Mathematics With Woody

7.1 Algebraic Proof

7.1 Quiz

7.2 Identities

7.2 Quiz

7.3 Inequalities

7.4 Proof by Exhaustion

7.5 Proof by Counterexample

7.5 Quiz

7.6 Fun Geometric Proof

Proof - 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

Binomial Expansion - Exam Questions

9.1 The Sine Rule: Lengths

9.1 Quiz

9.2 The Sine Rule: Angles

9.2 Quiz

9.3 The Cosine Rule: Lengths

9.3 Quiz

9.4 The Cosine Rule: Angles

9.4 Quiz

9.5 The Cosine Rule: Algebraic Problems

9.6 The Area of a Triangle

9.6 Quiz

9.7 The Sine Graph

9.8 The Cosine Graph

9.9 The Tan Graph

9.7/9.8/9.9 Quiz

9.10 Transformations of Trig Graphs

9.11 Applications of Transformations

9.10/9.11 Quiz

Trigonometry - Triangles and Graphs - Exam Questions

10.1 Multiple Sine Solutions

10.1 Quiz

10.2 Multiple Cosine Solutions

10.2 Quiz

10.3 Multiple Tan Solutions

10.3 Quiz

10.4 Trig Identities

10.5 Solving Trig Equations With the Tan Identity

10.5 Quiz

10.6 Solving Quadratic Trig Equations (Part 1)

10.7 Solving Quadratic Trig Equations (Part 2)

10.6/10.7 Quiz

10.8 Further Trig Equations (Part 1)

10.9 Further Trig Equations (Part 2)

10.8/10.9 Quiz

10.10 Proving Trig Identities (Part 1)

10.11 Proving Trig Identities (Part 2)

Trigonometry - Equations and Identities - Exam Questions

11.1 Vector Notation

11.1 Quiz

11.2 Comparing Coefficients

11.2 Quiz

11.3 Magnitude and Direction

11.3 Quiz

11.4 Position Vectors

11.4 Quiz

11.5 Geometric Vector Problems (Part 1)

11.6 Geometric Vector Problems (Part 2)

11.7 Geometric Vector Proof

Vectors - Exam Questions

12.1 Gradients of Curves

12.2 First Principles at a Point

12.2 Quiz

12.3 First Principles in General

12.4 The x^n Rule

12.4 Quiz

12.5 Differentiating Simple Polynomials

12.5 Quiz

12.6 Differentiating Negative Powers

12.6 Quiz

12.7 Differentiating Fractional Powers

12.7 Quiz

12.8 Differentiating Mixed Functions

12.8 Quiz

12.9 Using Gradient Functions

12.9 Quiz

12.10 Tangents and Normals (Part 1)

12.11 Tangents and Normals (Part 2)

12.10/12.11 Quiz

12.12 Increasing and Decreasing Functions

12.12 Quiz

12.13 Stationary Points

12.13 Quiz

12.14 Second Derivatives

12.14 Quiz

12.15 Sketching Gradient Functions

12.16 Optimisation (Part 1)

12.17 Optimisation (Part 2)

12.18 Calculator Use

Differentiation - Exam Questions

13.1 Integration Intro

13.1 Quiz

13.2 Finding Functions

13.2 Quiz

13.3 Areas

13.3 Quiz

13.4 Areas Under the X-Axis

13.4 Quiz

13.5 Areas Between Functions

13.5 Quiz

13.6 Integration Problem Solving (Part 1)

13.7 Integration Problem Solving (Part 2)

13.8 Integration Problem Solving (Part 3)

13.6/13.7/13.8 Quiz

13.9 Calculator Use

13.10 Why Integration Gives Area

Integration - Exam Questions

14.1 Exponentials Intro

14.1 Quiz

14.2 The Exponential Function

14.2 Quiz

14.3 Differentiating e^x

14.3 Quiz

14.4 Exponential Modelling

14.4 Quiz

14.5 Logarithms Intro

14.5 Quiz

14.6 Simplifying Logs

14.7 Log Laws

14.8 Using the Log Laws

14.8 Quiz

14.9 Log Equations (Part 1)

14.9 Quiz

14.10 Log Equations (Part 2)

14.10 Quiz

14.11 The Natural Log

14.11 Quiz

14.12 Graphs of Logs

14.12 Quiz

14.13 Non-Linear Data - Exponential Models

14.13 Quiz

14.14 Non-Linear Data - Polynomial Models

14.14 Quiz

14.15 Non-Linear Data - Exam Question

14.15 Quiz

Exponentials and Logarithms - 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 Standard Deviation - For MEI Students

2.8 Using the Calculator to Find Standard Deviation

2.8 Quiz

2.9 Variance

2.10 Standard Deviation from Grouped Data

2.10 Quiz

2.11 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 Analysis - Exam Questions

5.1 Regression

5.1 Quiz

5.2 Correlation

5.2 Quiz

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

Probability - Exam Questions

7.1 Introduction to the Binomial Distribution

7.2 The Binomial Formula (Part 1)

7.2 Quiz

7.3 The Binomial Formulae (Part 2)

7.3 Quiz

7.4 Conditions for Using the Binomial Distribution

7.4 Quiz

7.5 Calculator Use - the Binomial Probability Distribution Function

7.5 Quiz

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

7.6 Quiz

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

7.7 Quiz

7.8 Other Binomial Calculations

7.8 Quiz

7.9 Forming New Binomial Distributions (Part 1)

7.9 Quiz

7.10 Forming New Binomial Distributions (Part 2)

7.11 Discrete Random Variables

7.11 Quiz

The Binomial Distribution - Exam Questions

8.1 Hypothesis Tests Introduction

8.1 Quiz

8.2 One-Tailed Tests

8.2 Quiz

8.3 Two-Tailed Tests

8.3 Quiz

8.4 Critical Regions

8.4 Quiz

8.5 Actual Significance Levels

8.5 Quiz

Hypothesis Testing - Exam Questions

9.1 Sampling and Populations

9.2 Random Sampling

9.3 Non-Random Sampling

Sampling - Exam Questions

Edexcel Large Data Set

AQA Large Data Set

OCR Large Data Set

MEI Large Data Set

Edexcel Specimen Paper

AQA Specimen Paper

OCR Specimen Paper

MEI Specimen Paper

2.1 SUVAT Intro

2.2 SUVAT Equations Proofs

2.3 Using the SUVAT Equations (Part 1)

2.4 Using the SUVAT Equations (Part 2)

2.3/2.4 Quiz

2.5 Two-Part Journeys

2.6 Two Moving Objects

2.6 Quiz

2.7 Projectiles Intro

2.8 Projectiles (Part 1)

2.9 Projectiles (Part 2)

2.8/2.9 Quiz

Constant Acceleration - Exam Questions

3.1 Force Diagrams (Part 1)

3.2 Force Diagrams (Part 2)

3.1/3.2 Quiz

3.3 Resultant Forces

3.3 Quiz

3.4 Magnitude and Direction

3.5 Forces as Vectors

3.6 Forces as Vectors Example

3.5/3.6 Quiz

3.7 Parallel Vectors

3.8 Newton's Second Law Introduction

3.9 Newton's Second Law (Part 1)

3.10 Newton's Second Law (Part 2)

3.9/3.10 Quiz

3.11 SUVAT and Forces

3.11 Quiz

3.12 Connected Particles (Part 1)

3.12 Quiz

3.13 Connected Particles (Part 2)

3.14 Connected Particles (Part 3)

3.13/3.14 Quiz

3.15 Changing Forces (Part 1)

3.16 Changing Forces (Part 2)

3.15/3.16 Quiz

3.17 Modelling Assumptions

Forces and Dynamics - Exam Questions

4.1 Motion as a Functions of Time

4.2 Using Differentiation (Part 1)

4.3 Using Differentiation (Part 2)

4.2/4.3 Quiz

4.4 Turning Points

4.5 Using Integration (Part 1)

4.6 Using Integration (Part 2)

4.5/4.6 Quiz

4.7 SUVAT Equations

Variable Acceleration - Exam Questions

5.1 Calculator use in mechanics

Edexcel Specimen Paper

AQA Specimen Paper

OCR Specimen Paper

MEI Specimen Paper

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 Combining Graph Transformations

2.5 Quiz

2.6 Mappings

2.6 Quiz

2.7 Domain and Range

2.7 Quiz

2.8 Composite Functions

2.8 Quiz

2.9 Inverse Functions

2.9 Quiz

2.10 Piecewise Functions

2.10 Quiz

Functions and Graphs - Exam Questions

3.1 Arithmetic Sequences

3.1 Quiz

3.2 Arithmetic Series

3.2 Quiz

3.3 Geometric Sequences (Part 1)

3.3 Quiz

3.4 Geometric Sequences (Part 2)

3.4 Quiz

3.5 Geometric Series

3.5 Quiz

3.6 Sums to Infinity

3.6 Quiz

3.7 Sigma Notation

3.7 Quiz

3.8 Partial Sums

3.8 Quiz

3.9 Recurrence Relations

3.9 Quiz

Sequences and Series - Exam Questions

4.1 The Binomial Expansion Formula

4.1 Quiz

4.2 Using the Binomial Expansion Formula

4.2 Quiz

4.3 When the First Term is Not 1

4.3 Quiz

4.4 Approximations

4.4 Quiz

4.5 Binomial Expansion and Algebraic Fractions

4.5 Quiz

4.6 Binomial Expansion and Partial Fractions

4.6 Quiz

Binomial Expansion - Exam Questions

5.1 Radians - Introduction

5.1 Quiz

5.2 Arc Lengths

5.2 Quiz

5.3 Sector Areas

5.3 Quiz

5.4 Solving Trigonometric Equations in Radians

5.4 Quiz

5.5 Small Angle Approximations

5.5 Quiz

5.6 Using Small Angle Approximations

5.6 Quiz

Radians - Exam Questions

6.1 Sec, Cosec and Cot

6.2 Graphs of Sec, Cosec and Cot

6.2 Quiz

6.3 Sec, Cosec and Cot - Proving Simple Identities

6.4 Sec, Cosec and Cot - Simple Equations

6.4 Quiz

6.5 The Pythagorean Identities

6.5 Quiz

6.6 The Pythagorean Identities - Proving Identities

6.6 Quiz

6.7 The Pythagorean Identities - Solving Equations

6.7 Quiz

6.8 Pythagorean Identities - Exam-Style Problems

6.8 Quiz

6.9 Inverse Trig Functions - Graphs

6.9 Quiz

6.10 Inverse Trig Functions - Calculations

6.10 Quiz

Trigonometric Functions - Exam Questions

7.1 The Addition Formulae

7.2 Using the Addition Formulae

7.2 Quiz

7.3 The Double Angle Formulae

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

7.4 Quiz

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

7.5 Quiz

7.6 The Double Angle Formulae - Proving Identities

7.6 Quiz

7.7 The Double Angle Formulae - Exam-Style Problems

7.7 Quiz

7.8 Harmonic Form - acosx+bsinx

7.8 Quiz

7.9 Harmonic Form - Solving Equations

7.9 Quiz

7.10 Harmonic Form - Minimum and Maximum (Part 1)

7.10 Quiz

7.11 Harmonic Form - Minimum and Maximum (Part 1)

7.11 Quiz

7.12 Modelling With Trig Equations

7.12 Quiz

Trigonometry - Identities and Modelling - Exam Questions

8.1 Differentiating Sinx and Cosx

8.1 Quiz

8.2 Using the Derivatives of Sinx and Cosx

8.2 Quiz

8.3 Differentiating Exponential Functions

8.3 Quiz

8.4 Differentiating lnx

8.4 Quiz

8.5 The Chain Rule: f(x)^n

8.5 Quiz

8.6 The Chain Rule: Trigonometric Functions

8.6 Quiz

8.7 The Chain Rule: Exponential Functions

8.7 Quiz

8.8 The Chain Rule: Logarithmic Functions

8.8 Quiz

8.9 The Product Rule

8.9 Quiz

8.10 The Quotient Rule

8.10 Quiz

8.11 Derivatives of Tan, Sec, Cosec and Cot

8.11 Quiz

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

8.12 Quiz

8.13 Implicit Differentiation

8.13 Quiz

8.14 Implicit Differentiation - Stationary and Critical Points

8.14 Quiz

8.15 Second Derivatives - Convex and Concave Functions

8.15 Quiz

8.16 Connected Rates of Change (Part 1)

8.17 Connected Rates of Change (Part 2)

8.16/8.17

Differentiation - Exam Questions

9.1 Integrating Standard Functions

9.1 Quiz

9.2 Integrating f(ax+b)

9.2 Quiz

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

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

9.3/9.4 Quiz

9.5 Reverse Chain Rule: Exponentials

9.5 Quiz

9.6 Reverse Chain Rule: Logarithmic Functions (Part 1)

9.7 Reverse Chain Rule: Logarithmic Functions (Part 2)

9.6/9.7 Quiz

9.8 Mixed Reverse Chain Rule Problems

9.9 Trig Identities For Integration: Pythagorean Identities

9.9 Quiz

9.10 Trig Identities For Integration: Double Angle Formulae

9.10 Quiz

9.11 Using Partial Fractions for Integration (Part 1)

9.12 Using Partial Fractions for Integration (Part 2)

9.11/9.12 Quiz

9.13 Integration by Parts: Polynomial x Exponential

9.13 Quiz

9.14 Integration by Parts: Polynomial x Trigonometric

9.14 Quiz

9.15: Integration by Parts: Polynomial x Logarithmic

9.15 Quiz

9.16 Integration by Parts: Exponential x Trigonometric

9.16 Quiz

9.17 Integration by Substitution: An Alternative to Reverse Chain Rule

9.17 Quiz

9.18 Integration by Substitution: u = f(x)

9.18 Quiz

9.19 Integration by Substitution: x = f(u)

9.19 Quiz

9.20 Integration by Substitution: Definite Integrals

9.20 Quiz

9.21 Problem Solving with Integration

9.21 Quiz

9.22 The Trapezium Rule

9.22 Quiz

9.23 Differential Equations: Separating Variables (Part 1)

9.24 Differential Equations: Separating Variables (Part 2)

9.23/9.24 Quiz

9.25 Forming Differential Equations

9.25 Quiz

9.26 Modelling With Differential Equations (Part 1)

9.27 Modelling With Differential Equations (Part 2)

9.26/9.27 Quiz

Integration - Exam Questions

10.1 Parametric Equations Intro

10.2 Converting Parametrics to Cartesian: Substitution

10.2 Quiz

10.3 Converting Parametrics to Cartesian: Pythagorean Identities

10.3 Quiz

10.4 Converting Parametrics to Cartesian: Double Angle Formulae

10.4 Quiz

10.5 Intersections of Parametrics and Lines

10.5 Quiz

10.6 Differentiating Parametric Equations

10.6 Quiz

10.7 Differentiating Parametric Curves: Stationary and Critical Points

10.7 Quiz

10.8 Integrating Parametric Equations (part 1)

10.9 Integrating Parametric Equations (part 2)

10.8/10.9 Quiz

Parametric Equations - Exam Questions

11.1 Locating Roots

11.1 Quiz

11.2 Iteration (Part 1)

11.3 Iteration (Part 2)

11.2/11.3 Quiz

11.4 The Newton-Raphson Procedure

11.4 Quiz

Numerical Methods - Exam Questions

12.1 3d Coordinates

12.1 Quiz

12.2 Vectors in 3d

12.2 Quiz

12.3 Angles Between Vectors and Coordinate Axes

12.3 Quiz

12.4 Geometric Problems

Vectors - Exam Questions

1.6 One-Tailed Tests for Correlation - Example

1.6 Quiz

1.7 Two Tailed Tests for Correlation

1.7 Quiz

1.8 Non-Linear Data - Exponential Models

1.8 Quiz

1.9 Non-Linear Data - Polynomial Models

1.9 Quiz

Correlation and Regression - Exam Questions

2.1 Set Notation

2.1 Quiz

2.2 Conditional Probability Intro

2.2 Quiz

2.3 Conditional Probability Formula

2.3 Quiz

2.4 Conditional Probability on Tree Diagrams

2.4 Quiz

2.5 Medical Testing Example

2.6 Conditional Probability With the Binomial Distributions

2.6 Quiz

Conditional Probability - Exam Questions

3.1 What is the Normal Distribution?

3.1 Quiz

3.2 The 68-95-99.7 Rule

3.2 Quiz

3.3 Calculating Normal Probabilities

3.3 Quiz

3.4 The Inverse Normal Function

3.4 Quiz

3.5 Finding Unknown Standard Deviations

3.5 Quiz

3.6 Finding Unknown Means

3.6 Quiz

3.7 Finding Unknown Means and Standard Deviations

3.7 Quiz

3.8 Normal Approximations to Binomial Distributions - Part 1

3.8 Quiz

3.9 Normal Approximations to Binomial Distributions - Part 2

3.9 Quiz

3.10 Normal Approximations to Binomial Distributions - Part 3

3.10 Quiz

3.11 Normal Hypothesis Tests - Intro

3.11 Quiz

3.12 One-Tailed Normal Hypothesis Tests

3.12 Quiz

3.13 Two-Tailed Normal Hypothesis Tests

3.13 Quiz

3.14 Critical Regions in Normal Hypothesis Tests

3.14 Quiz

3.15 Forming New Distributions From Normal Distributions

3.15 Quiz

3.16 Conditional Probability With Normal Distributions

3.16 Quiz

The Normal Distribution - Exam Questions

1.7 Rods at Angles

1.7 Quiz

1.8 Ladders

1.8 Quiz

1.9 Centres of Mass

1.9 Quiz

1.10 Tilting

1.10 Quiz

Moments - Exam Questions

2.1 Resultant Forces - Components

2.1 Quiz

2.2 Forces and Newton's Second Law

2.2 Quiz

2.3 Inclined Planes (Part 1)

2.4 Inclined Planes (Part 2)

2.3/2.4 Quiz

2.5 Friction

2.5 Quiz

2.6 Friction on an Inclined Plane (Part 1)

2.6 Quiz

2.7 Friction on an Inclined Plane (Part 2)

2.7 Quiz

Forces and Friction - Exam Questions

3.1 Projectiles Intro - Modelling Assumptions

3.1 Quiz

3.2 Horizontal Projection

3.2 Quiz

3.3 Components of Velocity

3.3 Quiz

3.4 Projection at an Angle: Distances

3.4 Quiz

3.5 Projection at an Angle: Speed (Part 1)

Copy of 3.5 Quiz

3.6 Projection at an Angle: Speed (Part 2)

3.6 Quiz

3.7 Projection at an Angle: Finding Angles

3.7 Quiz

3.8 Velocity as a Vector

3.8 Quiz

3.9 Projectile Motion Formulae

Projectiles - Exam Questions

4.1 Three Forces in Equilibrium

4.1 Quiz

4.2 Three Forces in Equilibrium - Triangle Method

4.2 Quiz

4.3 Equilibrium on an Inclined Plane

4.3 Quiz

4.4 Connected Particles on an Inclined Plane

4.4 Quiz

4.5 Hanging Objects

4.5 Quiz

4.6 Limiting Equilibrium

4.6 Quiz

4.7 Limiting Equilibrium on an Inclined Plane

4.7 Quiz

4.8 Limiting Equilibrium - Further Example

4.8 Quiz

4.9 Statics: Rods

4.9 Quiz

4.10 Statics: Ladders (Part 1)

4.11 Statics: Ladders (Parts 2)

4.10/4.11 Quiz

Equilibrium - Exam Questions

5.1 Motion on a Rough Plane: No Other Forces

5.1 Quiz

5.2 Motion on a Rough Inclined Plane: Parallel Forces

5.2 Quiz

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

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

5.3/5.4 Quiz

5.5 Connected Particles on a Rough Plane (Part 1)

5.5 Quiz

5.6 Connected Particles on a Rough Plane (Part 2)

5.6 Quiz

Dynamics - Exam Questions

6.1 Vectors: Constant Velocity

6.1 Quiz

6.2 Vectors: Constant Acceleration (Part 1)

6.3 Vectors: Constant Acceleration (Part 2)

6.2/6.3 Quiz

6.4 Vectors: Two Moving Objects

6.4 Quiz

6.5 Variable Acceleration in One Dimension (Part 1)

6.6 Variable Acceleration in One Dimension (Part 2)

6.7 Variable Acceleration in Two Dimensions (Part 1)

6.8 Variable Acceleration in Two Dimensions (Part 2)