A term is single number or letter, or the product of numbers and/or variables. Each term is separated by the operators + and –

Expressions contain one or more terms, where each term is separated by an operator.

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

An identity is an equation that holds true for all values of the variables. The symbol ≡ is used to show two expressions are equivalent and form an identity.

A formula is a rule linking sets of physical variables in context.

Further algebraic terminology

Maths

Checking and securing understanding of factorising

Checking and securing understanding of forming linear equations

Checking and securing understanding of solving and interpreting 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

A car travels at a constant speed of 60 miles per hour. Which of the following shows the correct relationship between the number of hours driven, $$h$$, and the total distance traveled, $$d$$?

A worker earns £15 per hour. Which of the following shows the correct relationship between the number of hours worked, $$h$$, and the total earnings, $$e$$?

If a tree grows 2 feet each year, which of the following shows the correct relationship between the number of years, $$y$$, and the total growth, $$g$$, of the tree?

A savings account earns 5% interest per year on a deposit of £100. Which of the following shows the correct relationship between the number of years, $$y$$, and the total interest earned, $$i$$

A farmer harvests 200 apples from each tree every year. Which of the following shows the correct relationship between the number of trees, $$t$$, and the total number of apples harvested, $$a$$?

A recipe requires 3 eggs to make a cake. Which of the following shows the correct relationship between the number of cakes, $$c$$, and the total number of eggs needed, $$e$$?

Evaluate the expression $$2x - 3$$ for $$x = 5$$

Evaluate the expression $$x^2 + 2x + 1$$ for $$x = 3$$

Evaluate the expression $$x^3 - 2x^2 + x - 1$$ for $$x = 2$$

Evaluate the expression $$\frac{x^2}{2} - 3x + 2$$ for $$x = 4$$

Collect the following like terms $$ 5a + 7a - 2a^2 $$

Collect the following like terms $$ 5ab + 7a - 2ab + b $$

Further algebraic terminology

Lesson outcome