Substitute means to put in place of another. In Algebra, substitution can be used to replace variables with values.

Checking and securing understanding of substitution

Maths

Checking and securing understanding of simplifying

Further algebraic terminology

Checking and securing understanding of expanding a single bracket

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

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

Evaluate the expression $$\frac{3x}{4}$$ for $$x = 8$$

Evaluate the expression $$4x^2$$ for $$x = 3$$

Evaluate the expression $$5(x - 3)$$ for $$x = 7$$

Evaluate the expression $$\frac{3x + 2}{4}$$ for $$x = 6$$

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

Simplify the following: $$3(2x + 1) + 2(2x + 1) = \square(2x + 1)$$

Simplify the following: $$4(x - 3) + 3(x - 3) = \square(x - 3)$$

If $$c = 4b + 2$$, what is $$3c$$?  Give your answer in expanded form.

Starter Quiz

Simplify the following: $$3(2x + 1) + 2(2x + 1) = \square(2x + 1)$$