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Course Content
Algebra 1
0/14
Expressions
Exercise Set A
Factorising
Exercise Set B
Algebraic Fractions
Exercise Set C
Binomial Expansions
Exercise Set D
Algebraic Identities
Exercise Set E
Linear Equations
Exercise Set F
Simultaneous Linear Equations
Exercise Set G
Algebra 2
0/16
Quadratic Equations
Exercise Set A
Quadratic Roots
Exercise Set B
Factor Theorem
Exercise Set C
Simultaneous Linear & Quadratic Equations
Exercise Set D
Forming Quadratic Equations
Exercise Set E
Maxima and Minima
Exercise Set F
Surd Equations
Exercise Set G
Polynomial Graphs
Exercise Set H
Trigonometry 1
0/18
Radians
Exercise Set A
Sine, Cosine & Tangent
Exercise Set B
The Unit Circle
Exercise Set C
Sine Rule
Exercise Set D
Cosine Rule
Exercise Set E
3D Problems
Exercise Set F
Trigonometric Graphs
Exercise Set G
Related Trigonometric Graphs
Exercise Set H
Solving Trigonometric Equations
Exercise Set I
Coordinate Geometry of the Line
0/14
Area of a Triangle
Exercise Set A
Equation of a Line
Exercise Set B
Dividing a Line Segment
Exercise Set C
Triangle Concurrencies
Exercise Set D
Distance from Point to Line
Exercise Set E
Angle between Lines
Exercise Set F
Real World Problems
Exercise Set G
Probability 1
0/14
Permutations
Exercise Set A
Combinations
Exercise Set B
Elementary Probability
Exercise Set C
Relative Frequencies
Exercise Set D
Mutually Exclusive Events
Exercise Set E
Independent Events
Exercise Set F
Conditional Probability
Exercise Set G
Geometry 1
0/6
Triangle & Parallelogram Theorems
Exercise Set A
Ratio Theorems
Exercise Set B
Circle Theorems
Exercise Set C
Differential Calculus
0/10
Limits
Exercise Set A
Derivatives from First Principles
Exercise Set B
Derivatives by Rule
Exercise Set C
Product, Quotient & Chain Rules
Exercise Set D
Second Derivatives
Exercise Set E
Trigonometry 2
0/10
Trigonometric Identities
Exercise Set A
Compound Angles
Exercise Set B
Double-Angle Formulae
Exercise Set C
Sum, Difference & Product Formulae
Exercise Set D
Inverse Trigonometric Functions
Exercise Set E
Sequences & Series
0/12
Arithmetic Sequences
Exercise Set A
Arithmetic Series
Exercise Set B
Geometric Sequences
Exercise Set C
Geometric Series
Exercise Set D
Limits of Sequences
Exercise Set E
Other Sequences
Exercise Set F
Statistics 1
0/9
Data
Population Sampling
Location & Variability
Exercise Set A
Stem & Leaf Diagrams
Exercise Set B
Histograms
Exercise Set C
Distribution Shapes
Coordinate Geometry of the Circle
0/14
Circles centred at Origin
Exercise Set A
Circle centred Elsewhere
Exercise Set B
Finding Equations of Circles
Exercise Set C
Tangents
Exercise Set D
Chords
Exercise Set E
Touching Circles
Exercise Set F
Circles Tangent to Axes
Exercise Set G
Algebra 3
0/16
Inequalities
Exercise Set A
Quadratic & Rational Inequalities
Exercise Set B
Modulus
Exercise Set C
Mathematical Proofs
Exercise Set D
Indices
Exercise Set E
Exponential Functions
Exercise Set F
Logarithmic Functions
Exercise Set G
Proofs by Induction
Exercise Set H
Complex Numbers
0/12
Introduction to Complex Numbers
Exercise Set A
Manipulating Complex Numbers
Exercise Set B
Conjugate Roots Theorem
Exercise Set C
Polar Coordinates
Exercise Set D
Argand Diagrams
Exercise Set E
De Moivre’s Theorem
Exercise Set F
Geometry 2
0/4
Enlargements
Exercise Set A
Constructions
Exercise Set B
Integration
0/8
Indefinite Integrals
Exercise Set A
Definite Integrals
Exercise Set B
Integration & Areas
Exercise Set C
Average Values of a Function
Exercise Set D
Differential Calculus Applications
0/8
Stationary Points
Exercise Set A
Graphs of Derivatives
Exercise Set B
Maxima and Minima Problems
Exercise Set C
Rates of Change
Exercise Set D
Financial Maths
0/8
Compound Interest
Exercise Set A
Depreciation
Exercise Set B
Annuities
Exercise Set C
Loans & Mortgages
Exercise Set D
Length, Area & Volume
0/6
Sectors of Circles
Exercise Set A
3D Objects
Exercise Set B
Trapezoidal Rule
Exercise Set C
Probability 2
0/9
Tree Diagrams
Exercise Set A
Expected Values
Exercise Set B
Bernoulli Trials
Exercise Set C
The Independence of Events
Exercise Set D
Simulations
Functions
0/15
Relations
Exercise Set A
Set Representation of Relations
Exercise Set B
Graphical Representation of Relations
Exercise Set C
Graphing Similar Relations
Introduction to Functions
Exercise Set E
Inverses & Compositions
Exercise Set F
Types of Functions
Exponential Functions
Logarithmic Functions
Functions & Graphs
Statistics 2
0/4
Scatter Diagrams
Lines of Best Fit
Normal Distributions
Exercise Set C
Inferential Statistics
0/6
Population Proportions
Exercise Set A
Central Limit Theorem
Exercise Set B
Population Means
Exercise Set C
Digital Lessons
About Lesson

Start with the quiz…

Knowledge Check Quiz

EXAMS.IE

Proofs by Induction

Hint

There is a difference between \(>\) and \(\geq\).

1 / 5

\(3^n>3n\) for \(n=1\).

Hint

This is equivalent to \(3^2>6\).

2 / 5

\(3^n>3n\) for \(n=2\).

Hint

This is equivalent to \(3^3>9\).

3 / 5

\(3^n>3n\) for \(n=3\).

Hint

This is equivalent to \(3^4>12\).

4 / 5

\(3^n>3n\) for \(n=4\).

Hint

We know the inequality is not true for \(n=1\).

5 / 5

Based on the previous four answers, which of the following proofs would be worth checking via induction?

Your score is

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