### Algebra, functions and graphing

Representing relationships (Level A)

- Writing relationships in words
- Writing relationships as formulas
- Representing relationships as graphs
- Describing relationships

Generalising numbers - Algebra (Level A)

- Simplifying expressions
- Rearranging equations
- Solving equations Equations involving powers and roots including Pythagoras' Theorem
- Simultaneous equations

Generalising numbers - Graphs** **(Level A)

- Gradients of line graphs (including finding the gradient of a given line, and drawing a line given the gradient)
- Linear equations (including special lines, and what if two lines cross) Introduction to curve
- Parabolic equations (including the axis of symmetry)
- Exponential equations (including a special number)
- When two graphs meet

Algebra: Tools for change (Level B)

- Describing relationships
- Manipulating relationships (including grouping like terms, factors and factorization, algebraic fractions and working with powers)
- Special relationships (including equations, solving equations, rearranging formulas, inequations, absolute value, quadratic equations, factorisation of quadratic equations, the quadratic formula, quadratic equations in the real world, solving simultaneous equations using substitution and elimination)

- What are relations and functions (including domain and range of relations and functions and function notation)
- The linear function (including rate of change of a linear function, the inverse – undoing a function and when two linear functions meet)
- The quadratic function (including sketching parabolas and rate of change of a quadratic function)
- Other functions

Relations and functions (Level C)

- What are functions Function toolbox (including functional notation, zero conditions of a function, average rate of change of a function, continuity and the inverse of a function)
- Families of functions (including polynomial functions (which include the constant function, the linear function, the quadratic function, and other polynomial functions), exponential and logarithmic functions, rational functions and functions over an integral domain (including arithmetic and geometric sequences)

Algebra, functions and geometry (Level D)

- Inequalities and the real number line (including operations on inequalities, and linear inequalities of two variables)
- Quadratic Equations and Completing the Square
- Functions (including polynomials, rational functions, other important non-linear functions, solving simultaneous equations algebraically and graphically inverse functions and continuity)

#### Video based resources (Algebra)

**Introduction to Algebra: relationships as words**(printable handouts)

This 12 minute video covers:- translating from words to symbols (relationships)
- variables and expressions
- collecting like terms.

**Substituting and rearranging equations**(printable handouts)

This 12 minute video covers:- substituting values into equations
- rearranging equations.
**Expanding Brackets**(printable handout)

This 19 minute video covers:- the distributive law
- expanding brackets (single, double and triple)
- common expressions to get to know.

**Algebra: factorising quadratic expressions**(printable handout)

This 13 minute video covers:- simple factorisations (adding one set of brackets)
- factoring quadratic expressions (two brackets).
**Solving****quadratic equations using factorisation**(printable handout)

This 7 minute video covers:- quadratic equations
- solving quadratic equations using factorisation.
**Solving quadratic equations using the quadratic formula**(printable handout)

This 12 minute video covers:- quadratic equations
- the quadratic equation
- using the quadratic equation
- finding the number of solutions a quadratic equation will have.
**Solving simultaneous equations (using the substitution method)**(printable handout)

This 15 minute video covers the use of substitution method to solve simultaneous equations (two unknown variables and two equations).**Solving simultaneous equations (using the elimination method)**(printable handout).

This 16 minute video covers the use of the elimination method to solve simultaneous equations (two unknown variables and two equations).**Inequalities**(printable handout)This 12 minute video covers graphing inequalities and rearranging inequalities.

**Cancelling with algebraic fractions**(printable handout)

This 12 minute video covers graphing inequalities and rearranging inequalities.

#### Video based resources (Graphing)

**Geometry**(printable handout)

This 7 minute video covers common shapes and their characteristics.**Pythagoras' Theorem**(printable handout)

This 4 minute video covers using Pythagoras' Theorem.**Relationships as graphs**(printable handout)

This 8 minute video covers the Cartesian co-ordinate system and drawing graphs.**Gradient**(printable handout)

This 7 minute video covers how to- find the gradient (or slope) of a straight (linear) line
- drawing a line using a point and the gradient.
**Exponential graphs**(printable handout)

This 3 minute video introduces the exponential equation for growth and decay along with with the corresponding graphs.