The quadratic formula is a formula for finding the solutions to any quadratic equation of the form ax^2 + bx + c = 0

Solving quadratic equations by using the formula

Maths

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

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

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 are the values of x that solve $$2x^2 + 12x + 10 = 0$$ ? (answer in the form "a,b")

What are the values of x that solve $$x^2 - 6x + 8 = 0$$ ? (answer in the form "a,b")

What are the values of x that solve $$3x^2 + 9x - 12 = 0$$ ? (answer in the form "a,b")

What are the values of x that solve $$x^2 + 4x - 21 = 0$$ ? (answer in the form "a,b")

What are the values of x that solve $$x^2 + 10x + 16 = 0$$ ? (answer in the form "a,b")

What are the values of x that solve $$ x^2 + 6x + 8 = 0$$ ? (answer in the form "a,b")

Using the formula $$3m = 20x + 12y$$, if $$x = 3$$ and $$y = 9$$, what calculation would find $$m$$? 

Using the formula $$2m = 14x + y$$, if $$x = 8$$ and $$y = 5$$, what calculation would find $$m$$? 

Using the formula $$x = 3a + t^2$$, if $$a = 5$$ and $$t = 6$$, what calculation would find $$x$$? 

Using the formula $$x = 3a + t^2$$, if $$a = 3$$ and $$t = 1$$, what calculation would find $$x$$? 

Rearrange $$3m + t + 12 = 14g$$ to make $$t$$ the subject

Rearrange $$3m - 5 = 14g - w$$ to make $$w$$ the subject

Starter Quiz

Using the formula $$3m = 20x + 12y$$, if $$x = 3$$ and $$y = 9$$, what calculation would find $$m$$?