Equations, Formulae and Identities

Worked examples (5)

• 1Expand a single bracket
• 2Expand a double bracket
• 3Square a binomial
• 4Expand three brackets
• 5Simplify by collecting like terms

Worked examples (5)

• 1Simplify using index laws
• 2Power of a product
• 3Negative indices in algebra
• 4Fractional indices in algebra
• 5Solve an equation using indices

Worked examples (4)

• 1Substitute values into a formula
• 2Substitute negative values
• 3Derive a formula from a word problem
• 4Use multiple formulae together

Worked examples (5)

• 1Factorise out a common factor
• 2Difference of two squares
• 3Factorise a quadratic with leading coefficient 1
• 4Factorise a quadratic with leading coefficient u003e 1
• 5Factorise fully — common factor + difference of squares

Worked examples (3)

• 1Algebraic direct proportion
• 2Algebraic inverse proportion
• 3Reverse-engineer the proportion equation

Worked examples (4)

• 1Simplify by factoring
• 2Add algebraic fractions
• 3Multiply algebraic fractions
• 4Divide algebraic fractions

Worked examples (4)

• 1Make $x$ the subject
• 2Rearrange with a power
• 3Subject appears on both sides
• 4Rearrange with a square root

Worked examples (5)

• 1Solve a simple linear equation
• 2Solve with brackets
• 3Unknown on both sides
• 4Equation with fractions
• 5Set up and solve from a word problem

Worked examples (5)

• 1Solve by factorising
• 2Solve using the quadratic formula
• 3Solve by factorising (a u003e 1)
• 4Quadratic that doesn't factor neatly
• 5Quadratic from a word problem

Worked examples (5)

• 1Elimination method
• 2Multiply to eliminate
• 3Substitution method
• 4Linear with quadratic
• 5Setting up from a word problem

Worked examples (4)

• 1Complete the square (a = 1)
• 2Complete the square (a u003e 1)
• 3Solve a quadratic using completing the square
• 4Find the turning point

Worked examples (5)

• 1Solve a linear inequality
• 2Flip when multiplying/dividing by negative
• 3Double inequality
• 4Quadratic inequality
• 5Integer solutions

Worked examples (4)

• 1Prove an identity
• 2Prove a divisibility property
• 3Prove an expression is a multiple of $n$
• 4Show that — algebraic manipulation