The additive inverse of a number is a number that, when added to the original number, gives the sum of 0.

The reciprocal is the multiplicative inverse of any non-zero number. Any non-zero number multiplied by its reciprocal is equal to 1

Like terms are terms that have the same set of variables and corresponding exponents.

Checking and securing understanding of solving and interpreting linear equations

Maths

Further algebraic terminology

Checking and securing understanding of factorising

Checking and securing understanding of forming linear equations

Checking and securing understanding of changing the subject

Checking and securing understanding of the product of two binomials

The product of three binomials

Factorising a quadratic expression

Factorising using the difference of two squares

Factorising quadratics of the form ax^2 + bx + c

Solving quadratic equations by factorising

Solving quadratic equations by factorising where rearrangement is required

Solving quadratic equations by completing the square

Solving complex quadratic equations by completing the square

Solving quadratic equations by using the formula

Advanced problem solving with algebraic manipulation

In this unit, pupils learnt to solve quadratic equations by factorising and this skill will be required in the future unit through manipulating two simultaneous equations to find the solutions. For pupils studying the higher content, solving quadratic equations is required if one of the simultaneous equations is a quadratic.

In the prior unit, pupils used the distributive law to find the product of two binomials. In algebraic manipulation, pupils use apply this knowledge in order to factorise quadratics.

In algebraic manipulation, pupils use apply knowledge of the distributive law to find the product of two binomaials in order to factorise quadratics.

Algebraic manipulation

What is the value of $$x$$ for $$5(x + 7) = 30$$

What is the value of $$x$$ for $$\frac{3x - 7}{4} = 11$$

What is the value of $$x$$ for $$2(x - 5) + 10 = 0$$

What is the value of $$x$$ for $$\frac{x + 9}{5} - \frac{x - 3}{3} = 2$$

What is the value of $$x$$ for $$4(3x - 2) + 2 = 3(2x + 4)$$

What is the value of $$x$$ for $$\frac{5x + 15}{3} = \frac{2x - 2}{2}$$

Fully factorise the expression $$7y^2 - 14y$$

Fully factorise the expression $$2x^2 +7x + 3$$

A rectangle has side lengths of $$3x + 5$$ and $$2x - 3$$. Write an expression for the perimeter of the shape.

A regular hexagon has side length $$3n - 4$$. Write an expression for the perimeter of the shape.

A rectangle has side lengths of $$9x - y$$ and $$2y$$. Write an expression for the perimeter of the shape.

A square has side length $$15x - y$$. Write an expression for the perimeter of the shape.

Starter Quiz

Fully factorise the expression $$7y^2 - 14y$$