smc-3088-30-Other patterns

Number and Algebra, NAP-J2-12

Trevor has poured milk into some glasses.

He makes them all exactly one quarter full.

Trevor counts by quarters to find out, in total, how many full cups of milk he has.

Which number does Trevor count next?

`5`	`3`	`1 1/2`	`2 1/4`	`2 1/2`

Show Answers Only

`1 1/2`

Show Worked Solution

`text(Add)\ 1/4\ text(for each additional cup.)`

`:.\ text(Next number)`	`= 1 1/4 + 1/4`
	`= 1 1/2`

Number and Algebra, NAP-J2-11 SA

A school teacher allocates pieces of cardboard to class groups depending on the number of students in each group.

The table below is used.

Using the pattern in the table, how many pieces of cardboard should a group of 3 students receive?

Show Answers Only

`9`

Show Worked Solution

`text(The pattern shows that each student receives)`

`text(3 pieces of cardboard.)`

`:.\ text(A group of 3 will be given 9 pieces.)`

Number and Algebra, NAP-D2-30 SA

The prices at an ice cream shop can be seen below.

Each extra scoop of ice cream costs the same amount of money.

How much will an ice cream with 5 scoops cost?

Show Answers Only

`$8.80`

Show Worked Solution

`text(C)text(ost of 1 extra scoop)`

`= 6.25-5.40`

`= 0.85`

`:.\ text(C)text(ost of an icecream with 5 scoops)`

`= $5.40 + 4\ text(extra scoops)`

`= 5.40 + (4 xx 0.85)`

`= 5.40 + 3.40`

`= $8.80`

Number and Algebra, NAP-D2-22

Ged has a screwdriver set which is pictured below.

The length of the screwdrivers make a pattern.

What is the length of screwdriver number 4?

`text(23.5 cm)`	`text(23.25 cm)`	`text(23 cm)`	`text(22.75 cm)`

Show Answers Only

`text(22.75 cm)`

Show Worked Solution

`text(Difference between screwdriver 1 and 2)`

`=26.5 – 25.25 =1.25\ text(cm)`

`text(Difference between screwdriver 2 and 3)`

`=25.25- 24 =1.25\ text(cm)`

`=>\ text(Each screwdriver is 1.25 cm shorter than)`

`text(the one before.)`

`:.\ text(Screwdriver 4)`	`=24-1.25`
	`=22.75\ text(cm)`

Number and Algebra, NAP-I2-35 SA

Byron counts the number of guinea pigs in his breeding yard every 2 months.

He records the number in the table below.

If this pattern continues, how many guinea pigs will be in his breeding yard after 8 months?

Show Answers Only

`512`

Show Worked Solution

`text(The pattern shows that each number is 4 times)`

`text(the previous number.)`

`:.\ text(Number of guinea pigs after 8 months)`

`=128 xx 4`

`= 512`

Number and Algebra, NAP-I2-11

George has no money in his bank account.

He deposits $6 in his account in week 1.

He then deposits twice the amount into his account each week than he did the previous week.

The total amount in his account is?

	always odd.
	always even.
	sometimes odd and sometimes even.

Show Answers Only

`text(always even.)`

Show Worked Solution

`text(In each successive week, an even number will)`

`text(will be added to an existing even number.)`

`:.\ text(His account total will always be even.)`