KS3 Maths · Year 7 · Chapter 10: Algebra · Lesson 2

Like terms

Year 7About 60 minutesNo calculator50 marks

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Date

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Quick questions to start.

A1
Needed today
Work out $3 - 8 + 2$ .
[1 mark]
Answer
A2
Last lesson
Write $5 \times a \times b \times a$ as simply as possible.
[1 mark]
Answer
A3
From chapter 4
Work out $15%$ of $80$ .
[1 mark]
Answer
A4
From chapter 1
Write down the highest common factor of $28$ and $42$ .
[1 mark]
Answer

Example, then your turn

Year 7

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

Example 1

Simplify each expression.

(a) $9 k + 4 k - k$

(b) $3 p - 8 p + 2 p$

Hint Like terms have exactly the same letters. Add and subtract the numbers in front, keeping each sign with its term.

B1
Simplify each expression.
(a) $6 t + 11 t - 3 t$
(b) $4 w - 9 w - w$
(c) $- 3 x y + 8 x y - 2 x y$
[3 marks]
Answer(a) $\dots\dots$ (b) $\dots\dots$ (c) $\dots\dots$

Example 2

Simplify each expression.

(a) $5 a - 2 ab + a + 6 ab$

(b) $3 x^{2} + 7 x - x^{2} - 9 x + 4$

Hint Put like terms next to each other first.

a

and

ab

are not like terms;

x^{2}

and

x

are not like terms.

B2
Simplify each expression.
(a) $8 m + 3 mn - 5 m - 7 mn$
(b) $4 y^{2} - 3 y + 2 y^{2} + y - 6$
[2 marks]
Answer(a) $\dots\dots$ (b) $\dots\dots$

Example 3

Simplify each expression.

(a) $3 x - \frac{x}{2}$ (b) $2.6 n - 0.9 n$

Hint

\frac{x}{2}

is the same as

\frac{1}{2} x

. Write

3 x

\frac{6}{2} x

B3
Simplify each expression.
(a) $5 y - \frac{3 y}{4}$
(b) $4.2 t - 1.5 t$
(c) $\frac{w}{5} + \frac{3 w}{5}$
[3 marks]
Answer(a) $\dots\dots$ (b) $\dots\dots$ (c) $\dots\dots$

Example 4

$2 n$ , $2 n + 2$ and $2 n + 4$ are three even numbers in a row.

(a) Write them down when $n = 7$ .

(b) Write and simplify their sum.

Hint For (c), look at your expression: can every term be divided by

6

B4
$n$ , $n + 1$ , $n + 2$ and $n + 3$ are four whole numbers in a row.
(a) Write them down when $n = 19$ .
(b) Write and simplify their sum.
(c) Explain why the sum is always even.
[3 marks]

Example 5

The side lengths of this triangle are in centimetres.

(a) Write and simplify an expression for the perimeter.

(b) Work out the perimeter when $a = 3$ .

Not drawn accurately

Hint Add all three sides. Collect the

a

terms, then the numbers.

B5
The side lengths of this trapezium are in centimetres.
(a) Write and simplify an expression for the perimeter.
(b) Work out the perimeter when $x = 3$ .
[3 marks]
Not drawn accurately
Answer(a) $\dots\dots$ cm (b) $\dots\dots$ cm

Practice

Year 7

C1
Two of these expressions can be simplified and one cannot. Say which one cannot. Simplify the other two.
$A 3 ab + 2 a - b + 4$
$B 5 m + 2 mn - 3 m$
$C x^{2} + 4 x - x^{2}$
[3 marks]
C2
Write down the missing term.
$4 p + 3 q + 0000 - q = 9 p + 2 q$
[1 mark]
Answer

C3
Simplify $4 x^{2} - \frac{x ^{2}}{3}$ .
[2 marks]
Answer
C4
Simplify $2 + 5 x - x^{2} - 7 - 5 x + 3 x^{2}$ .
[2 marks]
Answer
C5
Simplify $\frac{9}{k} + \frac{6}{k} - \frac{2}{k}$ .
[1 mark]
Answer
C6
In this pyramid, each brick is the sum of the two bricks below it. Complete the pyramid. Simplify each expression.
[3 marks]

Exam-style questions

GCSE Foundation

D1
Tom says, " $5 x + 3 y$ simplifies to $8 x y$ ."
Tom is wrong. Explain why.
[2 marks]

D2
Simplify fully
(a)
$7 m - 2 m + m$
[1 mark]
Answer
(b)
$4 a + 3 b - a + 2 b$
[2 marks]
Answer
(c)
$6 x^{2} + 2 x - x^{2} - 5 x$
[2 marks]
Answer
Total for D2: 5 marks
D3
Here is a rectangle.
Not drawn accurately
(a)
Show that the perimeter of the rectangle is $(8 x + 2)$ cm.
[2 marks]
(b)
The perimeter of the rectangle is $50$ cm. Work out the value of $x$ .
[2 marks]
Answer
(c)
Work out the length of the longer side of the rectangle.
[1 mark]
Answer
Total for D3: 5 marks
D4
A pen costs $x$ pence and a pencil costs $y$ pence. Ann buys $4$ pens and $3$ pencils. Ben buys $2$ pens and $5$ pencils.
(a)
Write an expression, in pence, for the total amount Ann and Ben spend together. Simplify your answer.
[2 marks]
Answer
(b)
Write an expression, in pence, for how much more Ann spends than Ben. Simplify your answer.
[2 marks]
Answer
Total for D4: 4 marks

Extension

Stretch

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

E1
In this pyramid, each brick is the sum of the two bricks below it. The top brick is $64$ .
Work out the value of $x$ .
[4 marks]
Hint 1 · What to try
Fill in each row from the bottom up. Simplify each brick.
Hint 2 · The first line
The second row is $4 x + 2$ , $3 x + 5$ , $2 x + 4$ . The third row is $7 x + 7$ and $5 x + 9$ .
Hint 3 · The full method
The top is $7 x + 7 + 5 x + 9 = 12 x + 16$ . So $12 x + 16 = 64$ , $12 x = 48$ and $x = 4$ .
Answer $x = \dots\dots$

How did it go?

Colour one circle on each line.

	Not yet	Nearly	Yes
I can collect like terms, including negative ones.
I can simplify expressions with two kinds of term, such as $x^{2}$ and $x$ .
I can simplify terms with fractions or decimals in front.
I can write and simplify an expression for a perimeter or a sum.

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