GCSE-readyKS3 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.
Number
- Place value, ordering and rounding
- Not “0.6”. 0.6 = 0.600, which is smaller than 0.606.
- Not “0.065”. 0.065 has 0 tenths, so it is the smallest.
- Not “<”. 7 is bigger than 3, but −7 is further below zero than −3.
- Calculating with decimals
- Not “The answer is more than 45”. That happens when you multiply by a number bigger than 1.
- Not “The answer is less than 0.8”. 45 lots of 0.8 is much more than 0.8.
- Factors, multiples and primes
- Not “47”. 47 has only the factors 1 and 47.
- Not “53”. 53 has only the factors 1 and 53.
- Not “59”. 59 has only the factors 1 and 59.
Algebra
- Algebraic notation, simplifying and substitution
- Not “y3”. y3 means y × y × y.
- Not “3 + y”. 3 + y is written with a plus sign.
- Expressions, equations, formulae and identities
- Not “5y − 2 = 8”. This is an equation: it is true only when y = 2.
- Not “A = πr2”. This is a formula linking A and r.
- Not “3(a + 1) ≡ 3a + 3”. The ≡ sign makes this an identity.
- Sequences and the nth term
- Not “2, 6, 10, 14”. That adds 4 each time, so it is arithmetic.
- Not “1, 4, 9, 16”. Those are square numbers.
- Not “1, 1, 2, 3”. That is the start of the Fibonacci sequence.
Ratio, proportion and rates of change
- Metric units and converting measures
- Not “3 hours 40 minutes”. That treats the hour as 100 minutes. An hour has 60 minutes.
Geometry and measures
- Angle facts
- Not “132°”. 132° is the angle next to it on the straight line.
- Symmetry and properties of 2-D shapes
- Not “Parallelogram”. A parallelogram has two pairs of parallel sides.
- Not “Kite”. A kite has no parallel sides.
- Not “Square”. A square has 4 lines of symmetry.
- Perimeter and area
- Not “m”. Metres measure length or perimeter.
- Not “m3”. Cubic metres measure volume.
Number
- Terminating decimals, fractions and percentages
- Not “16”. 6 = 2 × 3. The 3 makes it recur: 0.1666...
- Not “29”. 9 = 32, so 29 = 0.222... recurs.
- Not “512”. 12 = 22 × 3. The 3 makes it recur.
Ratio, proportion and rates of change
- Percentage change and simple interest
- Not “0.08”. × 0.08 just finds 8%.
- Not “1.8”. 1.8 would be an 80% increase.
- Not “0.92”. 0.92 is an 8% decrease.
- Real-life graphs and rates of change
- Not “The object is moving at constant speed”. Constant speed is a sloping straight line.
Algebra
- Expanding and factorising brackets
- Not “2(4a + 6)”. 2(4a + 6) is correct but not fully factorised: 4a + 6 still has a factor of 2.
- Not “8(a + 12)”. 8 × 12 = 96, not 12.
- Not “4(2a + 12)”. 4 × 12 = 48, not 12.
- Harder equations and inequalities
- Not “x ≤ 4”. The sign stays strict (<), so 4 itself is not included.
- Inequalities and number lines
- Not “x < 4”. x < 4 would use an open circle.
- Not “x ≥ 4”. x ≥ 4 would point to the right.
- Not “x ≥ 213”. You subtracted 4 instead of adding it.
- Arithmetic and geometric sequences
- Not “No, because 78 is not a multiple of 4”. The sequence is 4n + 2, not 4n. Solve the equation instead.
- Not “1, 2, 4, 8, ...”. This multiplies by 2: it is geometric.
- Not “1, 4, 9, 16, ...”. These are square numbers: the differences change.
- Coordinates and straight-line graphs
- Not “(5, 3)”. 2 × 5 − 1 = 9, not 3.
- Not “(2, 5)”. 2 × 2 − 1 = 3, not 5.
- Not “(0, 1)”. 2 × 0 − 1 = −1, not 1.
Geometry and measures
- Angles in parallel lines and polygons
- Not “Alternate angles”. Alternate angles form a Z shape.
- Not “Co-interior angles”. Co-interior angles form a C shape and add to 180°.
- Geometric reasoning and simple proofs
- Not “Co-interior angles are equal”. Co-interior angles add to 180°; they are not equal.
- Not “Alternate angles are equal”. Alternate angles need parallel lines.
- Circles: circumference and area
- Not “A tangent”. A tangent touches the circle at just one point.
- Not “An arc”. An arc is curved: part of the circumference.
Probability and statistics
- Tables, charts and diagrams
- Not “The number of goals scored”. Goals are counted, so that is discrete.
- Not “Favourite flavours of crisps”. Flavours are words, so that is categorical.
- Not “The number of people in a car”. People are counted, so that is discrete.
- Stem-and-leaf diagrams and frequency tables
- Not “7”. 8 − 1 = 7 uses the frequencies, not the goal values.
Number
- Index laws and standard form
- Not “3.2 × 103”. A positive power gives a big number, 3 200.
- Not “32 × 10−4”. 32 is not between 1 and 10.
- Not “0.32 × 10−2”. 0.32 is less than 1.
- Significant figures, estimation and error intervals
- Not “59.5 ≤ m < 60.5”. That would be for rounding to the nearest 1 kg.
- Not “55 < m ≤ 65”. 55 itself rounds to 60, so it is included; 65 rounds to 70, so it is not.
- Calculator skills and types of number
- Not “√9”. √9 = 3, which is an integer.
- Not “0.25”. 0.25 = 14.
- Not “27”. 27 is already a fraction of two integers.
Ratio, proportion and rates of change
- Compound units and converting measures
- Not “2 hours 40 minutes”. That treats 0.4 hours as 40 minutes, but an hour has 60 minutes.
- Direct and inverse proportion, and original values
- Not “A curve that gets closer to both axes”. That is the shape for inverse proportion.
Algebra
- Gradients, intercepts and y = mx + c
- Not “(1, 2)”. (1, 2) is on y = x + 1, but 3 × 1 − 3 = 0, not 2.
- Not “(3, 4)”. (3, 4) is on y = x + 1, but 3 × 3 − 3 = 6, not 4.
- Simultaneous equations
- Not “(6, 3)”. Check: y = 2x would need 3 = 12.
- Not “Infinitely many”. That only happens when the two equations are the same line.
- Not “x = 3, y = 2”. 2(3) − 2 = 4, not 7.
- Double brackets and quadratic graphs
- Not “An upside-down U-shaped curve”. That happens when the x2 term is negative.
- Cubic, reciprocal and exponential graphs
- Not “A U-shaped curve”. That is a quadratic.
- Not “An S-shaped curve through the origin”. That is a cubic like y = x3.
- Not “y = x3”. x3 is a cubic.
- Formulae and changing the subject
- Not “x = y4 − 3”. You must subtract 3 before dividing, so all of y − 3 is divided by 4.
Geometry and measures
- Transformations
- Not “(−4, 2)”. That is a reflection in the y-axis.
- Not “(2, 4)”. That is a reflection in y = x.
- Not “(−1, 3)”. That is 90° anticlockwise.
- Constructions, congruence and similarity
- Not “AAA”. AAA is not a congruence condition at all.
- Trigonometry in right-angled triangles
- Not “Cosine”. Cosine uses the adjacent side.
- Not “Tangent”. Tangent uses opposite and adjacent.
- Properties of 3-D shapes and cylinders
- Not “Cylinder”. A cylinder has two flat circular faces.
- Not “Sphere”. A sphere has no flat faces.
- Not “Triangular prism”. A prism has only flat faces.
Probability and statistics
- Grouped data and estimating the mean
- Not “10 ≤ t < 20”. Only 13 values are below 20, so the 15th is not in this class.
- Scatter graphs and correlation
- Not “Shoe size and test score”. There is no reason for these to be linked.
- Not “Age of a car and its value”. Older cars are usually worth less: negative.
- Not “Temperature and coats sold”. Warmer weather usually means fewer coats sold: negative.