry & ShapesDividing by one ratio part instead of the total
"The Part-Total Mixup"
Number & ProportionFinding $c^2$ instead of $c$
"The Forgotten Root"
Geometry & ShapesFinding median without ordering data first
"The Middle Muddle"
Probability & StatisticsForgetting to change the sign when moving terms
"The Sign Slip"
Algebra & GraphsForgetting to include radii in sector perimeter
"The Missing Radii"
Geometry & ShapesGetting the order wrong in composite functions H
"The Order Flip"
Algebra & GraphsGiving probability greater than 1
"The Impossible Probability"
Probability & StatisticsHalving instead of doubling for angle at centre H
"The Half-Double Confusion"
Geometry & ShapesHaving A greater than or equal to 10
"The Ten Trap"
Number & ProportionIncomplete transformation description
"The Missing Detail"
Geometry & ShapesJoining plotted points with straight lines
"The Connect-the-Dots"
Algebra & GraphsMoving the decimal point the wrong way
"The Backwards Shift"
Number & ProportionMultiplying indices instead of adding when multiplying powers
"The Power Multiplier"
Number & ProportionNot applying operations to entire expressions
"The Partial Operation"
Algebra & GraphsNot reversing the sign when dividing by negative
"The Flip Forget"
Algebra & GraphsOnly giving one solution to a quadratic
"The Missing Root"
Algebra & GraphsPlotting cumulative frequency at class midpoints
"The Midpoint Mistake"
Probability & StatisticsSign errors when subtracting equations
"The Subtraction Slip"
Algebra & GraphsThinking $(a + b)^2 = a^2 + b^2$
"The Binomial Blunder"
Algebra & GraphsUsing 180° as the sum for all polygons
"The Triangle Default"
Geometry & ShapesUsing diameter instead of radius in circle formulas
"The D-R Disaster"
Geometry & ShapesUsing frequency for the height instead of frequency density H
"The Height Mistake"
Probability & StatisticsUsing length scale factor for area
"The Area Scale Slip"
Geometry & ShapesUsing simple interest formula for compound interest
"The Simple Mistake"
Number & ProportionUsing the wrong inequality sign for upper bound H
"The Inequality Slip"
Number & ProportionUsing the wrong trigonometric rule H
"The Rule Mix-Up"
Geometry & ShapesAdding adjacent instead of opposite angles in cyclic quadrilateral H
"The Adjacent Angle Error"
Geometry & ShapesAdding when finding a shorter side
"The Plus-Minus Mixup"
Geometry & ShapesApplying index laws to different bases
"The Base Blunder"
Number & ProportionAveraging the values column instead of using frequencies
"The Frequency Forgetter"
Probability & StatisticsCalculator set to radians instead of degrees
"The Mode Mishap"
Geometry & ShapesConfusing gradient and y-intercept
"The m-c Mixup"
Algebra & GraphsConfusing interior and exterior angle formulas
"The Inside-Out Error"
Geometry & ShapesDividing by the new value instead of the original
"The Denominator Disaster"
Number & ProportionDividing numerator and denominator by different numbers
"The Unequal Split"
Number & ProportionDividing the wrong way round
"The Fraction Flip"
Algebra & GraphsErrors when expanding negative brackets
"The Negative Neglect"
Algebra & GraphsFinding only one variable
"The Halfway Stop"
Algebra & GraphsGetting the angle fraction upside down
"The Fraction Flip"
Geometry & ShapesGiving shares to the wrong people
"The Swap Error"
Number & ProportionMatching wrong corresponding sides
"The Side Mismatch"
Geometry & ShapesMeasuring anticlockwise instead of clockwise
"The Wrong Direction"
Geometry & ShapesNot changing fractions for without replacement
"The Replacement Forget"
Probability & StatisticsNot fully simplifying a surd H
"The Partial Simplify"
Number & ProportionNot multiplying all terms when finding common denominator
"The Missing Multiply"
Algebra & GraphsOnly doing the operation on one side
"The One-Sided Operation"
Algebra & GraphsPlacing the turning point at wrong coordinates
"The Misplaced Vertex"
Algebra & GraphsReading quartiles at wrong cumulative frequency values
"The Quartile Confusion"
Probability & StatisticsReading the height instead of calculating the area H
"The Reading Error"
Probability & StatisticsSign error in the cosine rule H
"The Sign Slip"
Geometry & ShapesSolving without setting equal to zero first
"The Zero Forgetter"
Algebra & GraphsThinking 1 is a prime number
"The One Error"
Number & ProportionThinking inverse means reciprocal H
"The Reciprocal Trap"
Algebra & GraphsTreating extrapolation as reliable
"The Extrapolation Overreach"
Probability & StatisticsUsing 1 + r instead of 1 - r for depreciation
"The Depreciation Direction"
Number & ProportionUsing first term instead of common difference
"The Difference Confusion"
Algebra & GraphsUsing slant height instead of perpendicular height
"The Slant Slip"
Geometry & ShapesUsing wrong bounds for subtraction H
"The Subtraction Swap"
Number & ProportionUsing wrong circle type on number line
"The Circle Confusion"
Algebra & GraphsUsing wrong sign for small numbers
"The Sign Slip"
Number & ProportionUsing wrong total for denominator
"The Total Trouble"
Probability & StatisticsWrong signs in translation vectors
"The Vector Sign Slip"
Geometry & ShapesCalculating the wrong class width H
"The Width Blunder"
Probability & StatisticsComparing box plots without using values
"The Vague Comparison"
Probability & StatisticsCross-multiplying when adding fractions
"The Cross-Multiply Confusion"
Algebra & GraphsDrawing line of best fit through all points
"The Connect-the-Dots Error"
Probability & StatisticsDrawing reciprocal graph through the origin H
"The Origin Error"
Algebra & GraphsEnlarging from wrong point
"The Centre Confusion"
Geometry & ShapesErrors when collecting x terms
"The Collection Confusion"
Algebra & GraphsFinding percentage of final amount for reverse problems
"The Backwards Blunder"
Number & ProportionForgetting tangent-radius is 90° H
"The Right Angle Oversight"
Geometry & ShapesForgetting the ½ in triangle area
"The Missing Half"
Geometry & ShapesForgetting to convert percentage to decimal
"The Percentage Slip"
Number & ProportionForgetting to square root or doing it incorrectly H
"The Root of the Problem"
Algebra & GraphsGetting the ratio the wrong way round
"The Flip"
Number & ProportionIncluding or excluding wrong integers at boundaries
"The Boundary Blunder"
Algebra & GraphsLabelling the wrong side as the hypotenuse
"The Hypotenuse Hijack"
Geometry & ShapesLeaving a surd in the denominator H
"The Forgotten Rationalise"
Number & ProportionMixing up alternate and co-interior angles
"The Z and C Confusion"
Geometry & ShapesMultiplying only one side of an equation
"The One-Sided Multiply"
Algebra & GraphsNot adjusting after calculation
"The Unadjusted Answer"
Number & ProportionNot substituting properly into function expressions H
"The Substitution Slip"
Algebra & GraphsNot taking out the highest common factor
"The Partial Factor"
Algebra & GraphsNot using inverse functions to find angles
"The Inverse Forget"
Geometry & ShapesNot using three figures for bearings
"The Missing Zero"
Geometry & ShapesSign errors in the quadratic formula H
"The Formula Fumble"
Algebra & GraphsSubtracting the wrong value for complementary events
"The Complement Confusion"
Probability & StatisticsThinking AAA proves congruence
"The AAA Assumption"
Geometry & ShapesThinking negative index gives negative answer H
"The Negative Confusion"
Number & ProportionThinking percentage means out of 100 literally
"The Literal Hundred"
Number & ProportionThinking perpendicular lines have the same gradient H
"The Perpendicular Puzzle"
Algebra & GraphsTreating truncation the same as rounding H
"The Truncation Trap"
Number & ProportionTree diagram branches not summing to 1
"The Branch Blunder"
Probability & StatisticsUsing class boundaries instead of midpoints
"The Boundary Blunder"
Probability & StatisticsUsing diameter instead of radius in arc/sector formulas
"The D for R Disaster"
Geometry & ShapesUsing the full second difference instead of half H
"The Half Slip"
Algebra & GraphsUsing the wrong angle in the area formula H
"The Wrong Angle"
Geometry & ShapesWriting prime factorisation without index notation
"The Index Omission"
Number & ProportionAdding equations when you should subtract
"The Operation Confusion"
Algebra & GraphsAdding highest and lowest instead of subtracting
"The Range Reversal"
Probability & StatisticsAdding/subtracting wrong amount for bounds H
"The Half-Step Slip"
Number & ProportionAssuming fg(x) equals gf(x) H
"The Commutative Confusion"
Algebra & GraphsConfusing clockwise and anticlockwise
"The Direction Dilemma"
Geometry & ShapesDividing by x and losing a solution
"The Vanishing Root"
Algebra & GraphsFinding LCM by just multiplying the two numbers
"The Multiply Mistake"
Number & ProportionIgnoring the ambiguous case H
"The Missing Answer"
Geometry & ShapesLeaving gaps between histogram bars H
"The Gap Problem"
Probability & StatisticsMixing up exact trig values for 30° and 60° H
"The 30-60 Swap"
Geometry & ShapesMixing up percentage and decimal forms
"The Percentage Pickle"
Probability & StatisticsMultiplying base by fraction for fractional indices H
"The Fraction Fumble"
Number & ProportionNot factorising before cancelling
"The Hasty Canceller"
Algebra & GraphsSubtracting interest to find original amount
"The Reverse Mistake"
Number & ProportionThinking exponential graphs cross the x-axis H
"The Impossible Intercept"
Algebra & GraphsUsing degree formula with radians or vice versa H
"The Radian Wrangle"
Geometry & ShapesWriting the inequality the wrong way round
"The Backwards Inequality"
Algebra & GraphsConfusing expected frequency with probability
"The Expected Error"
Probability & StatisticsGiving the position as the answer instead of the value
"The Position Problem"
Probability & StatisticsAssuming outcomes are equally likely when they are not
"The Fair Fallacy"
Probability & Statistics