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Number and Algebra, NAP-J2-28v1

Dostoy has 73 match sticks.

He uses 6 match sticks to make two small triangles.
 

 
What is the largest number of small triangles that Dostoy can make with his 73 match sticks?

`19` `21` `24` `27`
 
 
 
 
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`24`

Show Worked Solution

`text(3 match sticks are used for 1 triangle.)`

`text(Number of triangles)` `= 73 ÷ 3`
  `= 24\ text(remainder 1)`

 
`:.\ text(24 triangles.)`

Number and Algebra, NAP-K2-08

Oliver is using matchsticks to make a pattern of squares.
 

 
How many matchsticks will Oliver need to make square 5?

5 16 20 24
 
 
 
 
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`20`

Show Worked Solution

`text(Pattern 1 = 4)`

`text(Pattern 2 = 8)`

`text(Pattern 3 = 12)`

`=> 4\ text(matchsticks are added each square)`
 

`:.\ text(Square 5)\ =5 xx 4 = 20\ text(matchsticks)`

Number and Algebra, NAP-B2-23

Jake makes a pattern with black and white balls.
 

 
Altogether, how many balls are needed for the 5th pattern?

`13` `14` `15` `18`
 
 
 
 
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`14`

Show Worked Solution

`text(White ball pattern: 2, 3, 4, 5, 6 …)`

`text(Black ball pattern: 4, 5, 6, 7, 8, …)`

`:.\ text(Total balls in pattern 5)`

`=6\ text(white balls) + 8\ text(black balls)`

`=14\ text(balls)`

Number and Algebra, NAP-E1-15

Grace used sticks to create a pattern.

 

She used 4 sticks in her first shape, 7 sticks in her second shape and 10 sticks in her third shape.

How many sticks are needed for the next shape in Grace's pattern?

`9` `10` `11` `13`
 
 
 
 
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`13`

Show Worked Solution

`text(Each shape adds an extra 3 sticks.)`

`=>\ text(Sticks in the next shape)`

`=10+3`

`=13`

Number and Algebra, NAP-G1-27 SA

Marcus hangs 2 pairs of pants on a line.

Any trousers next to each other share a peg.

He uses 3 pegs.

How many pegs would Marcus use to hang 5 pairs of pants?
Show Answers Only

`6`

Show Worked Solution

`text(1 pair of trousers = 2 pegs)`

`text(2 pairs of trousers = 3 pegs)`

`text(3 pairs of trousers = 4 pegs)`

`vdots`

`text(5 pairs of trousers = 6 pegs)`