AQA GCSE maths: tips for tricky topics
Did you know that after each set of exams, examiners write reports explaining what students did well and which topics they found more tricky?
We’ve looked at where the reports for AQA GCSE Maths identify ‘topics where students struggled’ and pulled these together with some examples and support that you can find in your Oxford Revise AQA GCSE Maths revision guide.
Are you ready to ace those tricky topics?
Useful links
Accuracy, number and conversions
Bounds (Higher only)
Bounds often proved challenging. For example, if a mass is given as 60kg to the nearest 5kg, the value could be as high as 62.5kg. But when asked for the maximum possible outcome some students used 60 in their calculations.
TIP
If a question asks for the ‘maximum possible’ value or ‘minimum possible’ value, use the upper or lower bound.
LOOK AT
Oxford Revise: Higher Chapter 2 Rounding, truncating, error intervals, and estimating.
Converting units
TIP
When converting units, ask: should the number get bigger or smaller? For example, converting centimetres to kilometers should make the number smaller. If it increases, something’s wrong!
LOOK AT
Oxford Revise: Foundation Chapter 14 Units and measures, and Higher Chapter 17 Compound measures and multiplicative reasoning.
Algebra and equations
Algebra marks were often lost because equations were set up incorrectly or the algebraic meaning was misinterpreted, rather than because the maths itself was too difficult.
Sequences
The term-to-term rule and the nth-term formula were commonly confused.
TIP
The term-to-term rule tells you how to get from ont term to the next. The nth term formula lets you find any term from its position, n, in the sequence.
LOOK AT
Oxford Revise: Foundation Chapter 13 Sequences; Higher Chapter 12 Sequences
Inequalities
A common issue was forgetting to reverse the inequality sign when multiplying or dividing by a negative number.
Others used the wrong boundary lines or shaded the wrong region.
TIP
If you solve -2𝑥 > 6 and write 𝑥 > -3, you’ve forgotten that dividing by -2 reverses the sign. The correct answer is 𝑥 < -3.
LOOK AT
Oxford Revise: Higher Chapter 8 Solving inequalities in 1 or 2 variables.
Circles (Higher only)
In circle equations, not recognising the form (𝑥 – 𝑎 )² + (𝑦 – 𝑏 )² made centre and radius harder to identify.
LOOK AT
Oxford Revise: Higher 26 Circle theorems and circle geometry
Proof
In proof questions, a common approach was to test a few values instead of giving a general algebraic argument. Testing n =1,2,3 isn’t proof. You must rewrite the expression, so that it proves the statement algebraically.
LOOK AT
Oxford Revise: Higher Chapter 15 Algebraic fractions, rearranging formulae with algebraic fractions, proof, functions and composite functions
Graphs
Straight line graphs
With straight line graphs, it was easy to forget that a horizontal line has gradient zero.
TIP
A horizontal line has gradient 0.
𝑦 = 3 is an equation of a line, not its gradient.
LOOK AT
Oxford Revise: Foundation Chapter 8 Straight line graphs and Higher Chapter 6 Linear graphs
Drawing curves
On Higher papers, plotting the points wasn’t enough; curves needed to be smooth and accurate.
TIP
Curves should be smooth, show the correct shape (U-shape for quadratics, S-shape for cubics), and extend beyond the plotted points if required.
LOOK AT
Oxford Revise: Higher Chapter 13 Cubic graphs, reciprocal graphs, exponential graphs, transformation of graphs
Geometry and shape
Volume
A common mistake in volume questions was using the diameter instead of the radius.
TIP
Volume formulas generally use the radius. If a question gives the diameter, divide by 2 to find the radius, before substituting into the formula to find volume.
LOOK AT
Oxford Revise: Foundation Chapter 21 Circles, cylinders, cones, and spheres and Higher Chapter 20 Surface area and volume
Similarity
Similarity caused confusion, especially with scale factors. It was common to think that if the length doubles, then the area should also double, as the area depends on two dimensions.
TIP
area scale factor = (length scale factor)²
volume scale factor = (length scale factor)³
LOOK AT
Oxford Revise: Foundation Chapter 22 Similarity and congruence and Higher Chapter 22 Similarity and congruence
Pythagoras
With Pythagoras questions, the formula was usually remembered – but the right-angled triangle wasn’t always spotted. Sometimes the triangle is hidden inside a larger shape.
TIP
Before doing any calculations, draw over the diagram, mark the right angle clearly and label the hypotenuse.
LOOK AT
Oxford Revise: Chapter 24 Pythagoras and trigonometry and Higher Chapter 21 Pythagoras and 2D trigonometry
Bearings
Bearings were sometimes measured from the wrong direction.
TIP
Bearings are always measured clockwise from North.
LOOK AT
Oxford Revise: Chapter 25 Constructions, loci, and bearings and Higher Chapter 24 Plans, elevations, constructions, bearings
Data and probability
Venn diagram
Values were sometimes double-counted, or ‘A and B’ was confused with ‘A or B’.
TIP
When filling Venn diagrams, fill the overlap first, then the outer sections, then check everything adds up. Remember that ∩ means A and B (the intersection), and ∪ means A or B or both (the union).
LOOK AT
Oxford Revise: Foundation Chapter 28 Expected results, tree diagrams, set notation, and probability from tables and diagrams and Higher Chapter 28 Probability
Inter-quartile range
Range and inter-quartile range were sometimes confused.
TIP
range = highest – lowest
inter-quartile range = Q3 − Q1
LOOK AT
Oxford Revise: Higher Chapter 31 Data collection, cumulative frequency, box plots
Relative frequency
Experimental probability was sometimes treated as if it had to match theoretical probability exactly. These questions often ask whether results are ‘fair’. Experimental results don’t have to match theoretical probability exactly.
LOOK AT
Oxford Revise: Foundation Chapter 27 Theoretical probability, mutually exclusive events, possibility spaces, and probability experiments
Other things to watch for
The reports also highlighted some common habits that can cost marks across many different questions. Keeping these in mind during revision and in the exam can help avoid easy mistakes.
Write clearly. Make sure digits such as 4 and 9 are easy to distinguish, and don’t use very small handwriting.
Avoid rounding too early. Keep full calculator values during your working and round only at the final step unless the question tells you otherwise.
Check your calculator mode. Trigonometry questions require degree mode, not radians.
Copy numbers carefully. Always double-check values copied from the question or from earlier steps in your working.