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Year 7 Mathematics Patterns and Algebra Practice Test 4

1 Complete the table below using the given rule to work out the correct output numbers Rule subtract 3 from each input number

Input 4 10 35 128 Output

2 Complete the table below using the given rule to work out the correct output numbers Rule multiply each input number by 5 and subtract 2

Input 3 1 5 20 Output

3 Use the rule given below to work out the missing input and output numbers Rule Add 4 to each input number

Input 1 5 25

Output

6 34 130

4 Rewrite the following expressions leaving out the multiplication signs

a) a x 4 + 3

b) (m + 2) x 5

c) (2 x b ? 6) x 3

5 Look at the table below and find the rule

a 3 6 8 15 20 b 5 8 10 17 22 6 Look at the table below and find the rule

a 6 5 4 13 7 b 7 5 3 21 9

7 If a = 3b ? 6 substitute the given values of b into the formula to find the value of a

a) b = 5

b) b = 14

Number of matchsticks 3

6

9

12 15 18

The pattern in the bottom row is 3, 6, 9, . . .; we can see that the rule here is `add 3'. We can also look for a relationship between the number of triangles and the number

of matchsticks in each shape. If you examine the table, you will see that a relationship

8 Find the vcanlubee ofofumnd.bIyn swuobrdsst,ittuhetirneglattihoneshgiipviesn`tvhealnuuemobefraoifnmtoatcthhseticfoksrmequalals 3 times m = 3(2ath+e 3n)umberao=f t4riangles'.

WORKED Example 4

9 CLoonoskidaert tahseetpoafthteexrangoonfshceoxnasgtrounctsedcoanccsotrrduicntgedto uthseinpgatmterantcshhoews n below.

MQ QLD 1 - Chapter 05 Page 227 Wednesday, October 22, 2003 1:59 PM

227 a Using matches/pencils/..., construct the above figures. Draw the next two figures in the sae)rieDs. raw the next two figures in the patterCnh a p t e r 5 P a t t e r n s a n d f u n c t i o n s

b Draw up a table showing the relationship between the number of hexagons in the figure

Problem solving using algebra abn)d Dthreanwumubperaotfamblaetcshhesowusiendgtothcoenrsetrluactitotnheshfiigpurbee. tween the number of hexagon and the

c Devisneuamrubleertoodfemscaritbcehtehse nneuemdbeedr of matches required for each figure in terms of the d nUocdf)u)sem20ybUFoheiusrenerxodartfguhthohleeenFhdexstraiiaf.onvurfgdeeudloirenlefeneotgntseutorniaienmdnflpiptaitnanhuhttdeteetienntfirrhhugungmelouetownbrhroeueer.rrmmusfn.olbeaAuremncnrmauyoenlbfxame,abmmrseauapotabtclcfsehhvtmieietesurssyatsrihtaoeuconqrshweeuaefnilnurlsolebewtdepeolsrdotootwyebhom.dleeCuamottnkoon-eutsuiomnmasluvefiaebidtgnkheugoeerrvtes2eoear0ccfmhpohhnaengeiesrqeixuxuslataeeig.gnwogOoinnnthcssemyaonuy

WORKED 15 10 A farmer construEctxs taemmpporlaery sheep pens by making a square, as shown below. A wire fence is attached to the posts, which are placed at regular intervals around the pen. A farmer constructs temporary sheep pens by making a square, as shown below. A wire fence is attached to the posts which are placed at regular intervals around the pen.

Number of posts on each side = 2 Number of posts on each side = 3 Number of posts on each side = 4 Number of posts on each side = 5

Total number of posts = 4

Total number of posts = 8

Total number of posts = 12

Total number of posts = 16

HowHmowamnyanpyopsotsstswwiillll bbee rreeqquuirierdedfofroar saqusqarueapreenpwehnicwh hhaicsh45hpaoss4ts5opnoesatcshosnidee?ach side?

11 Writ(eHainnt:eTxhperaenssswioenr ifsonrotth4e?s4u5moro1f8P0 apnosdts!Q)

THINK

WRITE

12 If N r1epDrreaswena ttsabalenwyhnicuhmshboewrs, twherittweoesxeptsressiLoent sL froeprr:esent the number of posts on each

of numbers and choose a pronumeral to side and T represent the total number of posts.

a) 5 tliambeel seatchheronwu.mWbe ecarn call the number

1

11

of posts on each side L and the total

b) 2 lneusmsbtehraonf pthosetsnTu. mber

L23 45

2 Look at the change in L- and T-values.

c) 8 mThoerTe-vtahlaueninthcreeansuesmbybe4rfor every

increase in the L-value. This means that

d) 3thWtehenheruunmleLbw=eil2rl,dc2oinv?tia4din=edt8h.ebTtyoer6gmetLth?e4.

answer of 4 for T, we need to

e) thesunbetrxatctc4o.nsecutive number

T 4 8 12 16

4

44

4 Check that rule works in all cases. It does.

5 So the rule is T = L ? 4 - 4 or T = 4L - 4.

6 Write down the rule or formula. 7 To find the total number of posts, T, we

must substitute the value 45 for L.

T = 4L - 4 If L = 45 T = 4 ? 45 - 4 T = 180 - 4 T = 176

This means that 176 posts are required for a pen

with 45 posts on each side.

Notice in the example above that once we have found the formula which connects the two quantities, we can use it to find the number of posts that would be needed for a

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