IGCSE ONLY

Tutorial Videos

Differentiation from First Principles | Calculus | A-Level Maths Series

Differentiation from First Principles by The GCSE Maths Tutor

Applying First Principles to x² (1 of 2: Finding the Derivative)

Applying First Principles to x² (1 of 2: Finding the Derivative) by Eddie Woo

Introduction to Differentiation

Corbett Maths Introduction to Differentiation

Online Platforms (with Videos & Exercises)

• Khan Academy
  • The derivative as a limit (first principles): Videos & practice

Activities & Resources

• Pixi Maths
  • Differentiation from First Principles ppt
• BossMaths
  • Differentiation from First Principles (Interactive GeoGebra applets)

Worksheets

Dr Frost Video

Dr Frost Slides & Activities

• All in one summary sheet

Extra Questions

• Dr Frost Questions

Key Skills

Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost

• 511a: Estimate the gradient of a tangent to a curve (secant line) at a point by forming a chord from the point to another on the curve. (not yet active)
• 511b: Estimate the gradient of a tangent to a curve (secant line) at a point by forming a chord between points ether side of the on the curve. (not yet active)
• 511c: Use a secant line to obtain an initial expression for a limiting gradient for a function (xⁿ terms only).
• 511d: Differentiate from first principles and simplify to obtain an expression for the gradient of a secant line as an approximation to the gradient of a tangent line (xⁿ terms only).
• 511: Exam Practice: Differentiating from first principles for small positive powers of x

Tutorial Videos

Differentiation – Corbettmaths

Corbett Maths Differentiation

Gradient of a Curve – Corbettmaths

Corbett Maths Gradient of a Curve

Online Platforms (with Videos & Exercises)

• Khan Academy
  • Differentiating polynomials: Videos & practice

Activities & Resources

• Pixi Maths
  • Differentiation Introduction ppt
• Andy Lutwyche
  • Codebreakers – (GCSE Content)
  • Clumsy Clive
  • Simple Codebreaker
  • Crack The Safe
  • Advent Calendar
• PhET Interactive Simulations
  • PhET Calculus Grapher Interactive Simulation (embedded below)
• Acute Learning Problem Pairs
  • Level 2 FM: Basic Differentiation as PowerPoint or PDF
• Transum
  • Differentiation
• Interactive Maths
  • Differentiating Polynomials: QQI | 10QQI | Count Down | Relay | Bingo
  • Differentiating Polynomials: Worksheets
  • Finding Gradients of Curves: QQI | 10QQI
• BossMaths
  • Differentiating kx^n (Interactive)

Worksheets

• Dr Austin Maths
  • Rule Practice Strips (Word | PDF | Answers)
• Corbettmaths
  • Differentiation Practice Questions (Q1-6) & Solutions
  • Gradient of a Curve Practice Questions & Answers
• Maths 4 Everyone
  • The Rule for Polynomials First Steps
  • The Rule for Polynomials Strengthen
  • The Rule for Polynomials Extend
  • The Rule for Polynomials Topic Review
  • Gradient and Turning Points Topic Review (Ignore Final Row)
• Pixi Maths
  • Differentiation RAG
• MadAsMaths (T. Madas)
  • Calculus Introduction Exam Questions Q5, 8, 152, 164 (difficulty 2–3 of 5)
  • Differentiation Practice I The Operation of Differentiation Q1–2; Practice in Context Q1–3, 5

Dr Frost Video

Key Skill – Differentiate a single term in the form ax^n

K804: Differentiate a Single Term in the Form ax^b.

Key Skill – Differentiate a collection of terms in the form ax^b.

K805: Differentiate a Collection of Terms in the Form ax^b.

Dr Frost Slides & Activities

• Dr Frost Slides (4)

Extra Questions

• Dr Frost Questions

Key Skills

Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost

• 512a: Differentiate a single term given in the form ax^b
• 512b: Differentiate a collection of terms with integer exponents.
• 512c: Differentiate a collection of terms given in the form ax^b
• 512d: Differentiate a collection of terms given in the form ax^b involving an algebraic coefficient.
• 512: Exam Practice: Differentiating xⁿ for rational values of n

Videos & Other Multimedia

Second Order Derivatives

Corbett Maths Second Order Derivatives

Worksheets

• Corbettmaths
  • Second Order Derivatives AQA Level 2 Practice Questions & Solutions

Tutorial Videos

Differentiation after Rearranging – Corbettmaths

Corbett Maths Differentiation After Rearranging

Online Platforms (with Videos & Exercises)

Activities & Resources

Worksheets

• Dr Austin Maths
  • Harder by Rule Practice Strips (Word | PDF | Answers)
  • Harder Match-Up (Word | PDF | Answers)
• Corbettmaths
  • Differentiation Practice Questions (Q7 Onwards) & Solutions
• Maths 4 Everyone (Final Row)
  • The Rule for Polynomials Topic Review
• Starting Points Maths
  • Developing Indices Skills for Calculus · PDF

Dr Frost Video

Key Skill – Differentiate a collection of terms that require rewriting in the form ax^b.

K806: Differentiate a Collection of Terms That Require Rewriting in the Form ax^b.

Key Skill – Differentiate an expression requiring bracket expansion.

K807: Differentiate a Polynomial Expression Requiring Bracket Expansion.

Dr Frost Slides & Activities

• All in one summary sheet

Extra Questions

• Dr Frost Questions

Key Skills

Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost

• 512e: Differentiate a collection of terms that require rewriting in the form ax^b
• 512f: Differentiate xⁿ to find the gradient of a tangent to a curve (i.e. the instantaneous rate of change) at a given point.
• 512g: Determine the value of x which gives rise to a given gradient of the tangent to a curve.
• 512h: Determine the value of a constant given the gradient of the tangent to a curve at a point.
• 512i: Differentiate a polynomial expression requiring bracket expansion.
• 512j: Differentiate a polynomial expression written as a fraction with a single term on the denominator.
• 512k: Differentiate an expression written as a fraction with a single term on the denominator and that contains a root.
• 512: Exam Practice: Differentiating xⁿ for rational values of n

Further Practice

• Practise Questions (may include angles in a triangle and on a straight line)

Tutorial Videos

Stationary Points – Corbettmaths

Corbett Maths Stationary Points

Online Platforms (with Videos & Exercises)

Activities & Resources

• Pixi Maths
  • Differentiation and Graphs ppt
• Acute Learning Problem Pairs
  • Level 2 FM: Stationary Points as PowerPoint or PDF
  • Level 2 FM: Graph Sketching as PowerPoint or PDF
• Interactive Maths
  • Finding Turning Points of Curves: QQI | 10QQI

Worksheets

• Dr Austin Maths
  • Practice Strips (Word | PDF | Answers)
  • Fill In The Blanks (Word | PDF | Answers)
  • Applied Calculus Problems Practice Strips (Word | PDF | Answers)
• Corbettmaths
  • Stationary Points Practice Questions & Solutions
• Maths 4 Everone
  • Gradient and Turning Points Topic Review (Final Row)
• Pixi Maths
  • Differentiation and Graphs RAG
• MadAsMaths (T. Madas)
  • Calculus Introduction Exam Questions Q215 (difficulty 4 of 5)

Dr Frost Video

Dr Frost Slides & Activities

• All in one summary sheet

Extra Questions

• Dr Frost Questions

Key Skills

Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost

• 515a: Determine the second derivative of a function.
• 515b: Evaluate the second derivative of a function at a specific point.
• 515c: Determine the point on a curve which has a given second derivative.
• 516a: Understand the terms increasing and decreasing and apply to a drawn graph.
• 516b: Determine the interval for which a quadratic function is increasing or decreasing.
• 516c: Determine whether a function is increasing or decreasing at a specific point on the curve.
• 516d: Determine the interval for which a cubic function is increasing or decreasing.
• 516e: Prove that a function is increasing or decreasing.
• 516f: Determine the range of values for which a function is increasing/decreasing involving a reciprocal term.
• 517a: Determine the stationary point of a quadratic function using differentiation.
• 517b: Determine the stationary points of a cubic function.
• 517c: Determine the stationary points of a quartic function or higher power.
• 517d: Determine whether a stationary point is a maximum or minimum by using the second derivative.
• 517e: Determine whether a stationary point is a maximum, minimum or point of inflection by using the gradients either side of the point.
• 517f: Determine the stationary points of a curve involving negative powers of x
• 517g: Determine the stationary points of a curve involving roots and fractional powers of x
• 517h: Determine the maximum or minimum value of a function within a closed interval.
• 517i: Draw a cubic graph by using its stationary points.
• 517j: Determine coefficients of an equation given a turning point.
• 517k: Determine the turning point of a sketched cubic graph, where one turning point touches the x-axis.
• 517l: Use the discriminant to determine the number of stationary points of a cubic function.
• 517m: Determine the number of roots of cubic, quartic and quintic equations by considering turning points.
• 515: Exam Practice: Second derivative of a polynomial function (involving powers of x only)
• 516: Exam Practice: Increasing and decreasing polynomial functions (involving powers of x only)
• 517: Exam Practice: Maxima and minima and stationary points for powers of x

Further Practice

• Practise Questions (may include angles in a triangle and on a straight line)

Videos & Other Multimedia

Solving Problems using Differentiation – Corbettmaths

Corbett Maths Solving Problems Using Differentiation

Worksheets

• Corbettmaths
  • Using Differentiation to Solve Problems AQA Level 2 Practice Questions & Solutions

Tutorial Videos

Equation of a Tangent to a Curve – Corbettmaths

Corbett Maths Equation of a Tangent to a Curve

Online Platforms (with Videos & Exercises)

• Khan Academy
  • Derivatives & tangent lines: Videos & practice

Activities

• Pixi Maths
  • Tangents, Normals and Stationary Points ppt
• Andy Lutwyche
  • Codebreaker
• Acute Learning Problem Pairs
  • Level 2 FM: Tangents & Normals as PowerPoint or PDF
• BossMaths
  • Tangents & Normals (Interactive)

Worksheets

• Corbettmaths
  • Equation of a Tangent Practice Questions & Solutions
• Pixi Maths
  • Tangents, Normals and Stationary Points RAG
• MadAsMaths (T. Madas)
  • Calculus Introduction Exam Questions Q11, 35, 110, 141, 154, 190, 214 (difficulty 2–4 of 5)
  • Differentiation Practice I Tangents & Normals Q1–2, 4–5; Practice in Context Q6, 11, 18–19

Dr Frost Video

Dr Frost Slides & Activities

• Slides & Worksheet

Topic Test

• Standard Test

Extra Questions

• Dr Frost Questions

Key Skills

Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost

• 520a: Determine the equation of a tangent or normal to a curve at a turning point.
• 520b: Determine the equation of the tangent or normal to a curve at a given point, where the gradient function is given.
• 520c: Find an equation of a tangent to a polynomial curve.
• 520d: Find an equation of a normal to a polynomial curve.
• 520e: Determine the coordinate of a point on a curve given the function and the gradient of the tangent or normal.
• 520f: Determine the coordinate of a point on a curve given the equation of a line parallel to the tangent or normal.
• 520g: Determine the equation of a tangent or normal to a curve where the function involves fractional or negative powers.
• 520h: Determine the equation of the tangent or normal of a curve at an intercept with the axes.
• 520i: Determine the coordinates of the point where a tangent or normal to a curve at one point intercepts with the coordinate axes.
• 520j: Determine the equation of the tangent or normal of a curve in the form ax + by + c = 0
• 520k: Determine a triangular area formed by a tangent or normal to a curve. (not yet active)
• 520l: Determine the coordinates of the point where a tangent or normal to a curve at one point intercepts with the curve again. (not yet active)
• 520m: Determine an unknown coefficient in a function given the gradient of the tangent/normal. (not yet active)
• 520n: Determine an unknown coefficient in a function given the tangent/normal to the curve is parallel to another line. (not yet active)
• 520o: Determine an unknown coefficient or constant in the equation of a tangent or normal. (not yet active)
• 520: Exam Practice: Equations of tangents and normals (powers of x only)

Further Practice

• Practise Questions

Other Videos & Multimedia

Equation of a Normal – Corbettmaths

Corbett Maths Equation of a Normal

Worksheets

• Corbettmaths
  • Equation of a Normal Practice Questions & Solutions

Tutorial Videos

Differentiation (Increasing and Decreasing Functions)

Differentiation (Increasing and Decreasing Functions) by 1st Class Maths

Increasing and Decreasing Functions – Corbettmaths

Increasing and Decreasing Functions – Corbettmaths by corbettmaths

Differentiation : Increasing & Decreasing Functions : ExamSolutions

Differentiation : Increasing & Decreasing Functions : ExamSolutions by ExamSolutions

Activities & Resources

• Acute Learning Problem Pairs
  • Level 2 FM: Increasing & Decreasing Functions as PowerPoint or PDF
• Andy Lutwyche
  • Codebreaker
• Math = Love (Sarah Carter)
  • Increasing & Decreasing Intervals

Dr Frost Video

• Topic Video

Extra Questions

• Dr Frost Questions

Key Skills

Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost

• 516a: Understand the terms increasing and decreasing and apply to a drawn graph.
• 516b: Determine the interval for which a quadratic function is increasing or decreasing.
• 516c: Determine whether a function is increasing or decreasing at a specific point on the curve.
• 516d: Determine the interval for which a cubic function is increasing or decreasing.
• 516e: Prove that a function is increasing or decreasing.
• 516: Exam Practice: Increasing and decreasing polynomial functions (involving powers of x only)

Tutorial Videos

Differentiation (Maxima and Minima)

Differentiation (Maxima and Minima) by 1st Class Maths

Using the Second Derivative (2 of 2: Determining nature of stationary points)

Using the Second Derivative (2 of 2: Determining nature of stationary points) by Eddie Woo

AQA Core 1 7.11 The Second Derivative: Maximums and Minimums

AQA Core 1 7.11 The Second Derivative: Maximums and Minimums by TLMaths

Online Platforms (with Videos & Exercises)

• Khan Academy
  • Second derivatives: Videos & practice
  • The second derivative test: Videos & practice

Activities & Resources

• Acute Learning Problem Pairs
  • Level 2 FM: Second Derivative & Maxima/Minima as PowerPoint or PDF
• Andy Lutwyche
  • Second Derivatives Codebreaker

Worksheets

• Corbettmaths
  • Second Order Derivatives AQA Level 2 Practice Questions & Solutions
• MadAsMaths (T. Madas)
  • Calculus Introduction Exam Questions Q13 (difficulty 2 of 5)
  • Differentiation Practice I Stationary Points Q1

Dr Frost Video

KS5 – The Second Derivative & The Nature of Turning Points

Whole Topic Video (from 3:43) Second Derivatives

Extra Questions

• Dr Frost Questions

Key Skills

Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost

• 515a: Determine the second derivative of a function.
• 515b: Evaluate the second derivative of a function at a specific point.
• 517d: Determine whether a stationary point is a maximum or minimum by using the second derivative.
• 517e: Determine whether a stationary point is a maximum, minimum or point of inflection by using the gradients either side of the point.
• 515: Exam Practice: Second derivative of a polynomial function (involving powers of x only)
• 517: Exam Practice: Maxima and minima and stationary points for powers of x

Tutorial Videos

A-Level Maths: G3-26 [Optimisation: Maximising Volume of a Box]

A-Level Maths: G3-26 [Optimisation: Maximising Volume of a Box] by TLMaths

Find Maximum Area Enclosed by a Fence

Find Maximum Area Enclosed by a Fence by Math and Stats Help

Optimisation Grade 12: Maximum Volume Box

Optimisation Grade 12: Maximum Volume Box by Kevinmathscience

Online Platforms (with Videos & Exercises)

• Khan Academy
  • Optimisation: Videos & practice

Activities & Resources

• Acute Learning Problem Pairs
  • Level 2 FM: Optimisation as PowerPoint or PDF
• The Chalkface
  • Baked Beans Optimisation: PowerPoint · PDF
  • Oil Drum Optimisation: PDF

Worksheets

• Dr Austin Maths
  • Applied Calculus Problems Practice Strips (Word | PDF | Answers)
• Corbettmaths
  • Using Differentiation to Solve Problems AQA Level 2 Practice Questions & Solutions
• MadAsMaths (T. Madas)
  • Calculus Introduction Exam Questions Q41, 54 (difficulty 3 of 5)
  • Differentiation Optimisation Problems Q1, 3, 6, 8–10 (difficulty 3 of 5)

Dr Frost Video

• Topic Video (from 7:48)

Extra Questions

• Dr Frost Questions

Key Skills

Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost

• 518a: Form an expression for a physical quantity in terms of one variable by combining an expression to optimise with a constraint equation.
• 518b: Use differentiation to find the minimum or maximum value of a physical quantity, and the value of a controllable quantity that gives rise to this. (not yet active)
• 518c: Determine whether the optimum value for a physical quantity was a minimum or maximum. (not yet active)
• 518: Exam Practice: Optimisation problems involving powers of x

Tutorial Videos

IGCSE Differentiation 4 – Displacement, Velocity and Acceleration

IGCSE Differentiation 4 – Displacement, Velocity and Acceleration by Maths Genie

❖ Position, Velocity, Acceleration using Derivatives ❖

❖ Position, Velocity, Acceleration using Derivatives ❖ by Patrick J

Displacement, velocity and acceleration using derivatives

Displacement, velocity and acceleration using derivatives by Cowan Academy

Online Platforms (with Videos & Exercises)

• Khan Academy
  • Motion problems with differentiation: Videos & practice

Activities

• Andy Lutwyche
  • (Time) Codebreaker

Worksheets

• Dr Austin Maths
  • Motion of a Particle Practice Strips (Word | PDF | Answers)
• Maths 4 Everyone
  • Displacement, Velocity and Acceleration Topic Review

Dr Frost Video

Dr Frost Slides & Activities

• Slides & Worksheet

Topic Test

• Standard Test

Extra Questions

• Dr Frost Questions

Key Skills

Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost

• 558a: Use differentiation to find an expression for the velocity or the acceleration of a particle.
• 558b: Determine when a particle is instantaneously at rest, given an expression for the velocity.
• 558c: Determine when a particle is instantaneously at rest, given an expression for the displacement.
• 558d: Use differentiation once to find the velocity or acceleration of a particle at a given instant.
• 558e: Use differentiation twice to find the acceleration of a particle at a given instant.
• 558: Exam Practice: Calculus in kinematics for motion in a straight line, e.g. v = dr/dt, in 1 dimension

Further Practice

• Practise Questions

Acute Learning Problem Pairs

• Differentiation as PowerPoint or PDF

Worksheets

• Maths 4 Everyone
  • Differentiation GCSE Questions and Solutions
• Andy Lutwyche
  • Careless Casey – Calculus
• Mathshelper (Jon Stone)
  • Differentiation I
  • Differentiation II
  • Differentiation III
  • Differentiation IV
• MathedUp
  • Differentiation & Stationary Points: Worksheet · Practice · Quiz · Question Gallery
  • Tangents & Normals: Worksheet · Practice · Quiz · Question Gallery
  • Increasing/Decreasing & Optimisation: Worksheet · Practice · Quiz · Question Gallery
  • Kinematics (Calculus): Worksheet · Practice · Quiz · Question Gallery

Activities

• MathsPad
  • Drawing tangents tool✦