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Subjects

CCambridge EPearson Edexcel AQAAQA OCROCR

Competitive Log in Create free account

Mathematics · 9709

Pure Mathematics 1

01Quadratics

Solving Quadratics7

Solving Quadratic Equations Factorising Quadratics by Hand Fractions and Valid Roots Completing the Square Using the Completed Square Form The Quadratic Formula Quadratics in Another Form

The Quadratic Graph3

The Graph and the Vertex Quadratic Range and Restricted Domains Quadratic Inequalities

Roots and Intersections3

The Discriminant Where a Line Meets a Curve Tangency and Parameter Conditions

02Functions

Function Language3

Functions and Domains One-One and Many-One Functions The Range of a Function

Combining and Reversing Functions3

Composite Functions Inverse Functions The graph of a function and its inverse

Transforming Graphs3

The Four Function Transformations Describing Function Transformations Combined Function Transformations

03Coordinate Geometry

Coordinates and Lines4

Distance and Midpoint Gradient and Line Relationships Equations of Straight Lines Perpendicular Bisectors

Circle Equations and Geometry4

The Equation of a Circle Expanded Circle Equations Circles Through Three Points Circle Geometry and Tangents

Line-Circle Problems2

Line-Circle Intersections Intersection and Tangency Conditions

04Circular Measure

Radians and Sectors3

Radians Length of an Arc Area of a Sector

Chords and Segments2

Chords and Segment Perimeters Area of a Circular Segment

Circular Geometry Problems5

Exact Circular-Measure Problems Shaded-Region Problems Perimeters with Arcs and Straight Lines Overlapping Circles Fixed-Perimeter Sectors

05Trigonometry

Ratios and Angles3

Trig Ratios and the Unit Circle Exact Values and Reference Angles Finding Related Trig Ratios

Graphs and Inverses5

Graphs of sin, cos and tan Transforming Trigonometric Graphs Reading Trigonometric Graphs Inverse Trigonometric Functions Inverses of Restricted Trig Functions

Equations and Identities5

Solving Trigonometric Equations Trigonometric Identities Quadratic Trig Equations Multiple-Angle Trig Equations Equations with Trigonometric Identities

06Series

Arithmetic Progressions4

Arithmetic Progressions Sums of Arithmetic Progressions Finding Terms from Sums Selecting and Counting AP Terms

Geometric Progressions5

Geometric Progressions Finite Geometric Series Infinite Geometric Series Selected Geometric Series Modelling Geometric Series

Linked Progressions1

Linked Progressions

Binomial Expansion5

The Binomial Expansion Finding Binomial Terms Products of Binomial Expansions Unknown Binomial Coefficients Using Binomial Expansions

07Differentiation

Derivatives and Gradients2

Derivatives and the Gradient Function Calculating Chord Gradients

Differentiation Rules4

The Power Rule Differentiating Roots and Fractions The Chain Rule Second Derivatives

Applying Derivatives6

Finding Points with a Given Gradient Tangents and Normals Intersections of Tangents and Normals Areas from Tangents and Normals Unknown Coefficients from Gradients Conditions on Derivatives

08Further Differentiation

Function Behaviour6

Increasing and Decreasing Functions Stationary Points Sketching Curves Using Stationary Points Conditions from Stationary Points Counting Stationary Points Finding the Minimum Gradient

Optimisation4

Optimisation Maximising the Volume of a Box Minimising Surface Area Optimisation with Geometric Constraints

Rates of Change4

Rates of Change Connected Rates on a Curve Finding Unknown Rates Filling and Emptying Containers

09Integration

Finding Original Functions7

Reversing Differentiation Preparing Expressions for Integration Finding the Constant of Integration Finding a Curve from Conditions Integrating Twice Integrating Powers of a Linear Bracket Recognising Reverse Chain Rule

Definite Integrals and Area6

Definite Integrals Area Under a Curve Integrating with Respect to y Area Between Curves Areas with Changing Boundaries Finding an Unknown Integration Limit

Improper Integrals2

Infinite Integration Limits Integrals with Undefined Endpoints

Volumes of Revolution5

Volumes of Revolution Rotation About the y-axis Hollow Solids of Revolution Finding Unknowns from a Volume Water Volumes in a Curved Container

Revision Notes Practice Questions Topical Past Paper Questions Past Papers

Resources

Revision Notes Practice Questions Topical Past Paper Questions Past Papers

Pure Mathematics 1/Further Differentiation

Optimisation with Geometric Constraints

Contents

Mathematics · 9709

Pure Mathematics 1

01Quadratics

Solving Quadratics7

Solving Quadratic Equations Factorising Quadratics by Hand Fractions and Valid Roots Completing the Square Using the Completed Square Form The Quadratic Formula Quadratics in Another Form

The Quadratic Graph3

The Graph and the Vertex Quadratic Range and Restricted Domains Quadratic Inequalities

Roots and Intersections3

The Discriminant Where a Line Meets a Curve Tangency and Parameter Conditions

02Functions

Function Language3

Functions and Domains One-One and Many-One Functions The Range of a Function

Combining and Reversing Functions3

Composite Functions Inverse Functions The graph of a function and its inverse

Transforming Graphs3

The Four Function Transformations Describing Function Transformations Combined Function Transformations

03Coordinate Geometry

Coordinates and Lines4

Distance and Midpoint Gradient and Line Relationships Equations of Straight Lines Perpendicular Bisectors

Circle Equations and Geometry4

The Equation of a Circle Expanded Circle Equations Circles Through Three Points Circle Geometry and Tangents

Line-Circle Problems2

Line-Circle Intersections Intersection and Tangency Conditions

04Circular Measure

Radians and Sectors3

Radians Length of an Arc Area of a Sector

Chords and Segments2

Chords and Segment Perimeters Area of a Circular Segment

Circular Geometry Problems5

Exact Circular-Measure Problems Shaded-Region Problems Perimeters with Arcs and Straight Lines Overlapping Circles Fixed-Perimeter Sectors

05Trigonometry

Ratios and Angles3

Trig Ratios and the Unit Circle Exact Values and Reference Angles Finding Related Trig Ratios

Graphs and Inverses5

Graphs of sin, cos and tan Transforming Trigonometric Graphs Reading Trigonometric Graphs Inverse Trigonometric Functions Inverses of Restricted Trig Functions

Equations and Identities5

Solving Trigonometric Equations Trigonometric Identities Quadratic Trig Equations Multiple-Angle Trig Equations Equations with Trigonometric Identities

06Series

Arithmetic Progressions4

Arithmetic Progressions Sums of Arithmetic Progressions Finding Terms from Sums Selecting and Counting AP Terms

Geometric Progressions5

Geometric Progressions Finite Geometric Series Infinite Geometric Series Selected Geometric Series Modelling Geometric Series

Linked Progressions1

Linked Progressions

Binomial Expansion5

The Binomial Expansion Finding Binomial Terms Products of Binomial Expansions Unknown Binomial Coefficients Using Binomial Expansions

07Differentiation

Derivatives and Gradients2

Derivatives and the Gradient Function Calculating Chord Gradients

Differentiation Rules4

The Power Rule Differentiating Roots and Fractions The Chain Rule Second Derivatives

Applying Derivatives6

Finding Points with a Given Gradient Tangents and Normals Intersections of Tangents and Normals Areas from Tangents and Normals Unknown Coefficients from Gradients Conditions on Derivatives

08Further Differentiation

Function Behaviour6

Increasing and Decreasing Functions Stationary Points Sketching Curves Using Stationary Points Conditions from Stationary Points Counting Stationary Points Finding the Minimum Gradient

Optimisation4

Optimisation Maximising the Volume of a Box Minimising Surface Area Optimisation with Geometric Constraints

Rates of Change4

Rates of Change Connected Rates on a Curve Finding Unknown Rates Filling and Emptying Containers

09Integration

Finding Original Functions7

Reversing Differentiation Preparing Expressions for Integration Finding the Constant of Integration Finding a Curve from Conditions Integrating Twice Integrating Powers of a Linear Bracket Recognising Reverse Chain Rule

Definite Integrals and Area6

Definite Integrals Area Under a Curve Integrating with Respect to y Area Between Curves Areas with Changing Boundaries Finding an Unknown Integration Limit

Improper Integrals2

Infinite Integration Limits Integrals with Undefined Endpoints

Volumes of Revolution5

Volumes of Revolution Rotation About the y-axis Hollow Solids of Revolution Finding Unknowns from a Volume Water Volumes in a Curved Container

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