SmarterEd

Aussie Maths & Science Teachers: Save your time with SmarterEd

Algebra, NAP-K3-CA25

Georgia is making a number pattern by drawing squares.
 

 
She draws up a table to record the number of squares in each figure.
 

 
How many squares will be in Figure 6?

`28` `34` `36` `40`
 
 
 
 
Show Answers Only

`40`

Show Worked Solution

`text(Consider the increase in squares between figures:)`

`text(Figure 1 → Figure 2 = 4 squares)`

`text(Figure 2 → Figure 3 = 6 squares)`

`text(Figure 3 → Figure 4 = 8 squares)`

`=> text(Figure)\ 5 = 18 + 10 = 28`
 

`:.\ text(Figure 6)` `= 28 + 12`
  `= 40\ text(squares)`

Algebra, NAP-A3-NC05

Flynn is making a pattern with soccer balls.
 

 
This table shows the number of balls he needs for each shape in the pattern.
 

  Pattern # 1 2 3 4 5
  Number of balls 1 4 9 16 ?

 
How many balls will Flynn need for Pattern #5?

`17` `23` `25` `30`
 
 
 
 
Show Answers Only

`25`

Show Worked Solution

`text(Solution 1)`

`text(By drawing the next shape, pattern #5 is)`

`:. 25\ text(balls needed for Pattern #5.)`

 

`text(Solution 2)`

`text(The table shows a pattern where the balls in each)`

`text(shape are the square of the pattern number:)`

`:.\ text(Balls in pattern #5) = 5^2 = 25`

Algebra, NAP-E3-NC14

Adam is making a pattern with black and white triangular tiles as shown below.
 

 
At each stage, tiles are added to edges that don't already have tiles on them.

What is the total number of tiles needed for Pattern 5?

`28` `34` `38` `42`
 
 
 
 
Show Answers Only

`38\ text(tiles)`

Show Worked Solution

`38\ text(tiles)`

Algebra, NAP-B3-CA24

This octagon pattern is made with sticks.
 

  
How many sticks are needed to make 10 of these octagons?

`71` `72` `75` `80`
 
 
 
 
Show Answers Only

`71`

Show Worked Solution

`text(1 octagon has 8 sticks.)`

`text(2 octagons have 15 sticks.)`

`text(3 octagons have 22 sticks.)`

`=>\ text(Each extra octagon needs 7 more sticks.)`

 

`:.\ text(10 octagons)` `= 8 + (9 xx 7)`
  `=8 + 63`
  `=71\ text(sticks)`

Algebra, NAP-E3-CA29 SA

Bill creates a pattern of branches and nodes on a computer.
 

 
Bill continued the pattern until the shape had 3279 branches.

How many nodes did the shape have?
Show Answers Only

`1093\ text(nodes)`

Show Worked Solution

`text(Pattern shows that:)`

`text(Number of branches)/text(Number of nodes)`

`= 3/1 = 12/4 = 39/13 = 120/40 =3`

 

`:.\ text(If there are 3279 branches,)`

`text(Number of nodes)` `= 3279/3`
  `= 1093\ text(nodes)`

Algebra, NAP-E3-CA23

Choon designs a line of tiles that repeats 5 different tiles in the same order, as shown below.
 

 
Each tile costs $11.50 and Choon uses $322 worth of tiles.

Which of these is the last tile in his line of tiles?

 
 
 
 
 
Show Answers Only

Show Worked Solution

`text(Total number of tiles used)`

`=322/11.50`

`=28`

 

`:.\ text(5 rows of 5 are used and the last tile is the 3rd)`

`text(in the pattern.)`

 

Algebra, NAP-D3-NC20 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`

Algebra, NAP-B3-NC10

Colin created the following pattern using plums from his orchard.
 

 
If this pattern continues, how many plums are in Column 7?

`4` `13` `19` `22`
 
 
 
 
Show Answers Only

`22`

Show Worked Solution

`text(Plums in column 1 = 4)`

`text(Plums in column 2 = 7)`

`text(Plums in column 3 = 10)`

`=>\ text(Each column has 3 extra plums.)`

 

`:.\ text(Plums in column 7)`

`=4 + (6 xx 3)`

`=22`

Algebra, NAP-G3-NC08

Rob uses sticks to make a pattern.

He starts with 3 sticks for Design 1.
 

 
How many sticks does Rob need for Design 5?

`39` `42` `45` `48`
 
 
 
 
Show Answers Only

`45`

Show Worked Solution

`text(One possible strategy:)`

`text(3 sticks are added to each “point” on the base)`

`text(of the triangle to form the next design.)`

`=>\ text(Design 4 has 5 points on the base.)`

`:.\ text(Total sticks)` `= 30 + (5 xx 3)`
  `= 30 + 15`
  `= 45`

Algebra, NAP-G3-CA23 SA

The number of dots in each pattern increases by the same amount each time.
 

 
How many dots are in Pattern 12?
Show Answers Only

`text(37 dots)`

Show Worked Solution

`text(Pattern 1) = 4`

`text(Pattern 2) = 7`

`text(Pattern 3) = 10`

`=>\ text(Pattern increases by 3 dots each time.)`

 

`:.\ text(Dots in pattern 12)`

`= 4 + (11 xx 3)`

`= 4 + 33`

`= 37` 

Algebra, NAP-H3-NC20

Adam is a tile designer. He is repeating 4 symbols as shown in the picture below.

Adam is using this pattern for a line of tiles that is 31 tiles long.

 

 
What will be the symbol on the 31st tile?

 
 
 
 
Show Answers Only

Show Worked Solution

`text(7 repeats of the 4 tile pattern make up)`

`text(the first 28 tiles.)`

`:.\ text(The 31st tile is the third tile in the pattern.)`

Algebra, NAP-I3-CA03

Penelope is making a pattern with black and white tiles, as shown below.
 

 
If the pattern continues, how many black tiles will there be in Design 8?

`4`   `16` `32` `44`
 
 
 
 
Show Answers Only

`32`

Show Worked Solution

`text(Each design adds 4 black tiles.)`

`:.\ text(Black tiles in design 8)` `=8 xx 4`
  `=32`