Exam-style questions by topic — AQA GCSE Mathematics
One question for each of 13 topics. These are written for this specification by MasteryMind. They are not past-paper questions, and they are not from AQA.
Structure and calculation
Rationalise the denominator of 6/√3, giving your answer in its simplest form.
Practise Structure and calculationFractions, decimals and percentages
In a school the ratio of students who walk to school to those who travel by bus is 2 : 7. What fraction of these students travel by bus?
Practise Fractions, decimals and percentagesMeasures and accuracy
A length L is truncated to 1 decimal place, giving 6.3 cm. Write an inequality for the possible values of L.
Practise Measures and accuracyNotation, vocabulary and manipulation
The functions f and g are defined by f(x) = 3x − 2 and g(x) = x² + 4. Work out the value of the composite function fg(2).
Practise Notation, vocabulary and manipulationGraphs
A quadratic curve has equation y = x² − 3x − 10. By solving the equation algebraically, find the x-coordinates where the curve crosses the x-axis.
Practise GraphsSolving equations and inequalities
Solve the simultaneous equations y = x² − 3x + 1 and y = 2x − 5.
Practise Solving equations and inequalitiesSequences
A Fibonacci-type sequence starts 3, 4, 7, 11, 18, ... Each term after the second is the sum of the two previous terms. What is the next term?
Practise SequencesRatio, proportion and rates of change
In a right-angled triangle, the side opposite angle θ is 6 cm and the adjacent side is 8 cm. A second right-angled triangle is similar to the first, and its adjacent side is 20 cm. Because the triangles are similar, the trigonometric ratio tan θ is the same for both. What is the length of the side opposite angle θ in the second triangle?
Practise Ratio, proportion and rates of changeProperties and constructions
Shape A is a rectangle with vertices (0, 0), (4, 0), (4, 2) and (0, 2). Shape B is the rectangle with vertices (0, 0), (0, 4), (−2, 4) and (−2, 0). Which single transformation maps A onto B?
Practise Properties and constructionsMensuration and calculation
A rectangular field measures 250 m by 180 m. A farmer sows grass seed at a rate of 35 grams per square metre. What mass of seed, in kilograms, is needed for the whole field?
Practise Mensuration and calculationVectors
Vector a is the column vector with top entry 3 and bottom entry 2. Vector b is the column vector with top entry 5 and bottom entry -1. What is the column vector for a + b?
Practise VectorsProbability
A fair spinner has eight equal sectors numbered 1 to 8. It is spun 400 times. Work out the expected number of times it lands on a number greater than 5.
Practise ProbabilityStatistics
A histogram is drawn for continuous data with unequal class intervals. The class 10 < x ≤ 20 has frequency 30 and is drawn with a bar of width 4 cm. What is the frequency density for this class?
Practise Statistics
Practise all 393 practice questions and see your weak topics.
A week of Premium from your first lesson · Then the free plan continues · No card, no charge