GCSE-readyGCSE and International GCSE Mathematics: common mistakes
The wrong answers students pick most often in our Mathematics questions, and why they are wrong. Read these before a test, then open the lesson for anything that surprises you.
Getting started
- Number skills: order of operations and written methods
- Not “2 + (3 × 4)”. 2 + 12 = 14.
- Not “2 + 3 × (4)”. That is still 2 + 12 = 14.
- The language of algebra
- Not “7y”. The numbers are multiplied, not added.
- Not “2n − 5”. That doubles first, then takes 5.
- Not “2x + 1”. That is an expression: there is no equals sign.
- Shapes, angles and coordinates
- Not “Obtuse”. Obtuse angles are between 90° and 180°.
- Not “Parallelogram”. A parallelogram has two pairs.
- Not “Kite”. A kite has no parallel sides in general.
- Measures: scales, time and money
- Not “3 hours 20 minutes”. An hour has 60 minutes, not 100.
- How GCSE Maths is assessed
- Not “9”. Grade 9 is only available on the Higher tier.
- Not “AO1”. AO1 is using standard techniques.
Number
- Prime factors, HCF and LCM
- Not “1”. 1 has only one factor, so it is not prime.
- Not “9”. 9 = 3 × 3, so it has the factor 3.
- Not “21”. 21 = 3 × 7, so it has the factors 3 and 7.
- Powers, roots and estimating
- Not “35 and 36”. Halving 70 does not give its square root.
- Fraction arithmetic
- Not “815”. That is 23 × 45. For division you flip the second fraction first.
- Not “65”. You flipped the first fraction. Keep the first one and flip the second.
- Laws of indices
- Not “512”. You multiplied the powers. When you multiply numbers, you add the powers.
- Not “257”. The base stays as 5. Only the powers change.
- Not “2512”. The base stays as 5, and the powers are added.
- Standard form
- Not “62 × 103”. 62 is not less than 10.
- Not “0.62 × 105”. 0.62 is less than 1.
- Simplifying surds
- Not “2√12”. 2√12 equals √48, but 12 still has a square factor (4). Use the biggest square factor, 16.
- Not “16√3”. You need the square root of 16, which is 4, not 16 itself.
- Not “3√16”. Put the square root of the square factor outside: √16 = 4 goes outside, 3 stays inside.
- Surds: brackets and harder denominators
- Not “5 − 2√3”. Check the sign of −2√3 + 4√3.
- Not “11 + 2√3”. √3 × √3 = 3, and it is subtracted.
- Not “9 + 2”. You must include the two middle terms.
Algebra
- Expressions, substitution and formulae
- Not “3x + 2 = 11”. That is an equation: true for only one value of x.
- Not “y = 3x + 2”. That is a formula or equation of a line.
- Not “3x + 2”. That is an expression.
- Expanding and factorising
- Not “x2 + 8”. You missed the middle terms 2x and 4x. Every term multiplies every term.
- Not “x2 + 6x + 6”. The last term is 4 × 2 = 8, not 4 + 2.
- Not “2x + 6”. x × x = x2, not 2x.
- Changing the subject of a formula
- Not “x = y5 − 2”. You must subtract 2 before dividing, so the whole of y − 2 is divided by 5.
- Solving linear equations
- Not “x = 3”. After subtracting 5 you get −2x = 6. Dividing by −2 gives a negative answer.
- Not “x = 8”. Check: 5 − 2 × 8 = −11, not 11.
- Not “x = −8”. Check: 5 − 2 × (−8) = 21, not 11.
- Forming and solving equations from words and diagrams
- Not “2(n + 7) = 31”. That adds 7 before doubling.
- Gradients of curves and areas under graphs
- Not “Distance travelled”. Distance is the area under the graph.
- Solving quadratics by factorising
- Not “(x + 15)(x + 1)”. 15 × 1 = 15, but 15 + 1 = 16, not 8.
- Not “(x + 8)(x + 15)”. The numbers must multiply to 15 and add to 8.
- Not “(x − 3)(x − 5)”. −3 + (−5) = −8. You need +8.
- Simultaneous linear equations
- Not “x = 3, y = 7”. Check x − y = 4: 3 − 7 = −4, not 4.
- Not “x = 6, y = 4”. Check x − y = 4: 6 − 4 = 2, not 4.
- Not “x = 14, y = −4”. Adding gives 2x = 14, so x = 7. Remember to divide by 2.
- Quadratic inequalities
- Not “(1, 3)”. At (1, 3): 3 > 3 is false.
- Not “(3, 5)”. At (3, 5): 5 > 7 is false.
- Algebraic fractions
- Not “x + 5x = 5”. x is a term on top, not a factor of the whole top.
- Not “x + 44 = x”. 4 is a term on top, not a factor.
- Graphs of sin x, cos x and tan x
- Not “x = 270°”. sin, not cos, reaches −1 at 270°.
Ratio, proportion and rates of change
- Ratio problems: fractions, 1 : n and changing ratios
- Not “2 : 3 : 5”. The b parts are 3 and 4, so they do not match yet.
- Simple interest, percentages over 100% and growth problems
- Not “1.5”. 1.5 is an increase of 50%.
- Proportion graphs and gradient as a rate
- Not “A straight line crossing the y-axis at 3”. A line with a y-intercept is linear but not proportional.
Geometry and measures
- Symmetry and the properties of quadrilaterals
- Not “Kite”. Only one diagonal of a kite is bisected.
- Angles in polygons
- Not “Yes, it has 7 sides”. A regular 7-sided polygon has exterior angles of 360° ÷ 7 ≈ 51.4°, so its interior angle is about 128.6°, not 130°.
- Not “Yes, it has 130 sides”. The number of sides comes from 360 ÷ exterior angle, not from the interior angle.
- Not “No, interior angles must be less than 120°”. Regular polygons can have large interior angles. A regular octagon has 135°.
- Circles, arcs and sectors
- Not “6π cm2”. 6π is the circumference.
- Not “28.3 cm2”. That is a decimal, not in terms of π.
- Coordinates, midpoints and shapes on a grid
- Not “(2.5, 5)”. That is the midpoint of A and M.
- Similar shapes: area and volume
- Not “1 : 9”. 1 : 9 is the area ratio.
- Pythagoras' theorem
- Not “5, 6, 7”. 52 + 62 = 61, but 72 = 49.
- Not “6, 8, 11”. 62 + 82 = 100, but 112 = 121.
- Not “4, 5, 7”. 42 + 52 = 41, but 72 = 49.
- Right-angled trigonometry
- Not “sin”. sin uses opposite and hypotenuse (SOH).
- Not “cos”. cos uses adjacent and hypotenuse (CAH).
- Not “none of them”. TOA: tan = opposite ÷ adjacent.
Probability
- Tree diagrams and combined events
- Not “The events cannot both happen”. That describes mutually exclusive events.
Getting started
- How International GCSE Maths is assessed
- Not “In Paper 1 only”. Unlike GCSE 1MA1, 4MA1 has no non-calculator paper.
- Not “1 to 5”. That is the Foundation tier.
3 Sequences, functions and graphs
- Stretches of graphs: y = af(x) and y = f(ax)
- Not “(12, 6)”. That would be a horizontal stretch.
- Not “(8, 6)”. Inside the bracket you divide, not multiply.
- Not “A stretch parallel to the x-axis, scale factor 12”. Inside the bracket works the opposite way.