7 syllabus subtopics
- 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
Revision notes ยท Cambridge A Level ยท 9709
Mathematics 9709 revision notes
Revision notes for Cambridge A Level Mathematics (9709), organised by the official syllabus chapters.
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Paper 1 ยท Pure Mathematics 1 AS Level
5 syllabus subtopics
- Formula and Basic Application
- Type One
- Particular Term
- Type Two
- Substitution
8 syllabus subtopics
- 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
8 syllabus subtopics
- 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 syllabus subtopics
- Angle Units and Conversion Rate
- Famous Angles and Values to Memorize
- Formulas
- Practice Questions (Basic)
- Practice Questions (Advanced)
15 syllabus subtopics
- 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
8 syllabus subtopics
- 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
9 syllabus subtopics
- 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
10 syllabus subtopics
- 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 ยท Pure Mathematics 3 A Level
4 syllabus subtopics
- Formula and Conditions
- Basic Application
- Advanced Application
- Five Mark Parts
7 syllabus subtopics
- 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
9 syllabus subtopics
- Indices
- Surds
- Logarithms: Basic Properties
- Bases
- Type 1
- Type 2
- Type 3
- Type 4
- Advanced Substitution Techniques
6 syllabus subtopics
- Long Division
- Remainder Theorem
- Factor Theorem
- Factorize an Expression Completely
- Basic Practice
- Advanced Practice
4 syllabus subtopics
- Identities
- Type 1: R sin ฮธ and R cos ฮธ Forms
- Type 2
- Identity Proving
11 syllabus subtopics
- 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
19 syllabus subtopics
- Operators and Rules
- Basic Practice of Rules
- How to Choose an Operator
- Integration Chart
- Odd/Even Powers of sin, cos and tan
- ln Operator
- tanโปยน 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
6 syllabus subtopics
- 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 syllabus subtopics
- 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
9 syllabus subtopics
- Linear, Quadratic and Cubic Graphs
- Reciprocal Graphs
- Exponential Graphs
- Logarithmic Graphs
- Absolute Value Function
- Transformations
- Inverse Functions
- Trigonometric Graphs
- Examples
2 syllabus subtopics
- Basic Questions and Concepts
- Practice
13 syllabus subtopics
- 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
Paper 4 ยท Mechanics AS Level
13 syllabus subtopics
- 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)
16 syllabus subtopics
- 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
6 syllabus subtopics
- 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)
3 syllabus subtopics
- Concept and Formula
- Principle of Conservation of Momentum (Basics)
- Examples of Exam Questions
Paper 5 ยท Probability & Statistics 1 AS Level
4 syllabus subtopics
- 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 syllabus subtopics
- Binomial Distribution: Conditions, Notation and Comprehensive Example
- Binomial Distribution Questions with Logarithms and Inequalities
2 syllabus subtopics
- Concept, Formulae and Notation
- Exam Questions and Practice
4 syllabus subtopics
- 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
12 syllabus subtopics
- 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)
2 syllabus subtopics
- Basics and Concepts with Small Examples
- Exam Questions and Practice (Including Questions Where a Student is Added to the Data)
5 syllabus subtopics
- 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