Perimeter | Adding the lengths by collecting like terms

In the diagram, all measurements are given in centimetres.

All angles are right angles.

Show that the perimeter of the shape can be written as 2(3x + 5).

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Solution

perimeter = side 1 + side 2 + side 3 + ...... (two sides are missing)

                = 2x + x + 3 + 2 + horizontal missing side + vertical missing side

                = 2x + x + 3 + 2 + 2x + 3 + x + 2

                = 6x + 10

                = 2(3 + 10) ......you've got to factorise to show

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Note: to get 4 full marks for this question, student must show (by calculation).

Prime Number, Square Number, Sequence

Here are 5 rows of numbers.

 

Row A

2

4

6

8

10

12

14

16

 

 

Row B

3

5

7

9

11

13

15

17

 

 

Row C

2

3

5

7

11

13

17

 

 

Row D

1

2

5

10

20

50

100

200

 

 

Row E

1

2

4

8

16

32

64

 

 

All the numbers are even in one of the rows.

 

(a)   Which row?

 

……………

 

(1)

 

(b)   The numbers in Row C are the first 7 prime numbers written in order of sizes.

 

 

 

Write the next prime number.

 

……………

(1)

 

(c)   Write down a square number from Row D.

 

 

 

……………

 

(1)

 

The numbers in Row E are the first 7 numbers of a sequence.

 

 

 

(d)   Work out the next number in the sequence.

 

……………

 

(1)

 

(Total 4 marks)

Answers

 

(a) Row A

(b) 19

(c) 100 (can also be 1)

(d) 128 ( each number doubles, nth term =  2n)

 

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Students note:

- knowing your square numbers (say the first 10) will help with finding answers to square roots, e.g. square root of 100 is 10

 

- there are two ways of finding nth term in a sequence: finding the right pattern and or working our the rule.

 

Teachers note:

It can be helpful to use the same test format when setting test