Prove by counter example
In this lesson, we will learn how to disprove a statement by providing a counter example.
Unit Overview: Algebraic Proof
Lessons:
4 lessons
Prove an expression will be a multiple of a given number
In this lesson, we will learn how to prove that an algebraic expression can represent all multiples of a particular number.
Consecutive number proofs
In this lesson, we will learn about algebraic proofs that involve algebraic representations of consecutive numbers.
Odd and even number proofs
In this lesson, we will learn about algebraic proofs that involve algebraic representations of odd and even numbers.
Units in Maths
- Simplifying Surds
- Adding surds
- Multiplying Surds
- Dividing and Rationalising surds
- Solving equations 2 (Simple algebraic fractions)
- Algebraic Fractions
- Factorise and solve a quadratic (a=1)
- Factorise and solve quadratics (a > 1)
- Substitution and Rearranging formulae
- Further Algebra (Change the subject/Binomial expansion)
- Similarity
- Trigonometry 1
- Trigonometry 2
- Trigonometry 3
- Types of Numbers and Rules of Indices
- Negative and Fractional Indices
- Recurring decimals
- Upper and Lower Bounds
- Straight Line Graphs (y=mx+C)
- Straight Line Graphs 2 (Parallel Lines)
- Higher Straight lines (Perpendicular Lines)
- Simultaneous Equations (Linear)
- Scatter Diagrams & Frequency Trees & Averages
- Higher Data 1 (CF and Box Plots)
- Probability 2 (Sample space, Venn diagrams and experimental)
- Higher Probability (Conditional and Further Set Notation)
- Further Quadratic equations
- Quadratic Graphs 1 (a=1)
- Quadratic Graphs 2 (a>1)
- Quadratic sequences
- One linear and one quadratic simultaneous equations
- Parts of a Circle 1 & 2
- Volume and Surface Area 1 (Prisms)
- Volume 2
- Surface Area 2
- Volume and Surface Area 2
- Advanced Trigonometry 1
- Advanced Trigonometry 2
- Advanced Trigonometry 3
- Directed Numbers
- Rules of indices (numbers)
- Standard Form (Writing and converting)
- Standard Form 4 Operations
- Collecting, Indices, Expand and Simplify, Solving Equations 1
- Adding and Subtracting Fractions
- Rotation and Enlargement
- Pythagoras Theorem 1
- Pythagoras Theorem 2
- Factors Multiple and Primes
- Venn Diagrams
- HCF and LCM
- Rounding and Estimating
- Simple Graphs
- Scatter diagrams and Frequency trees
- Averages (From a list and tables, Stem and Leaf)
- Ratio 1 & 2
- Percentage increase and decrease
- Repeated Percentage Change
- Fractions 1, 2, and Fractional Change
- Parts of circles 1 (Semi and quarter circles)
- Parts of circles 2 (Arcs and Sectors)
- Cylinders
- Area and Perimeter
- 4 Rules of Number
- Types of numbers
- Collecting like terms, simplifying
- Expand and simplify brackets
- Rules of Indices
- Solving equations 1 (One step, Two Step and Brackets)
- Reflection
- Factorising (single bracket)
- Solve Inequalities and Represent on Number Line
- Linear Sequences
- Fraction equivalents
- Fractions 1 (adding and subtracting)
- Fractions 2 (multiplying and dividing)
- Fraction Change
- Percentages
- FDP Equivalents
- Decimals
- Ratio 1
- Circles
- Revise - Angles, Polygons, Bearings
- Circle Theorems 1
- Circle Theorems 2
- Functions
- Revise - Simultaneous Equations
- Charts and Tables (Pie Chart and Two way tables)
- Revise - Data (Mean Table, CF Charts)
- Probability 3 (Tree diagrams)
- Histograms
- Cubic and Reciprocal Graphs
- Travel Graphs
- Graphs of Inequalities
- Compound measures
- Volume and Surface Area 1 & 2
- Translate and Vectors 1
- Vectors 2
- Constructions
- Loci
- Angle Facts
- Parallel Lines and Polygons 1
- Polygons 2 (Interior and Exterior)
- Ratio 2 (Ratio and Fractions/Direct Proportion/Best Buy)
- Revise - Solving Equations
- Frequency charts (Data Collection, Bar and Pictograms)
- Probability 1 (Scale and equally likely events)
- Bearings
- Views and Maps
- Constructions & Loci
- Solve equations numerically (Iteration)
- Direct and Inverse Proportion
- Further Algebraic Fractions
- Algebraic Proof
- Circle Graphs
- Data Collection Higher
- Revise - Linear and Quadratic Graphs
- Other Graphs (Trig, Exponetial and Transformations)
- Further graphs (Gradients/Area of curves)
- Volume and Surface Area Higher 3
- Higher Vectors 1
- Higher Vectors 2 and Congruent Triangles
- Enlargement and Similarity
- Algebraic Fractions
- Other Graphs (Trig, Exponetial and Transformations)
- Cubic and Reciprocal Graphs
- Further Algebraic Fractions
- Rules of Indices
- Graphs of Inequalities
- Simultaneous Equations (Linear)
- Expand and simplify brackets
- Quadratic sequences
- Direct and Inverse Proportion
- Functions
- Further graphs (Gradients/Area of curves)
- Revise - Linear and Quadratic Graphs
- Substitution and Rearranging formulae
- Quadratic Graphs 1 (a=1)
- Solving equations 2 (Simple algebraic fractions)
- Solve Inequalities and Represent on Number Line
- Linear Sequences
- Further Quadratic equations
- Solve equations numerically (Iteration)
- Compound measures
- Higher Straight lines (Perpendicular Lines)
- Quadratic Graphs 2 (a>1)
- Straight Line Graphs 2 (Parallel Lines)
- Circle Graphs
- Algebraic Proof
- One linear and one quadratic simultaneous equations
- Revise - Simultaneous Equations
- Simple Graphs
- Travel Graphs
- Factorise and solve quadratics (a > 1)
- Factorise and solve a quadratic (a=1)
- Collecting like terms, simplifying
- Straight Line Graphs (y=mx+C)
- Factorising (single bracket)
- Solving equations 1 (One step, Two Step and Brackets)
- Further Algebra (Change the subject/Binomial expansion)