An equation is used to show 2 expressions that are equal to each other.

An interior angle is an angle formed inside a polygon by two of its edges.

Vertically opposite angles are pairs of opposite angles formed when two lines intersect at a point. They are equal.

Checking and securing understanding of forming linear equations

Maths

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.

Algebraic manipulation

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

A triangle has side lengths of $$x + 2$$, $$2x + 3$$, and $$3x + 4$$. Write an expression for the perimeter of the shape.

A regular quadrilateral (square) has side length $$4y - 5$$. Write an expression for the perimeter of the shape.

A rectangle has side lengths of $$5a - 6$$ and $$3a + 2$$. Write an expression for the perimeter of the shape.

A regular pentagon has side length $$2z + 1$$. 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.

Expand and simplify $$5(x - 2) - 2(3x + 4)$$

Simplify the expression $$\frac{x^2 - 9}{x - 3}$$

Fully factorise the expression $$5x + 20$$

Fully factorise the expression $$3x^2 - 12$$

Fully factorise the expression $$x^2 - 9$$

Fully factorise the expression $$2x^2 + 8x$$

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