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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)`

Statistics, NAP-G2-30

Rory is captain of the chess club and keeps a record of the number of students in the club at the end of each week.
 

 

 
If no students have left the club, how many joined in Week 3?

`3` `4` `5` `13` `17`
 
 
 
 
 
Show Answers Only

`4`

Show Worked Solution

`text(New members in Week 3)`

`=\ text(Members at end Week 3 – Members at end Week 2)`

`= 17 – 13`

`= 4`

Number and Algebra, NAP-G2-29 SA

Marcel has the six cards pictured below
 

 

 
Marcel can arrange the six cards into a number sentence that make a total, as shown below.
 

  
What is the largest total Marcel can make using all the cards in a number sentence?
Show Answers Only

`971`

Show Worked Solution

`text(The largest total is made when the highest 3 digit)`

`text(number has the smallest 1 digit number deducted.)`

`=> 973 – 2 = 971`

Measurement, NAP-E2-20 SA

Mandy is cutting out luggage tags from a plastic sheet.

Each luggage tag is identical and is pictured below.
 

 
Mandy throws away all pieces of plastic that are not complete tags.
 

 
What is the greatest number of luggage tags that Mandy can cut from the plastic sheet?
Show Answers Only

`text(10 luggage tags)`

Show Worked Solution

`text(10 luggage tags is the most that can be cut.)`

Statistics, NAP-E2-32 SA

Matt and Libby planted 50 trees each over 3 weeks.

The bar chart below shows the amount of trees each planted in each week.
 

How many more trees did Libby plant than Matt in Week 2.
Show Answers Only

`5`

Show Worked Solution

`text(Trees planted by Matt in Week 2)`

`= 35 – 15`

`= 20`
 

`text(Trees planted by Libby in Week 2)`

`= 45 – 20`

`= 25`
 

`:.\ text(Libby planted 5 more trees than Matt in Week 2.)`

Number and Algebra, NAP-H2-31

Guy has a work truck that is 6 meters long.

His son Sam has a toy truck that is 5 cm long.

How many times as long as Sam's toy truck is Guy's truck?

`1` `30` `83` `120` `200`
 
 
 
 
 
Show Answers Only

`120`

Show Worked Solution

`text(Guy’s truck = 6 × 100 = 600 cm)`

`:.\ text(Number of times longer)` `= 600/5`
  `= 120`

Number and Algebra, NAP-G2-26

Leo shades in part of a circle.
 

 
What fraction is closest to the area of the circle that Leo shaded?

`5/8` `1/2` `3/5` `4/10`
 
 
 
 
Show Answers Only

`4/10`

Show Worked Solution

`text(The shaded area is slightly less than a half)`

`text(of the total area of the circle.)`

`:. 4/10\ \ text(is the closest fraction.)`

Measurement, NAP-I2-33

Kevin wanted to measure the width of a roll of toilet paper by measuring it against a section of his measuring tape.
 

 
What is the width of the toilet paper roll?

`text(8 centimetres)` `text(9 centimetres)` `text(13 centimetres)` `text(22 centimetres)`
 
 
 
 
Show Answers Only

`text(9 centimetres)`

Show Worked Solution
`text(Width)` `=22-13`
  `= 9\ text(centimetres)`

Number and Algebra, NAP-I2-32

Matt had a bag of 44 lollipops.

He gave an equal number to each of the other 7 players in his water polo team.

Matt gave each team mate as many lollipops as possible and kept the rest for himself.

How many lollipops did Matt get?

`2`    `6`   `9` `37`
 
 
 
 
Show Answers Only

`text(2 lollipops)`

Show Worked Solution

`text(Lollipops given to each player)`

`=44-:7`

`=6\ text(remainder 2)`
 

`:.\ text(Matt gets the 2 lollipops left over.)`

Number and Algebra, NAP-D2-34

The Big Merino in Goulburn is 15 m tall.

Justin owns a real merino sheep that is 75 cm tall.
 

 
How many times taller is the Big Merino than Justin's merino?

 
 `15`
 
 `20`
 
 `30`
 
 `60`
Show Answers Only

`20`

Show Worked Solution

`text(Converting the height of the big merino to cm)`

`=15 xx 100`

`=1500\ text(cm)`

 

`:.\ text(Times taller)` `=1500/75`
  `=(150 xx 10)/75`
  `=20`

Probability, NAP-D2-26

In a high school, all the boys were asked their favourite sport and the top five results were put in the table below.

Which of these statements is true of a boy who goes to the high school?

 
 His favourite sport is less likely to be soccer than AFL.
 
 His favourite sport is certain to be rugby league.
 
 His favourite sport is more likely to be rugby union than swimming.
 
 It is impossible that his favourite sport is golf.
Show Answers Only

`text(His favourite sport more likely to be)`

`text(rugby union than swimming.)`

Show Worked Solution

`text(His favourite sport is more likely to be)`

`text(rugby union than swimming.)`

Number and Algebra, NAP-D2-25

A tadpole is measured to be 9 mm long.

A few weeks later, the tadpole turns into a frog that is about 8 times longer than its tadpole length.

The difference between the length of the frog and its length as a tadpole is about

`text(1 mm)` `text(17 mm)` `text(63 mm)` `text(72 mm)`
 
 
 
 
Show Answers Only

`text(63 mm)`

Show Worked Solution
`text(Length of frog)` `=8 xx 9`
  `=72\ text(mm)`
   
`:.\ text(Difference)` `= 72 – 9`
  `=63\ text(mm)`

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)`

Geometry, NAP-I2-34

Jimmy drew a chess piece that is pictured below.
 

 
He reflected the piece across the dotted line.

He rotated it 90 degrees anticlockwise.

Which picture below shows what it looks like after this?

 
 
 
 
Show Answers Only

Show Worked Solution

`text(After the reflection:)`
 

  
`text(After the 90° anticlockwise rotation:)`

Probability, NAP-I2-31

A soccer competition has six teams playing on the same day.

The table below shows the draw. 

If no match ends in a draw, which of the following is possible?

 
 Tigers and Lions are the only teams that lose.
 
 Lions and Cheetahs both lose.
 
 Meercats and Civets both win.
 
 Lions, Leopards, Civets and Tigers all win.
Show Answers Only

`text(Meercats and Civets both win.)`

Show Worked Solution

`=>\ text(3 teams must win and 3 teams must lose.)`

`=>\ text(Teams playing each other cannot both lose).`

`:.\ text(Meercats and Civets both winning is the)`

`text(only option that is possible.)`

Statistics, NAP-I2-30

Obie does odd jobs around the house to earn pocket money.

He gets $6 per job.

The table below shows all the jobs he did in one week. 

If Obie does the same jobs for two weeks, how much money will he earn altogether?

`$12` `$48` `$72` `$144`
 
 
 
 
Show Answers Only

 `$144`

Show Worked Solution

`text(Total jobs in 1 week)`

`= 7 + 3 + 2`

`= 12`
 

`:.\ text(Money earned in 2 weeks)`

`= 2 xx (12 xx 6)`

`= 2 xx 72`

`= $144`

Algebra, NAP-C4-CA10

Tim produced a pattern with large squares and small triangles.
 

 
If Tim continues this pattern how many small triangles will be in the 12th shape?

`6`  `12` `26` `30`
 
 
 
 
Show Answers Only

`26`

Show Worked Solution

`text(Let)\ \ s = text(Number of large squares)`

`:.\ text(Number of triangles in the 12th shape)`

`= (s xx 2) + 2`

`= 12 xx 2 + 2`

`= 24 + 2`

`= 26`

Statistics, NAP-D4-CA15

 
Between 2007 and 2010, the number of people with type II diabetes in America increased by about

 
 `text(0.5 million people.)`
 
 `text(1 million people.)`
 
 `text(1.5 million people.)`
 
 `text(2 million people.)`
Show Answers Only

`text(2 million people.)`

Show Worked Solution

`33.21 – 31.16 = 2.05`

`:.\ text(The number increased by about 2 million people.)`

Measurement, NAP-D4-CA12

Bojack is going to paint the inside walls of his garage.

What information will best help him calculate the amount of paint he needs to buy?

 
 volume of the garage
 
 perimeter of the internal garage ceiling
 
 perimeter of all internal garage wall
 
 area of all internal garage walls
Show Answers Only

`text(area of all internal garage walls)`

Show Worked Solution

`text(area of all internal garage walls)`

Measurement, NAP-D4-CA11

Two bricks can be joined to make three different rectangular prisms. Two of them are shown here.
 

 
What would be the measurements of the third prism?

 
 `text(18 cm by 16 cm by 7 cm)`
 
 `text(36 cm by 8 cm by 7 cm)`
 
 `text(32 cm by 18 cm by 7 cm)`
 
 `text(36 cm by 14 cm by 8 cm)`
Show Answers Only

`text(36 cm by 8 cm by 7 cm)`

Show Worked Solution

`text(36 cm by 8 cm by 7 cm)`

Algebra, NAP-D4-CA10

Billy is setting up tables for a comedy night at his club.

An  X  is placed for every available seat at a table, as shown below.
 

 
Which of these rules can be used to work out how many people can sit on any row of tables?

 
 `text(number of tables) xx 6`
 
 `text(number of tables) ÷ 2 - 2`
 
 `text(number of tables) xx 4 + 2`
 
 `text(number of tables) xx 4 - 2`
Show Answers Only

`text(number of tables) xx 4 + 2`

Show Worked Solution

`text(Consider Option 3:)`

`text(1st table:)\ \ 1 xx 4 +2 = 6\ text(people)`

`text(2nd table:)\ \ 2 xx 4 +2 = 10\ text(people)`

`text(3rd table:)\ \ 3 xx 4 +2 = 14\ text(people)`

 

`:.\ text(number of tables) xx 4 + 2\ \ text(is the correct rule.)`

Algebra, NAP-D4-CA07

The surface area `(S)` of the prism below can be calculated by multiplying the perimeter of its face `(p)` by its height `(h)`, and adding twice the area of its face `(F)`.
 


 

Which one of these formulas could be used for this calculation?

 
 `S = 2 p h F`
 
 `S = p h + F`
 
 `S = p h + 2F`
 
 `S = 2 ph + 2F`
Show Answers Only

`S = p h + 2F`

Show Worked Solution

`S = p h + 2F`

Geometry, NAP-C4-CA07

Juanita wanted to print a larger copy of her photo of a tree.

She increased the scale by a factor of 3.

She named the first picture Photo A and the second picture Photo B.
 

If Photo B is 3.2 cm high, how high is Photo A?

`0.8\ text(cm)` `1.12\ text(cm)` `1.07\ text(cm)` `9.6\ text(cm)`
 
 
 
 
Show Answers Only

`1.07\ text(cm)`

Show Worked Solution

`text(S)text(ince Photo B is increased by a factor of 3,)`

`text(Height of Photo B)/text(Height of Photo A)` `=3`
`:.\ text(Height of Photo A)` `=text(Height of Photo B)/3`
  `=3.2/3`
  `=1.07\ text(cm)`

Statistics, NAP-B3-CA11

During picking season, four groups of people were hired to pick apples.

A group will receive a bonus if they pick more than 24 apples per person in a 10-minute period.

The table below shows the total amount of apples picked by each group in the first 10 minutes.
 

 
Which group would have received a bonus in the first 10-minute period?

`text(A)`   `text(B)`  `text(C)`  `text(D)`
 
 
 
 
Show Answers Only

`text(Group C)`

Show Worked Solution

`text{Calculate apples picked per person (in 10 mins) for each group:}`

`text(A) = 68 ÷ 3 = 22.67…`

`text(B) = 95 ÷ 4 = 23.75`

`text(C) = 122 ÷ 5 = 24.4`

`text(D) = 143 ÷ 6 = 23.83…`
 

`:.\ text(Group C would have received a bonus.)`

Algebra, NAP-D3-CA12

Billy is setting up tables for a comedy night at his club.

An  X  is placed for every available seat at a table, as shown below.
 

  
Which of these rules can be used to work out how many people can sit on any row of tables?

 
 `text(number of tables) xx 6`
 
 `text(number of tables) ÷ 2 - 2`
 
 `text(number of tables) xx 4 + 2`
 
 `text(number of tables) xx 4 - 2`
Show Answers Only

`text(number of tables) xx 4 + 2`

Show Worked Solution

`text(Consider Option 3:)`

`text(1st table:)\ \ 1 xx 4 +2 = 6\ text(people)`

`text(2nd table:)\ \ 2 xx 4 +2 = 10\ text(people)`

`text(3rd table:)\ \ 3 xx 4 +2 = 14\ text(people)`

 

`:.\ text(number of tables) xx 4 + 2\ \ text(is the correct rule.)`

Algebra, NAP-D4-NC19 SA

Robin was an archer and was aiming for the target below in archery game.
 

In the game, Robin shoots 3 arrows at the target, with each shape worth points.

The table below shows the results of Robin's first 3 turns, each shooting 3 arrows.
 

 

 In Robin's 4th turn, he hits the following 3 objects: 
 

 

How many points did he score in his 4th turn?
Show Answers Only

`85`

Show Worked Solution
`3 xx` `= 120`
  `= 40`
`=> 40 + 40 +` `= 90`
  `= 10`
`=>\ `   `+`   `+ 10` `= 80`
      `2 xx` `= 70`
        `= 35`

 

`:.\ \ ` `+`  `+`  `= 35 + 10 + 40`
            `= 85`

Number, NAP-D3-CA18

Richard is a runner.

The length of his last 4 half marathons are recorded in the table below.
 

  
Which half marathon had the shortest distance?

`1`    `2`   `3`   `4`
 
 
 
 
Show Answers Only

`text(half marathon 3)`

Show Worked Solution

`20.295\ text(is the shortest distance.)`

`:.\ text(Half marathon 3 was the shortest.)`

Measurement, NAP-C4-NC16

The sign shows opening hours of a car parking station.

Kenny wants to park his car for 2 hours to do some shopping, before collecting his car to drive home.
 


  

At which time below could he safely park his car and pick it up to drive home?

 
 11:30 am Wednesday
 
 3:00 pm Wednesday
 
 11:45 am Saturday
 
 3:00 pm Saturday
Show Answers Only

`text(11:30 am Wednesday)`

Show Worked Solution

`text(11:30 am on Wednesday plus 2 hours means that)`

`text(Kenny picks up his car at 1:30 pm which is within)`

`text(the opening hours of the parking station.)`

 

`:.\ text(He should park at 11:30 am on Wednesday.)`

Measurement, NAP-C4-NC15

Which of these is the longest distance?

`0.2405\ text(km)` `245\ text(m)` `2450\ text(cm)` `24\ 050\ text(mm)`
 
 
 
 
Show Answers Only

`text(245 m)`

Show Worked Solution

`text(Convert each option to metres:)`

`text(Option 1:  0.2405 km = 0.2405 × 1000 = 240.5 m)`

`text(Option 2:  245 m)`

`text(Option 3:  2450 cm) = 2450/100 = 24.5\ text(m)`

`text(Option 4:  24 050 mm) = (22\ 050)/1000 = 24.05\ text(m)`

 

`:.\ text(245 m is the longest distance.)`

Algebra, NAP-C4-NC14

The table shows how a sock company grew by selling more and more pairs of socks over 5 years.
 

 

 
Using this data, what is the best estimate for the number of pairs of socks sold in the sixth year?

 
 `3000`
 
 `4000`
 
 `8000`
 
 `16\ 000`
Show Answers Only

`8000`

Show Worked Solution

`text(The number of pairs sold is growing by a)`

`text(multiple of 4 each year.)`

`=>\ text(Socks sold in year 6)` `=2048 xx 4`
  `=8192`

`:.\ text(8000 is the best estimate.)`