GCSE Maths · Higher · Chapter 8: Algebraic manipulation · Lesson 1

Simplifying and factorising

Grades 4–7About 45 minutesNo calculator35 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
Simplify $8 x + 4 y - 3 x - 6 y$ .
[1 mark]
Answer
A2
From chapter 3
Score $0, 1, 2, 3$ with frequencies $4, 4, 3, 2$ . Find the median score.
[1 mark]
Answer
A3
From chapter 6
A regular polygon has exterior angle $3 0^{\circ}$ . How many sides does it have?
[1 mark]
Answer
A4
Last lesson
Points the same distance from $A$ and from $B$ lie on which line?
[1 mark]
Answer

Grades 4–6

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

Example 1

Work out the value of $2 x^{2} - 5 x$ when $x = - 3$ .

Hint Square first, then multiply. Two negatives multiplied make a positive.

Example 2

Factorise fully $12 p^{2} q - 20 pq$ .

Hint Find the HCF of the numbers, then the letters every term shares.

Grades 5–6

C1
Simplify $6 a - 2 b + 3 - 4 a - 5 b$ .
[2 marks]
Answer
C2
Work out the value of $\frac{p ^{2} + q}{3}$ when $p = - 5$ and $q = - 1$ .
[2 marks]
Answer

C3
Factorise fully $8 x^{2} - 12 x$ .
[2 marks]
Answer
C4
Is $2 (x + 6) = 2 x + 6$ an identity? Give a reason.
[2 marks]
C5
Write whether each is an expression, an equation, a formula or an identity.
(a) $v = u + a t$
(b) $3 x + 4 = 19$
(c) $5 (x + 2) \equiv 5 x + 10$
(d) $4 x^{2} - 7$
[2 marks]
C6
Simplify $\frac{4 a ^{2} b \times 6 a b ^{3}}{8 a ^{2} b}$ .
[2 marks]
Answer
C7
Expand and simplify $4 (3 x - 2) - 3 (2 x - 5)$ .
[2 marks]
Answer
C8
The sides of a triangle are $(2 x + 5)$ cm, $(4 x - 3)$ cm and $(x + 4)$ cm. Write an expression, as simply as possible, for its perimeter.
[2 marks]
Answer $\dots\dots\dots$ cm

Grades 6–7

D1
Ria says, "When $x = - 3$ , $5 x^{2} = 225$ ."
Explain why Ria is wrong, and give the correct value.
[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 substitute negative values into an expression.
I can collect like terms and tell an identity from an equation.
I can factorise fully by taking out the highest common factor.

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