The distributive law says that multiplying a sum is the same as multiplying each addend and summing the result.

Checking and securing understanding of expanding a single bracket

Maths

Checking and securing understanding of simplifying

Checking and securing understanding of substitution

Further algebraic terminology

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

Factorising a quadratic expression

Factorising using the difference of two squares

Solving quadratic equations by factorising

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

Expand $$5(x + 7) + 3(4x + 5)$$ and simplify where possible.

Expand $$2(3x - 4) - 5(x - 6)$$ and simplify where possible.

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

Expand $$3(x^2 - 2x) + 4(x - 3)$$ and simplify where possible.

Expand $$-2(x^2 + 3x) - 3(2x - 4)$$ and simplify where possible.

Expand $$4(2x - 3)^2 - 5(3x + 2)$$ and simplify where possible.

Evaluate the expression $$\frac{3x}{2x + 5}$$ for $$x = 3$$. Write your answer as a decimal.

Evaluate the expression $$\frac{x}{x + 1}$$ for $$x = 4$$. Write your answer as a decimal.

A company buys pencils in bulk for £2 per pen and sells them for £3.25 each. If the company sells $$x$$ pens, which of the following shows the correct expression for the profit, 'p'?

If a taxi charges a £15 base fare plus £2 per mile, which of the following represents the total cost, $$c$$, for a trip of $$x$$ miles?

A savings account offers 5% annual interest compounded yearly. If $$x$$ pounds are deposited, which expression represents the amount, $$a$$, in the account after one year?

A book store sells a book for £20, which is 20% more than its cost price. What is the cost price, 'p', of the book?

Starter Quiz

Evaluate the expression $$\frac{3x}{2x + 5}$$ for $$x = 3$$. Write your answer as a decimal.