Mathematics With Woody

7.1 Radians - Introduction

7.1 Quiz

7.2 Arc Lengths

7.2 Quiz

7.3 Sector Areas

7.3 Quiz

7.4 Solving Trigonometric Equations in Radians

7.4 Quiz

Circular Measure - Exam Questions

8.1 The Choose Function - Intro

8.1 Quiz

8.2 A Choose Function Puzzle

8.3 Binomial Expansion (Part 1)

8.4 Binomial Expansion (Part 2)

8.4 Quiz

8.5 Ascending Powers of x

8.5 Quiz

8.6 Binomial Problem Solving

8.6 Quiz

8.7 Binomial Estimation

8.7 Quiz

8.8 Arithmetic Sequences

8.8 Quiz

8.9 Arithmetic Series

8.9 Quiz

8.10 Geometric Sequences (Part 1)

8.10 Quiz

8.11 Geometric Sequences (Part 2)

8.11 Quiz

8.12 Geometric Series

8.12 Quiz

8.13 Sums to Infinity

8.13 Quiz

8.14 Recurrence Relations

Series - Exam Questions

9.1 Gradients of Curves

9.2 First Principles at a Point

9.2 Quiz

9.3 First Principles in General

9.4 The x^n Rule

9.4 Quiz

9.5 Differentiating Basic Polynomials

9.5 Quiz

9.6 Differentiating Negative Powers

9.6 Quiz

9.7 Differentiating Fractional Powers

9.7 Quiz

9.8 Differentiating Mixed Functions

9.8 Quiz

9.9 Using Gradient Functions

9.9 Quiz

9.10 Tangents and Normals (Part 1)

9.11 Tangents and Normals (Part 2)

9.11 Quiz

9.12 Increasing and Decreasing Functions

9.12 Quiz

9.13 Stationary Points

9.13 Quiz

9.14 The Chain Rule

9.15 Second Derivatives

9.15 Quiz

9.16 Sketching Gradient Functions

9.17 Optimisation (Part 1)

9.18 Optimisation (Part 2)

9.19 Calculator Use

Differentiation - Exam Questions

10.1 Integration Intro

10.1 Quiz

10.2 Finding Functions

10.2 Quiz

10.3 Areas

10.3 Quiz

10.4 Areas Under the X-Axis

10.4 Quiz

10.5 Areas Between Functions

10.5 Quiz

10.6 Integrating (ax+b)^n

10.7 Integrating (ax+b)^n - Areas

10.8 Integration Problem Solving (Part 1)

10.9 Integration Problem Solving (Part 2)

10.10 Integration Problem Solving (Part 3)

10.10 Quiz

10.11 Improper Integrals

10.12 Volumes of Revolution - Introduction

10.13 Volumes of Revolution Around the X-Axis

10.13 Quiz

10.14 Volumes of Revolution Around the X-Axis

10.14 Quiz

10.15 Volumes of Revolution - Addition and Subtraction

10.15 Quiz

10.16 Calculator Use

10.17 Why Integration Gives Area

Integration - Exam Questions

1.1 Exponentials Intro

1.1 Quiz

1.2 The Exponential Function

1.2 Quiz

1.3 Differentiating e^x

1.3 Quiz

1.4 Exponential Modelling

1.4 Quiz

1.5 Logarithms Intro

1.5 Quiz

1.6 Simplifying Logs

1.7 Log Laws

1.8 Using the Log Laws

1.8 Quiz

1.9 Log Equations (Part 1)

1.9 Quiz

1.10 Log Equations (Part 2)

1.10 Quiz

1.11 The Natural Log

1.11 Quiz

1.12 Graphs of Logs

1.12 Quiz

1.13 Non-Linear Data - Exponential Models

1.13 Quiz

1.14 Non-Linear Data - Polynomial Models

1.14 Quiz

1.15 Non-Linear Data - Exam Question

1.15 Quiz

Exponentials and Logarithms - Exam Questions

2.1 The Modulus Function - Graphs (Part 1)

2.1 Quiz

2.2 The Modulus Function - Graphs (Part 2)

2.2 Quiz

2.3 Modulus Equations and Inequalities (Part 1)

2.3 Quiz

2.4 Modulus Equations and Inequalities (Part 2)

2.4 Quiz

2.5 Polynomial Division Intro

2.5 Quiz

2.6 Division Examples (Part 1)

2.6 Quiz

2.7 Division Examples (Part 2)

2.7 Quiz

2.8 Remainders (Part 1)

2.8 Quiz

2.9 Remainders (Part 2)

2.9 Quiz

2.10 Factor Theorem

2.10 Quiz

2.11 Long Division

2.11 Quiz

Algebra - Exam Questions

3.1 Sec, Cosec and Cot

3.2 Graphs of Sec, Cosec and Cot

3.2 Quiz

3.3 Sec, Cosec and Cot - Proving Simple Identities

3.4 Sec, Cosec and Cot - Simple Equations

3.4 Quiz

3.5 The Pythagorean Identities

3.5 Quiz

3.6 The Pythagorean Identities - Proving Identities

3.6 Quiz

3.7 The Pythagorean Identities - Solving Equations

3.7 Quiz

3.8 Pythagorean Identities - Exam-Style Problems

3.8 Quiz

3.9 Inverse Trig Functions - Graphs

3.9 Quiz

3.10 Inverse Trig Functions - Calculations

3.10 Quiz

3.11 The Addition Formulae

3.12 Using the Addition Formulae

3.12 Quiz

3.13 The Double Angle Formulae

3.14 The Double Angle Formulae - Solving Equations (Part 1)

3.14 Quiz

3.15 The Double Angle Formulae - Solving Equations (Part 2)

3.15 Quiz

3.16 The Double Angle Formulae - Proving Identities

3.16 Quiz

3.17 The Double Angle Formulae - Exam-Style Problems

3.17 Quiz

3.18 Harmonic Form - acosx+bsinx

3.18 Quiz

3.19 Harmonic Form - Solving Equations

3.19 Quiz

3.20 Harmonic Form - Minimum and Maximum (Part 1)

3.20 Quiz

3.21 Harmonic Form - Minimum and Maximum (Part 1)

3.21 Quiz

3.22 Modelling With Trig Equations

3.22 Quiz

Trigonometry - Exam Questions

4.1 Differentiating Sinx and Cosx

4.1 Quiz

4.2 Using the Derivatives of Sinx and Cosx

4.2 Quiz

4.3 Differentiating Exponential Functions

4.3 Quiz

4.4 Differentiating lnx

4.4 Quiz

4.5 The Chain Rule: f(x)^n

4.5 Quiz

4.6 The Chain Rule: Trigonometric Functions

4.6 Quiz

4.7 The Chain Rule: Exponential Functions

4.7 Quiz

4.8 The Chain Rule: Logarithmic Functions

4.8 Quiz

4.9 The Product Rule

4.9 Quiz

4.10 The Quotient Rule

4.10 Quiz

4.11 Derivatives of Tan, Sec, Cosec and Cot

4.11 Quiz

4.12 Using the Derivatives of Tan, Sec, Cosec and Cot

4.12 Quiz

4.13 Implicit Differentiation

4.13 Quiz

4.14 Implicit Differentiation - Stationary and Critical Points

4.14 Quiz

4.15 Second Derivatives - Convex and Concave Functions

4.15 Quiz

4.16 Parametric Equations Intro

4.17 Converting Parametrics to Cartesian: Substitution

4.17 Quiz

4.18 Converting Parametrics to Cartesian: Pythagorean Identities

4.18 Quiz

4.19 Converting Parametrics to Cartesian: Double Angle Formulae

4.19 Quiz

4.20 Intersections of Parametrics and Lines

4.20 Quiz

4.21 Differentiating Parametric Equations

4.21 Quiz

4.22 Differentiating Parametric Curves: Stationary and Critical Points

4.22 Quiz

Differentiation - Exam Questions

5.1 Integrating Standard Functions

5.1 Quiz

5.2 Integrating f(ax+b)

5.2 Quiz

5.3 Trig Identities For Integration: Pythagorean Identities

5.3 Quiz

5.4 Trig Identities For Integration: Double Angle Formulae

5.4 Quiz

Integration - Exam Questions

6.1 Locating Roots

6.1 Quiz

6.2 Iteration (Part 1)

6.3 Iteration (Part 2)

6.2/6.3 Quiz

Numerical Methods - Exam Questions

7.5 Partial Fractions - Quadratic Factors

7.5 Quiz

7.6 The Binomial Expansion Formula

7.6 Quiz

7.7 Using the Binomial Expansion Formula

7.7 Quiz

7.8 When the First Term is Not 1

7.8 Quiz

7.9 Approximations

7.9 Quiz

7.10 Binomial Expansion and Algebraic Fractions

7.10 Quiz

7.11 Binomial Expansion and Partial Fractions

7.11 Quiz

Further Algebra - Exam Questions

8.1 Reverse Chain Rule: f'(x)[f(x)]^n (Part 1)

8.2 Reverse Chain Rule: f'(x)[f(x)]^n (Part 2)

8.1/8.2 Quiz

8.3 Reverse Chain Rule: Exponentials

8.3 Quiz

8.4 Reverse Chain Rule: Logarithmic Functions (Part 1)

8.5 Reverse Chain Rule: Logarithmic Functions (Part 2)

8.4/8.5 Quiz

8.6 Mixed Reverse Chain Rule Problems

8.7 Using Partial Fractions for Integration (Part 1)

8.8 Using Partial Fractions for Integration (Part 2)

8.7/8.8 Quiz

8.9 Integration by Parts: Polynomial x Exponential

8.9 Quiz

8.10 Integration by Parts: Polynomial x Trigonometric

8.10 Quiz

8.11 Integration by Parts: Polynomial x Logarithmic

8.11 Quiz

8.12 Integration by Parts: Exponential x Trigonometric

8.12 Quiz

8.13 Integration by Substitution: An Alternative to Reverse Chain Rule

8.13 Quiz

8.14 Integration by Substitution: u = f(x)

8.14 Quiz

8.15 Integration by Substitution: x = f(u)

8.15 Quiz

8.16 Integration by Substitution: Definite Integrals

8.16 Quiz

8.17 Integrating Arctan-Like Functions

8.18 Problem Solving with Integration

8.18 Quiz

8.19 The Trapezium Rule

8.19 Quiz

Integration - Exam Questions

9.1 Vector Notation

9.1 Quiz

9.2 Comparing Coefficients

9.2 Quiz

9.3 Magnitude and Direction

9.3 Quiz

9.4 Position Vectors

9.4 Quiz

9.5 The Vector Equation of a Straight Line

9.5 Quiz

9.6 Parallel and Skew Vectors

9.6 Quiz

9.7 Converting Vector Form to Cartesian Form

9.8 The Scalar (Dot) Product - Introduction

9.9 Using the Scalar Product to Find Angles

9.10 Using the Scalar Product to Find Shortest Distances

Vectors - Exam Questions

10.1 Differential Equations: Separating Variables (Part 1)

10.2 Differential Equations: Separating Variables (Part 2)

10.1/10.2 Quiz

10.3 Forming Differential Equations

10.3 Quiz

10.4 Modelling With Differential Equations (Part 1)

10.5 Modelling With Differential Equations (Part 2)

10.4/10.5 Quiz

Differential Equations - Exam Questions

11.1 Complex Numbers - Introduction

11.2 Addition, Subtraction and Multiplication of Complex Numbers

11.3 Division of Complex Numbers

11.4 Square Roots of Complex Numbers

11.5 Complex Roots of Quadratics

11.6 Complex Roots of Cubics and Quartics

11.7 The Argand Diagram

11.8 Modulus and Argument

11.9 Modulus-Argument and Polar Form

11.10 Exponential Form

11.11 Proof of Exponential Form

11.12 Multiplying Numbers in Modulus Argument Form - Part 1

11.13 Multiplying Numbers in Modulus Argument Form - Part 2

11.14 Multiplying Numbers in Modulus Argument Form - Part 3

11.15 Euler's Identity

11.16 Complex Loci - Circles

11.17 Complex Loci - Perpendicular Bisectors

11.18 Complex Loci - Arguments

Complex Numbers - Exam Questions

1.8 SUVAT Equations

1.9 SUVAT Equations Proofs

1.10 Using the SUVAT Equations (Part 1)

1.11 Using the SUVAT Equations (Part 2)

1.10/1.11 Quiz

1.12 Two-Part Journeys

1.13 Two Moving Objects

1.13 Quiz

1.14 The Gravitational Constant - g

1.15 Projectiles Intro

1.16 Projectiles (Part 1)

1.17 Projectiles (Part 2)

1.16/1.17 Quiz

Velocity and Acceleration - Exam Questions

2.1 Force Diagrams (Part 1)

2.2 Force Diagrams (Part 2)

2.1/2.2 Quiz

2.3 Resultant Forces

2.3 Quiz

2.4 Magnitude and Direction

2.5 Forces as Vectors

2.6 Forces as Vectors Example

2.5/2.6 Quiz

2.7 Parallel Vectors

2.8 Newton's Second Law Introduction

2.9 Newton's Second Law (Part 1)

2.10 Newton's Second Law (Part 2)

2.9/2.10 Quiz

2.11 SUVAT and Forces

2.11 Quiz

2.12 Connected Particles (Part 1)

2.12 Quiz

2.13 Connected Particles (Part 2)

2.14 Connected Particles (Part 3)

2.13/2.14 Quiz

2.15 Changing Forces (Part 1)

2.16 Changing Forces (Part 2)

2.15/3.16 Quiz

2.17 Modelling Assumptions

Forces and Motion - Exam Questions

3.1 Motion as a Functions of Time

3.2 Using Differentiation (Part 1)

3.3 Using Differentiation (Part 2)

3.2/3.3 Quiz

3.4 Turning Points

3.5 Using Integration (Part 1)

3.6 Using Integration (Part 2)

3.5/3.6 Quiz

3.7 SUVAT Equations

3.8 Calculator Use

Variable Acceleration - Exam Questions

4.1 Resultant Forces - Components

4.1 Quiz

4.2 Forces and Newton's Second Law

4.2 Quiz

4.3 Inclined Planes (Part 1)

4.4 Inclined Planes (Part 2)

4.3/4.4 Quiz

4.5 Friction

4.5 Quiz

4.6 Friction on an Inclined Plane (Part 1)

4.6 Quiz

4.7 Friction on an Inclined Plane (Part 2)

4.7 Quiz

4.8 Motion on a Rough Plane: No Other Forces

4.8 Quiz

4.9 Motion on a Rough Inclined Plane: Parallel Forces

4.9 Quiz

4.10 Motion on a Rough Inclined Plane: Non-Parallel Forces (Part 1)

4.11 Motion on a Rough Inclined Plane: Non-Parallel Forces (Part 2)

4.10/4.11 Quiz

4.12 Connected Particles on a Rough Plane (Part 1)

4.12 Quiz

4.13 Connected Particles on a Rough Plane (Part 2)

4.13 Quiz

Resolving Forces and Friction - Exam Questions

5.1 Three Forces in Equilibrium

5.1 Quiz

5.2 Three Forces in Equilibrium - Triangle Method

5.2 Quiz

5.3 Equilibrium on an Inclined Plane

5.3 Quiz

5.4 Connected Particles on an Inclined Plane

5.4 Quiz

5.5 Hanging Objects

5.5 Quiz

5.6 Limiting Equilibrium

5.6 Quiz

5.7 Limiting Equilibrium on an Inclined Plane

5.7 Quiz

5.8 Limiting Equilibrium - Further Example

5.8 Quiz

Equilibrium - Exam Questions

6.1 The Work Done by a Force

6.2 The Work Done by a Force - Components

6.3 Kinetic Energy

6.4 Gravitational Potential Energy - Part 1

6.5 Gravitational Potential Energy - Part 2

6.6 The Work-Energy Principle - Part 1

6.7 The Work-Energy Principle - Part 1

6.8 Power - Part 1

6.9 Power - Part 2

Work, Energy and Power - Exam Questions

7.1 Momentum

7.2 Conservation of Linear Momentum

7.3 Conservation of Momentum with Multiple Collisions

Momentum - Exam Questions

2.1 Inter-Quartile Range

2.2 Inter-Quartile Range Examples

2.1/2.2 Quiz

2.3 Inter-Quartile Range - Applications

2.4 Linear Interpolation to Find the IQR

2.4 Quiz

2.5 Standard Deviation Method 1

2.5 Quiz

2.6 Standard Deviation Method 2

2.6 Quiz

2.7 Using the Calculator to Find Standard Deviation

2.7 Quiz

2.8 Variance

2.9 Standard Deviation from Grouped Data

2.9 Quiz

2.10 Bonus: Proving the Two Standard Deviation formulae Are the Same

3.1 Merging Data - Means

3.1 Quiz

3.2 Merging Data - Standard Deviations

3.2 Quiz

3.3 Coding Data (Part 1)

3.4 Coding Data (Part 2)

3.3/3.4 Quiz

4.1 Outliers

4.1 Quiz

4.2 Outliers - an Alternative Definition

4.3 Boxplots

4.3 Quiz

4.4 Skew

4.4 Quiz

4.5 Cumulative Frequency Graphs

4.5 Quiz

4.6 Histograms - Drawing

4.7 Histograms - Interpreting

4.7 Quiz

4.8 Histograms - Dimensions and Problem Solving

4.8 Quiz

Data Handling and Representations of Data - Exam Questions

5.1 Factorial Notation

5.2 Permutations - No Repeates

5.3 Permutations With Repetitions

5.4 Permutations of r Objects Froms n

5.5 Permutations With Restrictions

5.6 Combinations

5.7 Probability Problems

Permutations and Combinations - Exam Questions

6.1 Venn Diagrams (Part 1)

6.1 Quiz

6.2 Venn Diagrams (Part 2)

6.2 Quiz

6.3 Independent Events (Part 1)

6.3 Quiz

6.4 Independent Events (Part 2)

6.4 Quiz

6.5 Mutually Exclusive Events

6.5 Quiz

6.6 Tree Diagrams

6.6 Quiz

6.7 Set Notation

6.7 Quiz

6.8 Conditional Probability Intro

6.8 Quiz

6.9 Conditional Probability Formula

6.9 Quiz

6.10 Conditional Probability on Tree Diagrams

6.10 Quiz

6.11 Medical Testing Example

Probability - Exam Questions

7.1 Discrete Random Variables

7.2 Discrete Random Variables - Expectation

7.3 Discrete Random Variables - Variance

Discrete Random Variables - Exam Questions

8.1 Introduction to the Binomial Distribution

8.2 The Binomial Formula (Part 1)

8.2 Quiz

8.3 The Binomial Formulae (Part 2)

8.3 Quiz

8.4 Conditions for Using the Binomial Distribution

8.4 Quiz

8.5 Calculator Use - the Binomial Probability Distribution Function

8.5 Quiz

8.6 Calculator Use - the Binomial Cumulative Distribution Function (Part 1)

8.6 Quiz

8.7 Calculator Use - the Binomial Cumulative Distribution Function (Part 2)

8.7 Quiz

8.8 Other Binomial Calculations

8.8 Quiz

8.9 Forming New Binomial Distributions (Part 1)

8.9 Quiz

8.10 Forming New Binomial Distributions (Part 2)

8.11 Discrete Random Variables

8.11 Quiz

8.12 The Geometric Distribution - Intro

8.13 The Geometric Distribution - The Mode

8.14 The Geometric Distribution - Expectation

Binomial and Geometric Distributions - Exam Questions

9.1 What is the Normal Distribution?

9.1 Quiz

9.2 The 68-95-99.7 Rule

9.2 Quiz

9.3 The Standard Normal Distribution

9.4 Standard Normal Probabilities - Tables

9.5 Standard Normal Probabilities - Calculator

9.6 Normal Probabilities

9.7 The Inverse Normal Function - Part 1

9.8 The Inverse Normal Function - Part 2

9.9 Finding Unknown Standard Deviations

9.9 Quiz

9.10 Finding Unknown Means

9.10 Quiz

9.11 Finding Unknown Means and Standard Deviations

9.11 Quiz

9.12 Normal Approximations to Binomial Distributions - Part 1

9.13 Normal Approximations to Binomial Distributions - Part 2

The Normal Distribution - Exam Questions

1.1 Hypothesis Tests Introduction

1.1 Quiz

1.2 One-Tailed Tests

1.2 Quiz

1.3 Two-Tailed Tests

1.3 Quiz

1.4 Critical Regions

1.4 Quiz

1.5 Actual Significance Levels

1.5 Quiz

1.6 Type I and Type II Errors

1.6 Quiz

Hypothesis Testing - Exam Questions

2.1 The Poisson Distribution - Introduction

2.1 Quiz

2.2 Conditions for the Poisson Distribution

2.2 Quiz

2.3 The Poisson Distribution - Calculator Use

2.3 Quiz

2.4 The Cumulative Poisson Function

2.4 Quiz

2.5 Different Intervals

2.5 Quiz

2.6 Poisson Approximations to Binomials Distributions

2.6 Quiz

2.7 Normal Approximations to Poisson Distributions

2.7 Quiz

2.8 Hypothesis Tests with Poisson Distributions - Part 1

2.8 Quiz

2.9 Hypothesis Tests with Poisson Distributions - Part 2

2.9 Quiz

The Poisson Distribution - Exam Questions

3.1 Linear Combinations of Random Variables - Expectation and Variance

3.1 Quiz

3.2 Sums and Differences of Random Variables

3.2 Quiz

3.3 Linear Combinations of Normal Distributions

3.3 Quiz

3.4 Linear Combinations of Poisson Distributions

3.4 Quiz

Linear Combinations of Random Variables

4.1 Continuous Random Variables - Introduction - Part 1

4.1 Quiz

4.2 Continuous Random Variables - Introduction - Part 2

4.2 Quiz

4.3 Medians and Percentiles - Part 1

4.4 Medians and Percentiles - Part 2

4.3/4.4 Quiz

4.5 Expectation of a Continuous Random Variable

4.5 Quiz

4.6 Variance of a Continuous Random Variable

4.7 Continuous Random Variables - Exam Problems

4.6 Quiz

5.1 Random Sampling

5.1 Quiz

5.2 The Distribution of Sample Means

5.2 Quiz

5.3 The Central Limit Theorem - Introduction

5.4 The Central Limit Theorem - Examples

5.3/5.4 Quiz

6.1 Unbiased Estimates of the Population Mean and Variance

6.2 Hypothesis Tests for Population Means - Known Variance

6.3 Hypothesis Tests for Population Means - Unknown Variance

6.4 Confidence Intervals - Known Variance

6.5 Confidence Intervals - Unknown Variance

6.6 Confidence Intervals for Proportions - Part 1

6.7 Confidence Intervals for Proportions - Part 2