Cambridge A-level Maths Year 13 revision

Topic 3.1: Algebra

It builds on what you learned at AS Level in Quadratics and Series, and takes it further.

There are 4 parts: we start with modulus functions, and finish with binomial expansion for any rational power, and when it is valid.

1. 3.1.1Modulus functions: graphs, equations and inequalities44 questions
2. 3.1.2Proof, functions and partial fractionsFree 26 questions
3. 3.1.3Partial fractions: linear factors, repeated factors and improper fractions37 questions
4. 3.1.4Binomial expansion for any rational power, and when it is valid44 questions

Topic 3.2: Logarithmic and exponential functions

We will go through it step by step.

1. 3.2.1Logarithmic and exponential functions: ln x, eˣ, solving equations and linear forms36 questions

Topic 3.3: Trigonometry

It builds on what you learned at AS Level in Trigonometry, and takes it further.

There are 2 parts: we start with reciprocal trigonometric functions (sec, cosec, cot) and inverse trigonometric functions, and finish with addition and double-angle formulae, and the R sin(x+α) form.

1. 3.3.1Reciprocal trigonometric functions (sec, cosec, cot) and inverse trigonometric functions57 questions
2. 3.3.2Addition and double-angle formulae, and the R sin(x+α) form31 questions

Topic 3.4: Differentiation

It builds on what you learned at AS Level in Differentiation, and takes it further.

There are 5 parts: we start with further differentiation and integration, and finish with implicit differentiation and connected rates of change.

1. 3.4.1Further differentiation and integrationFree 56 questions
2. 3.4.2Radians, trigonometry and parametric equationsFree 52 questions
3. 3.4.3Parametric equations: converting to Cartesian form and sketching curves26 questions
4. 3.4.4Differentiating and integrating parametric equations54 questions
5. 3.4.5Implicit differentiation and connected rates of change65 questions

Topic 3.5: Integration

It builds on what you learned at AS Level in Integration, and takes it further.

There are 3 parts: we start with integration by substitution and by parts, and finish with numerical integration.

1. 3.5.1Integration by substitution and by partsFree 58 questions
2. 3.5.2Integration using partial fractions and trigonometric identities63 questions
3. 3.5.3Numerical integration: the trapezium rule74 questions

Topic 3.6: Numerical solution of equations

We will go through it step by step.

1. 3.6.1Iterative methods and the Newton–Raphson method85 questions

Topic 3.7: Vectors

There are 2 parts: we start with numerical methods and 3D vectors, and finish with vectors in three dimensions.

1. 3.7.1Numerical methods and 3D vectorsFree 67 questions
2. 3.7.2Vectors in three dimensions42 questions

Topic 3.8: Differential equations

We will go through it step by step.

1. 3.8.1First-order separable differential equations48 questions

Topic 3.9: Complex numbers

We will go through it step by step.

1. 3.9.1Complex numbers: arithmetic, Argand diagrams, modulus–argument form and loci43 questions

Topic 6.1: The Poisson distribution

It builds on what you learned at AS Level in Discrete random variables, and takes it further.

We will go through it step by step.

1. 6.1.1The Poisson distribution: conditions, probabilities and approximations53 questions

Topic 6.2: Linear combinations of random variables

It builds on what you learned at AS Level in Discrete random variables, and takes it further.

We will go through it step by step.

1. 6.2.1Linear combinations of random variables: expectation, variance and sums of normal variables31 questions

Topic 6.3: Continuous random variables

We will go through it step by step.

1. 6.3.1Continuous random variables: probability density functions, median, mean and variance53 questions

Topic 6.4: Sampling and estimation

It builds on what you learned at AS Level in The normal distribution, and takes it further.

We will go through it step by step.

1. 6.4.1Sampling and estimation: unbiased estimates, the central limit theorem and confidence intervals57 questions

Topic 6.5: Hypothesis tests

It builds on what you learned at AS Level in Discrete random variables, and takes it further.

There are 2 parts: we start with hypothesis test for the mean of a normal distribution, and finish with hypothesis testing with correlation and the normal distribution.

1. 6.5.1Hypothesis test for the mean of a normal distribution81 questions
2. 6.5.2Hypothesis testing with correlation and the normal distribution75 questions

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