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Pure Mathematics 3 Practice
128 Tests • 1,920 Questions
Paper 3 • 75 marks • 1 hour 50 minutes
3.1 Algebra
3.1.1 Modulus equations, inequalities and graphs
2 Tests • 30 Questions3.1.2 Polynomial division, factor theorem and remainder theorem
2 Tests • 30 Questions3.1.3 Partial fractions
2 Tests • 30 Questions3.1.4 Binomial expansion for rational powers
2 Tests • 30 Questions
3.2 Logarithmic and exponential functions
3.2.1 Logarithms, indices and logarithmic laws
2 Tests • 30 Questions3.2.2 Exponential and logarithmic functions and graphs
1 Test • 15 Questions3.2.3 Exponential equations and inequalities
2 Tests • 30 Questions3.2.4 Transforming relationships to linear form
1 Test • 15 Questions
3.3 Trigonometry
3.3.1 Secant, cosecant and cotangent functions and graphs
2 Tests • 30 Questions3.3.2 Trigonometric identities and exact evaluation
2 Tests • 30 Questions3.3.3 Compound-angle and double-angle formulae
2 Tests • 30 Questions3.3.4 R sin(θ ± α) and R cos(θ ± α) forms and equations
2 Tests • 30 Questions
3.4 Differentiation
3.4.1 Derivatives of exponential, logarithmic and trigonometric functions
3 Tests • 45 Questions3.4.2 Product, quotient and chain rules
2 Tests • 30 Questions3.4.3 Parametric differentiation
1 Test • 15 Questions3.4.4 Implicit differentiation, tangents and normals
2 Tests • 30 Questions
3.5 Integration
3.5.1 Standard exponential, logarithmic and trigonometric integrals
2 Tests • 30 Questions3.5.2 Integration using trigonometric identities
2 Tests • 30 Questions3.5.3 Integration using partial fractions
2 Tests • 30 Questions3.5.4 Integration by parts
2 Tests • 30 Questions3.5.5 Integration using a given substitution
2 Tests • 30 Questions
3.6 Numerical solution of equations
3.6.1 Locating roots using graphs and sign changes
2 Tests • 30 Questions3.6.2 Iterative formulae and sequences of approximations
2 Tests • 30 Questions3.6.3 Accuracy, convergence behaviour and interpretation
1 Test • 15 Questions
3.7 Vectors
3.7.1 Vector notation, operations, magnitude and unit vectors
2 Tests • 30 Questions3.7.2 Position vectors and vector geometry
2 Tests • 30 Questions3.7.3 Vector equations of straight lines
2 Tests • 30 Questions3.7.4 Parallel, intersecting and skew lines
1 Test • 15 Questions3.7.5 Scalar product, angles and perpendicularity
2 Tests • 30 Questions
3.8 Differential equations
3.8.1 Forming differential equations from rate statements
2 Tests • 30 Questions3.8.2 Separable first-order differential equations
3 Tests • 45 Questions3.8.3 Initial conditions and particular solutions
1 Test • 15 Questions3.8.4 Interpreting solutions in context
1 Test • 15 Questions
3.9 Complex numbers
3.9.1 Complex numbers in Cartesian form
2 Tests • 30 Questions3.9.2 Modulus, argument, conjugates and conjugate roots
2 Tests • 30 Questions3.9.3 Argand diagrams and geometric representation
2 Tests • 30 Questions3.9.4 Polar form, multiplication and division
2 Tests • 30 Questions3.9.5 Square roots of complex numbers
1 Test • 15 Questions3.9.6 Loci in the Argand diagram
2 Tests • 30 Questions
Topic Mixed Practice
3.1 Algebra
4 Tests • 60 Questions3.2 Logarithmic and exponential functions
4 Tests • 60 Questions3.3 Trigonometry
4 Tests • 60 Questions3.4 Differentiation
4 Tests • 60 Questions3.5 Integration
4 Tests • 60 Questions3.6 Numerical solution of equations
4 Tests • 60 Questions3.7 Vectors
4 Tests • 60 Questions3.8 Differential equations
4 Tests • 60 Questions3.9 Complex numbers
4 Tests • 60 Questions
Full-Syllabus Mixed Practice
Pure Mathematics 3 Full-Syllabus Mixed Practice
20 Tests • 300 Questions
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