CIE AS & A Level Maths : Pure Mathematics Paper 3 Exam Questions New Syllabus - 2025-2027
CIE A Level Maths : Pure Mathematics Paper 3 Exam Questions – New Syllabus 2025-2027
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Pure Mathematics 3 – Paper 3
Topic-wise Exam Style Questions with syllabus-based subtopics for Paper \(3\)
Algebra
- Meaning and use of \(|x|\)
- Graphs of \(y=|ax+b|\)
- Polynomial division
- Factor theorem and remainder theorem
- Partial fractions
- Expansion of \((1+x)^n\) for rational \(n\)
Logarithmic & Exponential Functions
- Relationship between logarithms and indices
- Laws of logarithms
- Definition and properties of \(e^x\) and \(\ln x\)
- Graphs of exponential and logarithmic functions
- Solving equations and inequalities using logarithms
- Linearising relationships using logarithms
Trigonometry
- Secant, cosecant and cotangent functions
- Graphs and properties of all \(6\) trigonometric functions
- Identities such as \(\sec^2\theta=1+\tan^2\theta\) and \(\csc^2\theta=1+\cot^2\theta\)
- Expansions of \(\sin(A\pm B)\), \(\cos(A\pm B)\) and \(\tan(A\pm B)\)
- Formulae for \(\sin 2A\), \(\cos 2A\) and \(\tan 2A\)
- Expressing \(a\sin\theta+b\cos\theta\) as \(R\sin(\theta\pm\alpha)\) or \(R\cos(\theta\pm\alpha)\)
Differentiation
- Derivatives of \(e^x\), \(\ln x\), \(\sin x\), \(\cos x\), \(\tan x\) and \(\tan^{-1}x\)
- Constant multiples, sums, differences and composites
- Product rule
- Quotient rule
- Parametric differentiation
- Implicit differentiation
Integration
- Integration of \(e^{ax+b}\), \(\frac{1}{ax+b}\), \(\sin(ax+b)\), \(\cos(ax+b)\) and \(\sec^2(ax+b)\)
- Integration involving \(\frac{1}{x^2+a^2}\)
- Integration using trigonometric relationships
- Integration by partial fractions
- Integrals of the form \(\frac{kf'(x)}{f(x)}\)
- Integration by parts and given substitutions
Numerical Solution of Equations
- Locating roots graphically
- Searching for a sign change
- Sequences of approximations
- Iterative formulae of the form \(x_{n+1}=F(x_n)\)
- Finding roots to a required degree of accuracy
Vectors
- Vector notation in \(2\)D and \(3\)D
- Addition, subtraction and scalar multiplication
- Magnitude, unit vectors and position vectors
- Vector equation of a straight line
- Parallel, intersecting and skew lines
- Scalar product and angles between lines
Differential Equations
- Forming differential equations from rates of change
- Constants of proportionality
- Separable differential equations
- General and particular solutions
- Using initial conditions
- Interpreting solutions in context
Complex Numbers
- Real and imaginary parts of a complex number
- Modulus, argument and conjugate
- Operations in Cartesian form \(x+iy\)
- Argand diagrams
- Polar form \(r(\cos\theta+i\sin\theta)\)
- Square roots and loci in the Argand diagram
Pure Mathematics \(3\) – Paper \(3\) Full Access
Get complete access to CIE AS & A Level Mathematics \(9709\) Paper \(3\) topic-wise questions with detailed solutions.
AS & A Level Maths Paper \(3\) – Full Access