PrepWithTee owl logo PrepWithTee

Cambridge A Level · 9709

Mathematics topical past papers

Every Cambridge A Level Mathematics (9709) past-paper question from 2010–2025, sorted into 36 syllabus chapters and their subtopics, with the official mark schemes.

Questions
3,898
Chapters
36
Years
2010–2025
Create a free account to build papers

Paper 1 · Pure Mathematics 1 AS Level

  1. Coordinate Geometry 209 questions
    • Formulas and Gradient
    • Equation of a Line
    • Equation of a Perpendicular Bisector
    • Points of Intersection of Graph
    • Example Questions
    • Angle Between Two Lines
    • Special Shapes
  2. Binomial 29 questions
    • Formula and Basic Application
    • Type One
    • Particular Term
    • Type Two
    • Substitution
  3. Quadratics 56 questions
    • Forms of Equation
    • Standard Form to Completed Square Form
    • Standard Form to Root Form
    • Sketch of a Quadratic Curve
    • Maximum/Minimum Point
    • Roots
    • Intersection of a Line and a Curve
    • Inequalities
  4. Sequences 152 questions
    • Arithmetic Progression (AP)
    • Geometric Progression (GP)
    • Exam Tips and Values of d and r
    • Type 1: Formula-Based Questions
    • Type 2: AP to GP Conversion
    • Type 3: Given Formula Questions
    • Type 4: Scenario-Based Questions
    • Type 5: Sum of First n Terms
  5. Circular Measure 192 questions
    • Angle Units and Conversion Rate
    • Famous Angles and Values to Memorize
    • Formulas
    • Practice Questions (Basic)
    • Practice Questions (Advanced)
  6. Trigonometry 173 questions
    • Quadrants and Values
    • Basic Angles and Finding Exact Values (Without Calculator)
    • Equation Solving
    • Range Change
    • Introduction to Identities
    • Type 1: Solving Simple Equations
    • Type 2: Solving Quadratic Equations
    • Type 3: Identity Proving
    • Type 4: Identity Proving (Part 2)
    • Type 5: Questions with Diagrams
    • Type 6: Given Trigonometric Ratios
    • Type 7: Questions with Graphs
    • Basic Trigonometric Graphs
    • Amplitude and Baseline Variation
    • Frequency Variation
  7. Differentiation 258 questions
    • Introduction and Symbology
    • How to Differentiate
    • Equation of Tangent and Normal
    • Stationary Points
    • Type 1: Tangent and Normal Questions
    • Type 2: Stationary Points and Nature
    • Type 3: Rate of Change
    • Type 4: Proof Questions
  8. Integration 13 questions
    • Introduction
    • How to Integrate
    • Two Types of Integration
    • Area Under a Graph and Area Between Graphs
    • Volume of Rotation
    • Reverse Working
    • Type 1: Area Under Graph Practice
    • Type 2: Volume of Rotation Practice
    • Type 3: Reverse Working
  9. Functions 159 questions
    • Introduction
    • Inverse of a Function
    • Vertical and Horizontal Tests
    • Composite Functions
    • Sketch of a Function and Its Inverse
    • Domain
    • Range
    • Main Question to Memorize
    • Equation of a Circle
    • Transformation of Functions

Paper 3 · Pure Mathematics 3 A Level

  1. Binomial 57 questions
    • Formula and Conditions
    • Basic Application
    • Advanced Application
    • Five Mark Parts
  2. Partial Fractions 35 questions
    • Forms
    • Proper vs Improper
    • Type 1: Proper and Linear
    • Type 2: Proper and Repeated
    • Type 3: Proper and Quadratic
    • Improper Fractions
    • Full Question with Partial Fractions and Binomial
  3. Indices, Surds and Logs 90 questions
    • Indices
    • Surds
    • Logarithms: Basic Properties
    • Bases
    • Type 1
    • Type 2
    • Type 3
    • Type 4
    • Advanced Substitution Techniques
  4. Polynomials 150 questions
    • Long Division
    • Remainder Theorem
    • Factor Theorem
    • Factorize an Expression Completely
    • Basic Practice
    • Advanced Practice
  5. Trigonometry 357 questions
    • Identities
    • Type 1: R sin θ and R cos θ Forms
    • Type 2
    • Identity Proving
  6. Differentiation 10 questions
    • Operators
    • Single Operators
    • Multiple Operators
    • Product and Quotient Rule
    • Basic Outcomes
    • Nature of Stationary Points
    • Type 1 Questions
    • Parametric Equations
    • Type 2 Questions
    • Implicit Differentiation
    • Type 3 Practice
  7. Integration 27 questions
    • Operators and Rules
    • Basic Practice of Rules
    • How to Choose an Operator
    • Integration Chart
    • Odd/Even Powers of sin, cos and tan
    • ln Operator
    • tan⁻¹ Operator
    • Integration by Parts: Formula and Basic Example
    • Integration by Parts with Double Integration
    • Integration by Parts with Loop Variation
    • How to Decide u and v for Integration by Parts
    • How to Integrate ln x
    • Integration by Substitution: Basics
    • Type 1: With Differentiation
    • Type 2: With Partial Fractions
    • Type 3: With R cos
    • Type 4: With Trigonometric Identity
    • Type 5: Single Part
    • Type 6: With Substitution
  8. Differential Equations 63 questions
    • Introduction
    • Without Proof
    • Proof: Basic
    • Proof with In and Out
    • Proof with Chain Rule
    • What Happens to the Value of y as x Becomes Large
  9. Vectors 99 questions
    • Introduction
    • Magnitude and Unit Vector
    • Parallel and Collinear
    • Dot Product
    • Equation of a Line
    • Two Lines
    • Skew Lines and Point of Intersection
    • Angle of Intersection
    • Foot of the Perpendicular
  10. Graphs 21 questions
    • Linear, Quadratic and Cubic Graphs
    • Reciprocal Graphs
    • Exponential Graphs
    • Logarithmic Graphs
    • Absolute Value Function
    • Transformations
    • Inverse Functions
    • Trigonometric Graphs
    • Examples
  11. Iteration 103 questions
    • Basic Questions and Concepts
    • Practice
  12. Complex Numbers 133 questions
    • Introduction and Symbols
    • DMAS
    • Square Root of a Complex Number
    • Argand Diagram, Modulus and Argument
    • Multiplication and Division of Complex Numbers (with Practice)
    • Forms of a Complex Number
    • Exponential Form for Higher Powers and Square Roots
    • Locus and Correct Forms
    • Shading and Basic Examples
    • Advanced Questions with Diagrams
    • Practice Without Diagram (Hard Questions)
    • Practice With Diagram (Hard Questions)
    • Practice: Complex Numbers with Polynomials
  13. Linear Law 51 questions
  14. Inequalities and Modulus 22 questions

Paper 4 · Mechanics AS Level

  1. Forces 270 questions
    • Basics, Weight and Friction (Basics)
    • Components of a Force, Horizontal and Inclined Plane, Positioning of m and M
    • Tension in Strings, Pulleys and Pegs
    • Equilibrium (Basic)
    • Equilibrium with Vertical Ring
    • Equilibrium with Two Separate Diagrams (Distances and Forces)
    • Friction: Concept, Formula and Direction of Normal Force
    • Limiting Equilibrium: Basics, Formula and One Example
    • Basic Applications of Limiting Equilibrium
    • Advanced Limiting Equilibrium with Changed Point of Observation
    • Inequalities of Rest and Motion with Examples
    • Resultant of a Force (Basic)
    • Resultant of a Force (Advanced)
  2. Kinematics 510 questions
    • Introduction and Basics
    • Equations of Motion with One Basic and One Advanced Example
    • Time Delay: Concept and Examples
    • Equations of Motion on Horizontal, Inclined and Vertical Planes (Including Forces)
    • Non-Constant Acceleration: Basics, Differentiation and Integration Rules, Maximum/Minimum Values
    • Applications of Non-Constant Acceleration Rules (Basic Questions)
    • Split Journey Rules
    • Split Journey Examples
    • Kinematics Graphs and Exam Rules
    • Applications of Kinematics Graph Rules (Exam Questions)
    • Pulley Systems: Basic Rules
    • Main Pulley Question with All Variations
    • Pulley Questions with String Broken Mid-Air (Vertical Plane)
    • Pulley Questions with Inclined Plane on One End and Vertical on the Other
    • Pulley Questions with Inclined Planes on Both Ends
    • Pulley Questions with Horizontal Surface on One End and Vertical on the Other
  3. Work, Power and Energy 191 questions
    • Introduction, Basics and Formulae
    • Difference Between Forward Force and Driving Force
    • Type 1: Concept with Basic Questions
    • Type 1: Concept with Advanced Questions (Including Two Variables)
    • Type 2: Concept with Basic Questions
    • Type 2: Concept with Advanced Questions (Higher Weightage)
  4. Momentum 25 questions
    • Concept and Formula
    • Principle of Conservation of Momentum (Basics)
    • Examples of Exam Questions
  5. Newton's Laws of Motion 69 questions

Paper 5 · Probability & Statistics 1 AS Level

  1. Probability 171 questions
    • Basics and Sample Spaces with Tree Diagram Rules
    • Conditional Probability: Formula and Example
    • Conditional Probability Exam Questions (Listing, Tree Diagrams and Data Tables)
    • Mutually Exclusive and Independent Events
  2. Binomial Distribution 0 questions
    • Binomial Distribution: Conditions, Notation and Comprehensive Example
    • Binomial Distribution Questions with Logarithms and Inequalities
  3. Geometric Distribution 0 questions
    • Concept, Formulae and Notation
    • Exam Questions and Practice
  4. Random Variables 46 questions
    • Mean, Standard Deviation and Variance (Raw Data and Frequency Tables)
    • Random Variables: Basics, Expected Value, Standard Deviation and Variance
    • Basic Questions with Tables
    • Advanced Scenario-Based Questions
  5. Normal Distribution 3 questions
    • Conditions, Notation and Understanding the Z-Table
    • Using the Z-Table to Find Probabilities (7 Variations)
    • Type 1: Forward Working Rules and One Basic Example
    • Type 1: Exam Questions
    • Type 2: Reverse Working Rules and Positioning on the x-Axis
    • Type 2: Reading Z-Values from the Table (All Decimal Variations)
    • Type 2: Full Worked Examples
    • Type 2: Reverse Working Exam Questions (Basic and Advanced)
    • Type 3: Binomial to Normal Approximation (Basics and Continuity Correction)
    • Type 3: Binomial to Normal Approximation (Conditions and Justification)
    • Type 3: Binomial to Normal Approximation Exam Questions
    • Exam Questions Relating Binomial and Normal Distributions (Both Directions)
  6. Linear Transformation of Data 0 questions
    • Basics and Concepts with Small Examples
    • Exam Questions and Practice (Including Questions Where a Student is Added to the Data)
  7. Representation of Data 101 questions
    • Mean, Median, Mode, Standard Deviation and Variance (Raw Data, Frequency Tables and Probability Tables)
    • Histograms
    • Cumulative Frequency
    • Stem-and-Leaf Diagrams
    • Box-and-Whisker Plots
  8. Permutations and Combinations 53 questions