### Prove by counter example

In this lesson we will learn how to disprove a statement by providing a counter example.

8 lessons

In this lesson we will learn how to disprove a statement by providing a counter example.

In this lesson we will learn how to prove that an expression is a multiple of a particular number for all integer values of a variable.

In this lesson we will learn about proofs that involve consecutive numbers.

In this lesson we will learn about proofs that involve odd and even numbers.

In this lesson, we will use substitution skills and knowledge of order of operations to find a particular value of f(x)

In this lesson, we will use knowledge of using inverse functions to solve equations using f(x)

In this lesson, we will apply more than one function to a number or a variable using substitution, knowledge of expanding brackets and also apply these skills to solving equations such as fg(x) = h(x)

In this lesson, we will use knowledge of using inverse functions (function machines) and making x the subject to find inverse functions.

Units in Express Maths

Units in Algebra (A)

- Types of Numbers & Roots & Indices
- Rounding and Estimating
- Solving Equations 1 & 2
- Solve Inequalities and Represent on Number Line
- Factorise and solve a quadratic (a=1)
- Percentage increase and decrease
- Angle Facts & Parallel Lines
- Polygons 1 & 2
- Straight line graphs 1 & 2
- Quadratic Graphs & Cubic and Reciprocal Graphs
- Ratio 1 & 2
- Compound Measures & Direct and Inverse Proportion
- Parts of a circle 1 & 2
- Volume and Surface Area 2 & Views and Maps
- Scatter Diagrams & Frequency Trees & Averages
- Higher Data 1 (CF and Box Plots)
- Substitution and Rearranging Formulae & Rules of Indices
- Linear & Quadratic Sequences
- Pythagoras 1 & 2
- Trigonometry 1 & 2
- Repeated Percentage Change
- Standard Form 4 Operations
- Probability 2 & 3
- Rotation and Enlargement
- Similarity
- Constructions & Loci
- Simultaneous Equations
- Simultaneous Equations Linear & Quadratic
- Vectors 2
- Negative and Fractional Indices
- Upper and Lower Bounds
- Algebraic Fractions
- Factorise and solve quadratics (a > 1)
- Further Quadratic equations
- Recurring decimals
- Circle Theorems 1
- Circle Theorems 2
- Quadratic Graphs & Cubic and Reciprocal Graphs & Circle Graphs
- Straight Line Graphs 2 & Higher Straight Lines
- Further graphs (Gradients/Area of curves)
- Volume and Surface Area 2 & 3
- Histograms
- Quadratic Sequences & Further Algebra
- Algebraic Proof & Functions
- Advanced Trigonometry 1, 2, and 3
- Simplifying & Adding Surds
- Multiplying & Dividing Surds
- Higher Probability (Conditional and Further Set Notation)
- Enlargement and Similarity
- Other Graphs (Trig, Exponetial and Transformations)
- Solve equations numerically (Iteration)
- Higher Vectors 1 & 2
- Directed Numbers & 4 Rules & Rounding and Estimating
- Fractions 1 & 2
- Expand and Simplify & Factorise Linear & Solving Equations 1 & 2
- Percentages and FPD Equivalence
- Simple Graphs & Straight Line Graphs 1
- Quadratic Graphs & Travel Graphs
- Ratio 1
- Ratio 2 (Ratio and Fractions/Direct Proportion/Best Buy)
- Area and Perimeter & Circles
- Volume and Surface Area 1 (Prisms)
- Charts and tables & Frequency Charts
- Linear Sequences
- Pythagoras Theorem 1
- Pythagoras Theorem 2
- Factors, Multiples, and Primes & Venn Diagrams
- Standard Form Converting & 4 Operations
- Probability 1 & 2
- Bearings & Reflection
- Views and Maps & Constructions
- Solving equations 2 (Simple algebraic fractions)
- Translate and Vectors 1

- Simple Graphs & Straight Line Graphs 1
- Quadratic Graphs & Cubic and Reciprocal Graphs
- Simultaneous Equations Linear & Quadratic
- Quadratic Sequences & Further Algebra
- Simultaneous Equations
- Algebraic Proof & Functions
- Quadratic Graphs & Travel Graphs
- Solving Equations 1 & 2
- Expand and Simplify & Factorise Linear & Solving Equations 1 & 2
- Linear & Quadratic Sequences
- Substitution and Rearranging Formulae & Rules of Indices
- Straight line graphs 1 & 2
- Straight Line Graphs (y=mx+C)
- Simple Graphs
- Other Graphs (Trig, Exponetial and Transformations)
- Linear Sequences
- Solving equations 1 (One step, Two Step and Brackets)
- Collecting like terms, simplifying
- Factorise and solve a quadratic (a=1)
- Factorising (single bracket)
- Rules of Indices
- Graphs of Inequalities
- Travel Graphs
- Higher Straight lines (Perpendicular Lines)
- Algebraic Fractions
- Circle Graphs
- Algebraic Proof
- Solve equations numerically (Iteration)
- Revise - Simultaneous Equations
- Simultaneous Equations (Linear)
- Quadratic sequences
- Further Algebraic Fractions
- Factorise and solve quadratics (a > 1)
- Solving equations 2 (Simple algebraic fractions)
- Further graphs (Gradients/Area of curves)
- Direct and Inverse Proportion
- Further Algebra (Change the subject/Binomial expansion)
- Substitution and Rearranging formulae
- Solve Inequalities and Represent on Number Line
- Cubic and Reciprocal Graphs
- Further Quadratic equations
- Compound measures
- Quadratic Graphs 2 (a>1)
- One linear and one quadratic simultaneous equations
- Quadratic Graphs 1 (a=1)
- Straight Line Graphs 2 (Parallel Lines)
- Revise - Linear and Quadratic Graphs
- Expand and simplify brackets
- Functions