Sample Notes: Quadratics

Sample Quizzes For Preparation: Quadratics

Sample Quizzes For Preparation: Momentum

Sample Notes: Momentum

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Quadratics: Carry Out The Process Of Completing The Square For A Quadratic Polynomial ax² + bx + c And Use A Completed Square Form

Quadratics: Find The Discriminant Of A Quadratic Polynomial ax² + bx + c And Use The Discriminant

Quadratics: Solve Quadratic Equations, And Quadratic Inequalities, In One Unknown

Quadratics: Solve By Substitution A Pair Of Simultaneous Equations Of Which One Is Linear And One Is Quadratic

Quadratics: Recognise And Solve Equations In x Which Are Quadratic In Some Function Of x

Functions: Understand The Terms Function, Domain, Range, One-One Function, Inverse Function And Composition Of Functions

Functions: Identify The Range Of A Given Function In Simple Cases, And Find The Composition Of Two Given Functions

Functions: Identify The Range Of A Given Function In Simple Cases, And Find The Composition Of Two Given Functions

Functions: Illustrate In Graphical Terms The Relation Between A One-One Function And Its Inverse

Functions: Understand And Use The Transformations Of The Graph Of y = f(x) Given By y = f(x) + a, y = f(x + a), y = af(x), y = f(ax) And Simple Combinations Of These

Coordinate Geometry: Find The Equation Of A Straight Line Given Sufficient Information

Coordinate Geometry: Interpret And Use Any Of The Forms y = mx + c, y – y₁ = m(x – x₁), ax + by + c = 0 In Solving Problems

Coordinate Geometry: Understand That The Equation (x – a)² + (y – b)² = r² Represents The Circle With Centre (a, b) And Radius r

Coordinate Geometry: Use Algebraic Methods To Solve Problems Involving Lines And Circles

Coordinate Geometry: Understand The Relationship Between A Graph And Its Associated Algebraic Equation, And Use The Relationship Between Points Of Intersection Of Graphs And Solutions Of Equations

Circular Measure: Understand The Definition Of A Radian, And Use The Relationship Between Radians And Degrees

Circular Measure: Use The Formulae s = rθ And A = ½r²θ In Solving Problems Concerning The Arc Length And Sector Area Of A Circle

Trigonometry: Sketch And Use Graphs Of The Sine, Cosine And Tangent Functions (For Angles Of Any Size, And Using Either Degrees Or Radians)

Trigonometry: Use The Exact Values Of The Sine, Cosine And Tangent Of 30°, 45°, 60°, And Related Angles

Trigonometry: Use The Notations sin⁻¹x, cos⁻¹x, tan⁻¹x To Denote The Principal Values Of The Inverse Trigonometric Relations

Trigonometry: Use The Identities tanθ = sinθ / cosθ, sin²θ + cos²θ = 1

Trigonometry: Find All The Solutions Of Simple Trigonometrical Equations Lying In A Specified Interval

Series: Use The Expansion Of (a + b)ⁿ, Where n Is A Positive Integer

Series: Recognise Arithmetic And Geometric Progressions

Series: Use The Formulae For The nᵗʰ Term And For The Sum Of The First n Terms To Solve Problems Involving Arithmetic Or Geometric Progressions

Series: Use The Condition For The Convergence Of A Geometric Progression, And The Formula For The Sum To Infinity Of A Convergent Geometric Progression

Differentiation: Understand The Gradient Of A Curve At A Point As The Limit Of The Gradients Of A Suitable Sequence Of Chords, And Use The Notations f′(x), f″(x), dy/dx, d²y/dx² For First And Second Derivatives

Differentiation: Use The Derivative Of xⁿ (For Any Rational n), Together With Constant Multiples, Sums And Differences Of Functions, And Of Composite Functions Using The Chain Rule

Differentiation: Apply Differentiation To Gradients, Tangents And Normals, Increasing And Decreasing Functions And Rates Of Change

Differentiation: Locate Stationary Points And Determine Their Nature, And Use Information About Stationary Points In Sketching Graphs

Integration: Understand Integration As The Reverse Process Of Differentiation, And Integrate (ax + b)ⁿ (For Any Rational n Except –1), Together With Constant Multiples, Sums And Differences

Integration: Solve Problems Involving The Evaluation Of A Constant Of Integration

Integration: Evaluate Definite Integrals

Integration: Use Definite Integration To Find

Forces And Equilibrium: Identify The Forces Acting In A Given Situation

Forces And Equilibrium: Understand The Vector Nature Of Force, And Find And Use Components And Resultants

Forces And Equilibrium: Use The Principle That, When A Particle Is In Equilibrium, The Vector Sum Of The Forces Acting Is Zero, Or Equivalently, That The Sum Of The Components In Any Direction Is Zero

Forces And Equilibrium: Understand That A Contact Force Between Two Surfaces Can Be Represented By Two Components, The Normal Component And The Frictional Component

Forces And Equilibrium: Use The Model Of A ‘Smooth’ Contact, And Understand The Limitations Of This Model

Forces And Equilibrium: Understand The Concepts Of Limiting Friction And Limiting Equilibrium, Recall The Definition Of Coefficient Of Friction, And Use The Relationship F = μR Or F ≤ μR, As Appropriate

Forces And Equilibrium: Use Newton’s Third Law

Kinematics Of Motion In A Straight Line: Understand The Concepts Of Distance And Speed As Scalar Quantities, And Of Displacement, Velocity And Acceleration As Vector Quantities

Kinematics Of Motion In A Straight Line: Sketch And Interpret Displacement–Time Graphs And Velocity–Time Graphs, And In Particular Appreciate

Kinematics Of Motion In A Straight Line: Use Differentiation And Integration With Respect To Time To Solve Simple Problems Concerning Displacement, Velocity And Acceleration

Kinematics Of Motion In A Straight Line: Use Appropriate Formulae For Motion With Constant Acceleration In A Straight Line

Momentum: Use The Definition Of Linear Momentum And Show Understanding Of Its Vector Nature

Momentum: Use Conservation Of Linear Momentum To Solve Problems That May Be Modelled As The Direct Impact Of Two Bodies

Newton’s Laws Of Motion: Apply Newton’s Laws Of Motion To The Linear Motion Of A Particle Of Constant Mass Moving Under The Action Of Constant Forces, Which May Include Friction, Tension In An Inextensible String And Thrust In A Connecting Rod

Newton’s Laws Of Motion: Use The Relationship Between Mass And Weight W = mg

Newton’s Laws Of Motion: Solve Simple Problems Which May Be Modelled As The Motion Of A Particle Moving Vertically Or On An Inclined Plane With Constant Acceleration

Newton’s Laws Of Motion: Solve Simple Problems Which May Be Modelled As The Motion Of Connected Particles

Energy, Work And Power: Understand The Concept Of The Work Done By A Force, And Calculate The Work Done By A Constant Force When Its Point Of Application Undergoes A Displacement Not Necessarily Parallel To The Force

Energy, Work And Power: Understand The Concepts Of Gravitational Potential Energy And Kinetic Energy, And Use Appropriate Formulae

Energy, Work And Power: Understand And Use The Relationship Between The Change In Energy Of A System And The Work Done By The External Forces, And Use In Appropriate Cases The Principle Of Conservation Of Energy

Energy, Work And Power: Use The Definition Of Power As The Rate At Which A Force Does Work, And Use The Relationship Between Power, Force And Velocity For A Force Acting In The Direction Of Motion

Energy, Work And Power: Solve Problems Involving, For Example, The Instantaneous Acceleration Of A Car Moving On A Hill Against A Resistance

Quadratics

Functions

Coordinate Geometry

Circular Measure

Trigonometry

Series

Differentiation

Integration

Forces And Equilibrium

Kinematics of Motion In A Straight Line

Momentum

Newton’s Laws of Motion

Energy, Work And Power

Quadratics

Functions

Coordinate Geometry

Circular Measure

Trigonometry

Series

Differentiation

Integration

Forces And Equilibrium

Kinematics of Motion In A Straight Line

Momentum

Newton’s Laws of Motion

Energy, Work And Power

Quadratics

Quadratics: Carry Out The Process Of Completing The Square For A Quadratic Polynomial ax² + bx + c And Use A Completed Square Form

Quadratics: Find The Discriminant Of A Quadratic Polynomial ax² + bx + c And Use The Discriminant

Quadratics: Solve Quadratic Equations, And Quadratic Inequalities, In One Unknown

Quadratics: Solve By Substitution A Pair Of Simultaneous Equations Of Which One Is Linear And One Is Quadratic

Quadratics: Recognise And Solve Equations In x Which Are Quadratic In Some Function Of x

Functions: Understand The Terms Function, Domain, Range, One-One Function, Inverse Function And Composition Of Functions

Functions: Identify The Range Of A Given Function In Simple Cases, And Find The Composition Of Two Given Functions

Functions: Identify The Range Of A Given Function In Simple Cases, And Find The Composition Of Two Given Functions

Functions: Illustrate In Graphical Terms The Relation Between A One-One Function And Its Inverse

Functions: Understand And Use The Transformations Of The Graph Of y = f(x) Given By y = f(x) + a, y = f(x + a), y = af(x), y = f(ax) And Simple Combinations Of These

Coordinate Geometry: Find The Equation Of A Straight Line Given Sufficient Information

Coordinate Geometry: Interpret And Use Any Of The Forms y = mx + c, y – y₁ = m(x – x₁), ax + by + c = 0 In Solving Problems

Coordinate Geometry: Understand That The Equation (x – a)² + (y – b)² = r² Represents The Circle With Centre (a, b) And Radius r

Coordinate Geometry: Use Algebraic Methods To Solve Problems Involving Lines And Circles

Coordinate Geometry: Understand The Relationship Between A Graph And Its Associated Algebraic Equation, And Use The Relationship Between Points Of Intersection Of Graphs And Solutions Of Equations

Circular Measure: Understand The Definition Of A Radian, And Use The Relationship Between Radians And Degrees

Circular Measure: Use The Formulae s = rθ And A = ½r²θ In Solving Problems Concerning The Arc Length And Sector Area Of A Circle

Trigonometry: Sketch And Use Graphs Of The Sine, Cosine And Tangent Functions (For Angles Of Any Size, And Using Either Degrees Or Radians)

Trigonometry: Use The Exact Values Of The Sine, Cosine And Tangent Of 30°, 45°, 60°, And Related Angles

Trigonometry: Use The Notations sin⁻¹x, cos⁻¹x, tan⁻¹x To Denote The Principal Values Of The Inverse Trigonometric Relations

Trigonometry: Use The Identities tanθ = sinθ / cosθ, sin²θ + cos²θ = 1

Trigonometry: Find All The Solutions Of Simple Trigonometrical Equations Lying In A Specified Interval

Series: Use The Expansion Of (a + b)ⁿ, Where n Is A Positive Integer

Series: Recognise Arithmetic And Geometric Progressions

Series: Use The Formulae For The nᵗʰ Term And For The Sum Of The First n Terms To Solve Problems Involving Arithmetic Or Geometric Progressions

Series: Use The Condition For The Convergence Of A Geometric Progression, And The Formula For The Sum To Infinity Of A Convergent Geometric Progression

Differentiation: Understand The Gradient Of A Curve At A Point As The Limit Of The Gradients Of A Suitable Sequence Of Chords, And Use The Notations f′(x), f″(x), dy/dx, d²y/dx² For First And Second Derivatives

Differentiation: Use The Derivative Of xⁿ (For Any Rational n), Together With Constant Multiples, Sums And Differences Of Functions, And Of Composite Functions Using The Chain Rule

Differentiation: Apply Differentiation To Gradients, Tangents And Normals, Increasing And Decreasing Functions And Rates Of Change

Differentiation: Locate Stationary Points And Determine Their Nature, And Use Information About Stationary Points In Sketching Graphs

Integration: Understand Integration As The Reverse Process Of Differentiation, And Integrate (ax + b)ⁿ (For Any Rational n Except –1), Together With Constant Multiples, Sums And Differences

Integration: Solve Problems Involving The Evaluation Of A Constant Of Integration

Integration: Evaluate Definite Integrals

Integration: Use Definite Integration To Find

Forces And Equilibrium: Identify The Forces Acting In A Given Situation

Forces And Equilibrium: Understand The Vector Nature Of Force, And Find And Use Components And Resultants

Forces And Equilibrium: Use The Principle That, When A Particle Is In Equilibrium, The Vector Sum Of The Forces Acting Is Zero, Or Equivalently, That The Sum Of The Components In Any Direction Is Zero

Forces And Equilibrium: Understand That A Contact Force Between Two Surfaces Can Be Represented By Two Components, The Normal Component And The Frictional Component

Forces And Equilibrium: Use The Model Of A ‘Smooth’ Contact, And Understand The Limitations Of This Model

Forces And Equilibrium: Understand The Concepts Of Limiting Friction And Limiting Equilibrium, Recall The Definition Of Coefficient Of Friction, And Use The Relationship F = μR Or F ≤ μR, As Appropriate

Forces And Equilibrium: Use Newton’s Third Law

Kinematics Of Motion In A Straight Line: Understand The Concepts Of Distance And Speed As Scalar Quantities, And Of Displacement, Velocity And Acceleration As Vector Quantities

Kinematics Of Motion In A Straight Line: Sketch And Interpret Displacement–Time Graphs And Velocity–Time Graphs, And In Particular Appreciate

Kinematics Of Motion In A Straight Line: Use Differentiation And Integration With Respect To Time To Solve Simple Problems Concerning Displacement, Velocity And Acceleration

Kinematics Of Motion In A Straight Line: Use Appropriate Formulae For Motion With Constant Acceleration In A Straight Line

Momentum: Use The Definition Of Linear Momentum And Show Understanding Of Its Vector Nature

Momentum: Use Conservation Of Linear Momentum To Solve Problems That May Be Modelled As The Direct Impact Of Two Bodies

Newton’s Laws Of Motion: Apply Newton’s Laws Of Motion To The Linear Motion Of A Particle Of Constant Mass Moving Under The Action Of Constant Forces, Which May Include Friction, Tension In An Inextensible String And Thrust In A Connecting Rod

Newton’s Laws Of Motion: Use The Relationship Between Mass And Weight W = mg

Newton’s Laws Of Motion: Solve Simple Problems Which May Be Modelled As The Motion Of A Particle Moving Vertically Or On An Inclined Plane With Constant Acceleration

Newton’s Laws Of Motion: Solve Simple Problems Which May Be Modelled As The Motion Of Connected Particles

Energy, Work And Power: Understand The Concept Of The Work Done By A Force, And Calculate The Work Done By A Constant Force When Its Point Of Application Undergoes A Displacement Not Necessarily Parallel To The Force

Energy, Work And Power: Understand The Concepts Of Gravitational Potential Energy And Kinetic Energy, And Use Appropriate Formulae

Energy, Work And Power: Understand And Use The Relationship Between The Change In Energy Of A System And The Work Done By The External Forces, And Use In Appropriate Cases The Principle Of Conservation Of Energy

Energy, Work And Power: Use The Definition Of Power As The Rate At Which A Force Does Work, And Use The Relationship Between Power, Force And Velocity For A Force Acting In The Direction Of Motion

Energy, Work And Power: Solve Problems Involving, For Example, The Instantaneous Acceleration Of A Car Moving On A Hill Against A Resistance

Quadratics

Functions

Coordinate Geometry

Circular Measure

Trigonometry

Series

Differentiation

Integration

Forces And Equilibrium

Kinematics of Motion In A Straight Line

Momentum

Newton’s Laws of Motion

Energy, Work And Power

Quadratics

Functions

Coordinate Geometry

Circular Measure

Trigonometry

Series

Differentiation

Integration

Forces and Equilibrium

Kinematics of Motion In A Straight Line

Momentum

Newton’s Laws of Motion

Energy, Work and Power

Detailed Solutions For Past Papers: May June 2019 12

Detailed Solutions For Past Paper: May June 2019 Paper 11

Quadratics and Quadratic Equations

Functions

Trigonometry

Circular Measure

Coordinate Geometry

Velocity and Acceleration

Force and Motion

Vertical Motion

Resolving Forces

Friction

Connected Particles

Work, Energy and Power

Momentum

General Motion in a Straight Line

Quadratics: Carry Out The Process Of Completing The Square For A Quadratic Polynomial ax² + bx + c And Use A Completed Square Form

Quadratics: Find The Discriminant Of A Quadratic Polynomial ax² + bx + c And Use The Discriminant

Quadratics: Solve Quadratic Equations, And Quadratic Inequalities, In One Unknown

Quadratics: Solve By Substitution A Pair Of Simultaneous Equations Of Which One Is Linear And One Is Quadratic

Quadratics: Recognise And Solve Equations In x Which Are Quadratic In Some Function Of x

Functions: Understand The Terms Function, Domain, Range, One-One Function, Inverse Function And Composition Of Functions

Functions: Identify The Range Of A Given Function In Simple Cases, And Find The Composition Of Two Given Functions

Functions: Identify The Range Of A Given Function In Simple Cases, And Find The Composition Of Two Given Functions

Functions: Illustrate In Graphical Terms The Relation Between A One-One Function And Its Inverse

Functions: Understand And Use The Transformations Of The Graph Of y = f(x) Given By y = f(x) + a, y = f(x + a), y = af(x), y = f(ax) And Simple Combinations Of These

Coordinate Geometry: Find The Equation Of A Straight Line Given Sufficient Information

Coordinate Geometry: Interpret And Use Any Of The Forms y = mx + c, y – y₁ = m(x – x₁), ax + by + c = 0 In Solving Problems

Coordinate Geometry: Understand That The Equation (x – a)² + (y – b)² = r² Represents The Circle With Centre (a, b) And Radius r

Coordinate Geometry: Use Algebraic Methods To Solve Problems Involving Lines And Circles

Coordinate Geometry: Understand The Relationship Between A Graph And Its Associated Algebraic Equation, And Use The Relationship Between Points Of Intersection Of Graphs And Solutions Of Equations

Circular Measure: Understand The Definition Of A Radian, And Use The Relationship Between Radians And Degrees

Circular Measure: Use The Formulae s = rθ And A = ½r²θ In Solving Problems Concerning The Arc Length And Sector Area Of A Circle

Trigonometry: Sketch And Use Graphs Of The Sine, Cosine And Tangent Functions (For Angles Of Any Size, And Using Either Degrees Or Radians)

Trigonometry: Use The Exact Values Of The Sine, Cosine And Tangent Of 30°, 45°, 60°, And Related Angles

Trigonometry: Use The Notations sin⁻¹x, cos⁻¹x, tan⁻¹x To Denote The Principal Values Of The Inverse Trigonometric Relations

Trigonometry: Use The Identities tanθ = sinθ / cosθ, sin²θ + cos²θ = 1

Trigonometry: Find All The Solutions Of Simple Trigonometrical Equations Lying In A Specified Interval

Series: Use The Expansion Of (a + b)ⁿ, Where n Is A Positive Integer

Series: Recognise Arithmetic And Geometric Progressions

Series: Use The Formulae For The nᵗʰ Term And For The Sum Of The First n Terms To Solve Problems Involving Arithmetic Or Geometric Progressions

Series: Use The Condition For The Convergence Of A Geometric Progression, And The Formula For The Sum To Infinity Of A Convergent Geometric Progression

Differentiation: Understand The Gradient Of A Curve At A Point As The Limit Of The Gradients Of A Suitable Sequence Of Chords, And Use The Notations f′(x), f″(x), dy/dx, d²y/dx² For First And Second Derivatives

Differentiation: Use The Derivative Of xⁿ (For Any Rational n), Together With Constant Multiples, Sums And Differences Of Functions, And Of Composite Functions Using The Chain Rule

Differentiation: Apply Differentiation To Gradients, Tangents And Normals, Increasing And Decreasing Functions And Rates Of Change

Differentiation: Locate Stationary Points And Determine Their Nature, And Use Information About Stationary Points In Sketching Graphs

Integration: Understand Integration As The Reverse Process Of Differentiation, And Integrate (ax + b)ⁿ (For Any Rational n Except –1), Together With Constant Multiples, Sums And Differences

Integration: Solve Problems Involving The Evaluation Of A Constant Of Integration

Integration: Evaluate Definite Integrals

Integration: Use Definite Integration To Find

Forces And Equilibrium: Identify The Forces Acting In A Given Situation

Forces And Equilibrium: Understand The Vector Nature Of Force, And Find And Use Components And Resultants

Forces And Equilibrium: Use The Principle That, When A Particle Is In Equilibrium, The Vector Sum Of The Forces Acting Is Zero, Or Equivalently, That The Sum Of The Components In Any Direction Is Zero

Forces And Equilibrium: Understand That A Contact Force Between Two Surfaces Can Be Represented By Two Components, The Normal Component And The Frictional Component

Forces And Equilibrium: Use The Model Of A ‘Smooth’ Contact, And Understand The Limitations Of This Model

Forces And Equilibrium: Understand The Concepts Of Limiting Friction And Limiting Equilibrium, Recall The Definition Of Coefficient Of Friction, And Use The Relationship F = μR Or F ≤ μR, As Appropriate

Forces And Equilibrium: Use Newton’s Third Law

Kinematics Of Motion In A Straight Line: Understand The Concepts Of Distance And Speed As Scalar Quantities, And Of Displacement, Velocity And Acceleration As Vector Quantities

Kinematics Of Motion In A Straight Line: Sketch And Interpret Displacement–Time Graphs And Velocity–Time Graphs, And In Particular Appreciate

Kinematics Of Motion In A Straight Line: Use Differentiation And Integration With Respect To Time To Solve Simple Problems Concerning Displacement, Velocity And Acceleration

Kinematics Of Motion In A Straight Line: Use Appropriate Formulae For Motion With Constant Acceleration In A Straight Line

Momentum: Use The Definition Of Linear Momentum And Show Understanding Of Its Vector Nature

Momentum: Use Conservation Of Linear Momentum To Solve Problems That May Be Modelled As The Direct Impact Of Two Bodies

Newton’s Laws Of Motion: Apply Newton’s Laws Of Motion To The Linear Motion Of A Particle Of Constant Mass Moving Under The Action Of Constant Forces, Which May Include Friction, Tension In An Inextensible String And Thrust In A Connecting Rod

Newton’s Laws Of Motion: Use The Relationship Between Mass And Weight W = mg

Newton’s Laws Of Motion: Solve Simple Problems Which May Be Modelled As The Motion Of A Particle Moving Vertically Or On An Inclined Plane With Constant Acceleration

Newton’s Laws Of Motion: Solve Simple Problems Which May Be Modelled As The Motion Of Connected Particles

Energy, Work And Power: Understand The Concept Of The Work Done By A Force, And Calculate The Work Done By A Constant Force When Its Point Of Application Undergoes A Displacement Not Necessarily Parallel To The Force

Energy, Work And Power: Understand The Concepts Of Gravitational Potential Energy And Kinetic Energy, And Use Appropriate Formulae

Energy, Work And Power: Understand And Use The Relationship Between The Change In Energy Of A System And The Work Done By The External Forces, And Use In Appropriate Cases The Principle Of Conservation Of Energy

Energy, Work And Power: Use The Definition Of Power As The Rate At Which A Force Does Work, And Use The Relationship Between Power, Force And Velocity For A Force Acting In The Direction Of Motion

Energy, Work And Power: Solve Problems Involving, For Example, The Instantaneous Acceleration Of A Car Moving On A Hill Against A Resistance

Quadratics

Functions

Coordinate Geometry

Circular Measure

Trigonometry

Series

Differentiation

Integration

Forces and Equilibrium

Kinematics of Motion In A Straight Line

Momentum

Newton’s Law of Motion

Energy, Work and Power.

Formulae Sheet: Quadratics

Formulae Sheet: Functions

Formulae Sheet: Coordinate Geometry

Formulae Sheet: Circular Measure

Formulae Sheet: Trigonometry

Formulae Sheet: Series

Formulae Sheet: Differentiation

Formulae Sheet: Integration

Formulae Sheet: Forces and Equilibrium

Formulae Sheet: Kinematics of Motion In A Straight Line

Formulae Sheet: Momentum

Formulae Sheet: Newton’s Law of Motion

Formulae Sheet: Energy, Work and Power

Formulae Sheet:

Formula Sheet: Algebra

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