GCSE Maths · Higher · Chapter 17: Quadratic equations · Lesson 2

Solving quadratics by factorisation

Grades 4–7About 50 minutesNo calculator44 marks

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NameClassDate

Do Now

Grades 4–6

The first question is what today's lesson needs. The others bring back earlier topics.

A1
Needed today
Factorise $x^{2} + 2 x - 3$ .
[1 mark]
Answer
A2
Last lesson
Where does $y = (x - 1) (x + 4)$ cross the $x$ -axis?
[1 mark]
Answer
A3
From chapter 8
Expand $(x + 2) (x - 6)$ .
[1 mark]
Answer
A4
From chapter 16
A meal has 5 starters, 3 mains and 4 desserts. How many different meals?
[1 mark]
Answer

Grades 4–6

Your teacher works through each example with you. Then try the one beside it.

Example 1

Solve $x^{2} - x - 72 = 0$ .

Hint Find two numbers that multiply to

- 72

and add to

- 1

B1
Solve $x^{2} + 6 x - 55 = 0$ .
[2 marks]
Answer $x = \dots\dots$ or $x = \dots\dots$

Example 2

Solve $2 x^{2} + x - 21 = 0$ .

Hint Find two numbers that multiply to

2 \times (- 21) = - 42

and add to

1

. Use them to split the

x

term.

B2
Solve $3 x^{2} + 7 x - 6 = 0$ .
[3 marks]
Answer $x = \dots\dots$ or $x = \dots\dots$

Grades 5–6

C1
Solve $(x + 4) (2 x - 9) = 0$ .
[2 marks]
Answer $x = \dots\dots$ or $x = \dots\dots$
C2
Solve $3 x^{2} = 21 x$ .
[2 marks]
Answer $x = \dots\dots$ or $x = \dots\dots$

C3
Solve $x^{2} + 4 x = 32$ .
[2 marks]
Answer $x = \dots\dots$ or $x = \dots\dots$
C4
Solve $9 x^{2} - 25 = 0$ .
[2 marks]
Answer $x = \dots\dots$ or $x = \dots\dots$
C5
Solve $(x + 10) (x - 1) = 60$ .
[3 marks]
Answer $x = \dots\dots$ or $x = \dots\dots$
C6
Solve $x + \frac{24}{x} = 10$ .
[3 marks]
Answer $x = \dots\dots$ or $x = \dots\dots$
C7
Solve $x^{2} - 24 x + 144 = 0$ . How many different solutions are there?
[2 marks]
Answer $x = \dots\dots$ , $\dots\dots$ solution(s)
C8
The solutions of $x^{2} + b x + c = 0$ are $x = - 12$ and $x = 5$ . Work out $b$ and $c$ .
[2 marks]
Answer $b = \dots\dots$ $c = \dots\dots$

Grades 6–7

D1
Priya solves $2 x^{2} = 14 x$ . She divides both sides by $2 x$ and writes, " $x = 7$ ."
Explain what is wrong with her method, and give the full solution.
[2 marks]

Grade 8 and beyond

No route is given. The hints are at the end of the sheet. Use one at a time.

Colour one circle on each line.

	Not yet	Nearly	Yes
I can solve a quadratic equation by factorising it.
I can rearrange an equation to equal zero before I factorise.
I can set up a quadratic from a shape and reject a solution that makes no sense.

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