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Number and Algebra, NAP-I1-26

Harriet and Eva have 44 toys altogether.

Harriet has 29 toys.

Which number sentence can be used to find the number of toys Eva has?

`44 - 29 = 15` `44 + 29 = 73` `29 - 44 = 15` `29 - 15 = 14`
 
 
 
 
Show Answers Only

`44 – 29 = 15`

Show Worked Solution
`text(Eva’s toys)` `=44-29`
  `=15`

Measurement, NAP-I1-25

Dean balances four objects on a set of scales, as pictured below.
 


 

Which object is the heaviest?

 
 
 
 
Show Answers Only

Show Worked Solution

`text(The following logic solves the problem:)`

`text(Money bag weighs more than the gold bar.)`

`text(Bowling ball is the same weight as the money bag.)`

`text(Lead weight is heavier than the bowling ball.)`

`=>\ text(Lead weight must be heaviest.)`

Number and Algebra, NAP-I1-21

In a soccer competition, there were 5 teams.

Over the season, a total of 55 goals were scored.

Each team scored the same number of goals for the season.

How many goals did each team score?

`60` `50` `12` `11`
 
 
 
 
Show Answers Only

`11`

Show Worked Solution

`text(Goal scored by each team)`

`= 55 ÷ 5`

`= 11`

Number and Algebra, NAP-I1-19

Emma uses the number sentence  `8 xx 4 = 32`  to solve a problem.

Which of the problems below would the number sentence solve?

 
 Emma has 8 students and gets 4 more.
How many students does she have now?
 
 Emma has 8 students. She gives each of them 4 pencils.
How many pencils does Emma give to her students?
 
 Emma has 8 pencils. She shares them with 4 students.
How many pencils does each student get?
 
 Emma has 8 pencils and gives 4 away.
How many pencils does she have now?
Show Answers Only

`text(Emma has 8 students. She gives each of them 4 pencils.)`

`text(How many pencils does Emma give to her students?)`

Show Worked Solution

`text(If Emma has 8 students, and gives each of them)`

`text(4 pencils,)`

`text(Pencils given away)` `= 8 xx 4`
`=> 32` `= 8 xx 4`

Number and Algebra, NAP-H1-28

Conrad created a number pattern by adding four to a number to get the next number.

Which of these could be the first four numbers of Conrad's pattern?

`4, 14, 24, 34` `5, 9, 14, 20` `7, 12, 17, 22` `9, 13, 17, 21`
 
 
 
 
Show Answers Only

`9, 13, 17, 21`

Show Worked Solution

`9+4=13`

`13+4=17`

`17+4=21`

`:.\ text(Conrad’s pattern is:  9, 13, 17, 21)`

Number and Algebra, NAP-H1-21

Michelle, Lucy, Clare and Steph are sisters.

The years they were born are recorded in the table below.

Who is the second youngest sister?

`text(Michelle)` `text(Lucy)` `text(Clare)` `text(Steph)`
 
 
 
 
Show Answers Only

`text(Lucy)`

Show Worked Solution

`text(The order from oldest to youngest is:)`

`text{Clare (1977), Michelle (1978), Lucy (1987), Steph (1988).}`

`:.\ text(Lucy is the second youngest.)`

Number and Algebra, NAP-C2-13

A bag of marbles contains only white and grey marbles.
 

 

 
What fraction of the total marbles are grey ones?

`2/5` `1/3` `2/3` `3/5`
 
 
 
 
Show Answers Only

`3/5`

Show Worked Solution
`text(Fraction)` `= text(number of grey marbles) / text(total marbles)`
  `=3/5`

Geometry, NAP-C2-12

Andy leaves his classroom and walks east to get to the toilet block.
 

 
Which classroom was he in?

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

`text(Classroom D)`

Show Worked Solution

`text(Classroom D)`

Geometry, NAP-F2-16

A butterfly is displayed in a  museum exhibition.

The butterfly is twisted one quarter of a turn anti-clockwise.

Which of these shows the new position of the butterfly?

 
 
 
 
Show Answers Only

Show Worked Solution

`text(A quarter turn anti-clockwise is the same as a)`

`text(90° turn to the left.)`

Geometry, NAP-C2-14

Rahul draws a net, which is pictured below.
 

 
What 3D object will it make?

 
 Pentagonal prism
 
 Pentagonal pyramid
 
 Hexagonal pyramid
 
 Hexagonal prism
Show Answers Only

`text(Pentagonal pyramid)`

Show Worked Solution

`text(The net will have a pentagon shaped base, and)`

`text(converge to a point.)`

`:.\ text(Net will make a pentagonal pyramid.)`

Number and Algebra, NAP-C2-11

Joel is running a cooking class.

He has 26 students in the class and needs to give them 2 eggs each for a recipe.

Eggs are sold in cartons of 12.
 

 
What is the least number of egg cartons that Joel needs to buy?

`3` `4` `5` `6`
 
 
 
 
Show Answers Only

`5\ text(cartons)`

Show Worked Solution

`text(Cartons required)`

`=(26 xx 2) ÷ 12`

`=52 -: 12`

`= 4\ 4/12`

 

`:.\ text(Joel needs to buy 5 egg cartons.)`

Geometry, NAP-C2-10

Steve and Tony are planning to meet on the corner of two streets.

The location of the corner is in D4 on the map.
 

 
On the corner of which two streets will Steve and Tony meet?

 
 Vessuvio and Third
 
 Fourth and Cowra
 
 Farrar and Fourth
 
 Third and Solid
Show Answers Only

`text(Third and Solid)`

Show Worked Solution

`text(Third and Solid)`

Statistics, NAP-C2-08

Some students at a country school were asked to name their favourite animal.

The four most popular choices were put on the graph below.

  • Dogs were the most popular.
  • Sheep were more popular than cats.
  • Horses were less popular than sheep.

Which column shows sheep on the graph?
 

 

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

`text(B)`

Show Worked Solution

`text(Column D is dogs.)`

`text(S) text(ince horses are less popular than sheep)`

`text(and sheep are more popular than cats.)`

`=>\ text(Sheep are more popular than horses and cats.)`

`=>\ text(Column B is sheep.)`

Statistics, NAP-F2-12

Justin makes a tally chart to calculate the money in his cash drawer at the end of the day.

The part of the tally chart for the $1 and $2 coins is shown in the table below.

How much money does Justin have in total, in $1 and $2 coins?

`$21` `$26` `$29` `$34`
 
 
 
 
Show Answers Only

`$34`

Show Worked Solution

`text(Total of $1 coins = $8)`

`text(Total of $2 coins)` `= 13 xx 2`
  `= $26`

 
`:.\ text(Total) = 8 + 26 = $34`

Statistics, NAP-F2-08

A year 7 class split into boys and girls and each group collected butterflies in a jar.

The total number of butterflies in each jar is put in the table below.

How many more butterflies did the boys catch than the girls?

`5` `6` `7` `9`
 
 
 
 
Show Answers Only

`9`

Show Worked Solution

`text(Butterflies in the boys’ jar)`

`=7 xx 2 = 14`

`text(Butteflies in the girls’ jar)`

`=2.5 xx 2 = 5`

 

`:.\ text(The boys caught 9 more butterflies.)`

Geometry, NAP-E2-23

Max is a dog who stays in a kennel when his owners go on holiday.

A plan of the cages where the dogs sleep in the kennel is below.
 

 
Max's cage is in the south-west corner of the kennel.

Which of these could be Max's cage?

`text(D4)` `text(A5)` `text(B5)` `text(D1)`
 
 
 
 
Show Answers Only

`text(A5)`

Show Worked Solution

`text(A5)`

Statistics, NAP-E2-19

4 friends practiced taking soccer penalty goals.

They took 8 penalty with their right foot and another 8 penalty goals with their left foot.

The results are shown in the graph below.
 

 
Who scored the most penalty goals?

`text(Lionel)` `text(Kane)` `text(Tim)` `text(Pele)`
 
 
 
 
Show Answers Only

 `text(Pele)`

Show Worked Solution

`text(Consider each player:)`

`text(Lionel) = 3 + 7 = 10`

`text(Kane) = 6 + 4 = 10`

`text(Tim) = 7 + 2 = 9`

`text(Pele) = 6 + 5 = 11`

 `:.\ text(Pele scored the most penalty goals.)`

Geometry, NAP-E2-24

Irene placed three identical tiles together at their edges.

She drew around the outside to make this new shape.
 

 
Which of these could have been the shape of her tiles?

`text(triangles)` `text(rectangles)` `text(trapeziums)` `text(rhombuses)`
 
 
 
 
Show Answers Only

`text(rhombuses)`

Show Worked Solution

`text(rhombuses)`

Geometry, NAP-E2-21

Leonardo drew a shape.

Its diagonals meet at right angles and one is longer than the other.

Which of these could be Leonardo's shape?

       
 
 
 
 
Show Answers Only

Show Worked Solution

`text(Consider each option:)`

`text(Option 1: Rectangle’s diagonals don’t meet at right angles.)`

`text(Option 2: Trapezium’s diagonals don’t meet at right angles.)`

`text(Option 3: A rhombus has diagonals that intersect and have)`

`text(different lengths.)`

`text(Option 4: A squares diagonals are equal length.)`

 

`:.\ text(The shape must be a rhombus.)`

Number and Algebra, NAP-E2-16

Billy has this much money.
 

 
He buys an avocado for $1.35.

How much money does Billy have left

`text(25 cents)` `text(35 cents)` `text(40 cents)` `text(45 cents)`
 
 
 
 
Show Answers Only

`text(35 cents)`

Show Worked Solution

`text(Money at the start)`

`=$1 + 20¢ + 20¢ + 20¢ + 10¢`

`= $1.70`
 

`=>\ text(Money left)` `=$1.70 – $1.35`
  `= 35¢`

Measurement, NAP-E2-11

Alison buys paper clips that come in three sizes, small, medium and large.

The picture shows the lengths of the small and large clips.
 

 
What could the length of the medium paper clip be?

`text(1 centimetre)` `text(5 centimetres)` `text(7 centimetres)` `text(11 centimetres)`
 
 
 
 
Show Answers Only

`text(5 centimetres)`

Show Worked Solution

`text(Small paper clip) = 6-1.5 = 4.5\ text(cm)`

`text(Large paper clip) = 16-9=7\ text(cm)`

 

`text(Among the choices given, only 5 cm is between)`

`text(4.5 cm and 7 cm.)`

 

`:.\ text(The medium paper clip could be 5 cm.)`

Probability, NAP-E2-15

Jack rolls a standard dice three times.

He rolls a six each time.

Jack then has a forth roll.

Which of the following is true?

 
 He is more likely to roll a six than a four.
 
 He is certain to roll a six.
 
 He has an equal chance of rolling a six as a four.
 
 He is more likely to roll a four then a six.
Show Answers Only

`text(He has an equal chance of rolling a six as a four.)`

Show Worked Solution

`text(On any 1 given roll, all numbers have an)`

`text(equal chance.)`

`:.\ text(He has an equal chance of rolling a six as a four.)`

Number and Algebra, NAP-E2-14

A small country primary school has 17 more boys than girls.

Garoo knows there are 58 boys.

How can Garoo work out the number of girls at his primary school?

 
 add 58 to 17
 
 subtract 17 from 58
 
 multiply 17 by 58
 
 divide 58 by 7
Show Answers Only

`text(subtract 17 from 58)`

Show Worked Solution

`text(The number of girls can be calculated by subtracting)`

`text(the “extra” boys from the total number of boys.)`

`:.\ text(subtract 17 from 58)`

Measurement, NAP-G2-17


 

The French Open men's tennis final was held on 3 June.

5 days before the final, Rod arrived in Paris.

On what day of the week did Rod arrive in Paris?

`text(Monday)` `text(Tuesday)` `text(Wednesday)` `text(Thursday)` `text(Friday)`
 
 
 
 
 
Show Answers Only

`text(Tuesday)`

Show Worked Solution

`text(Tuesday)`

Number and Algebra, NAP-G2-13

Munro has $86.
 

 
How much more money does he need to buy the tennis racquet?

`$42` `$48` `$52` `$58`
 
 
 
 
Show Answers Only

`$48`

Show Worked Solution

`text(Extra money needed for racquet)`

`=134-86`

`=$48`

Measurement, NAP-H2-15

The table below shows the session times of movies.

Which of these movies lasts two and a half hours?

`text(Never Ever)` `text(Shake It Off)` `text(Bad Blood)` `text(Blank Space)`
 
 
 
 
Show Answers Only

`text(Bad Blood)`

Show Worked Solution

`text(7:20 pm to 9:50 pm)`

`= 2\ text(hours and 30 minutes)`

`:.\ text(Bad Blood)`

Measurement, NAP-H2-09

Andre's birthday is on the 28th of June.

His mother's birthday is 6 days later.
 


 

Which day of the week was his mother's birthday in 2016?

`text(Saturday)` `text(Sunday)` `text(Monday)` `text(Tuesday)`
 
 
 
 
Show Answers Only

`text(Monday)`

Show Worked Solution

`text(Monday)`

Statistics, NAP-H2-08

Virat had a stall that sold hats at the cricket.

The table below shows the number of hats of each size that he sold.

  • Large size were the most popular.
  • Small were less popular than extra large.
  • Medium were more popular than extra large.
     

 

 
Which column on the graph represents extra large?

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

`text(B)`

Show Worked Solution

`text{Large sold 15 (highest column).}`

`text(Extra large sold more than small and less)`

`text(than medium.)`

`:.\ text(Column B must be extra large.)`

Measurement, NAP-I2-18

Dean balances four objects on a set of scales, as pictured below.
 

 
Which object is the heaviest?

 
 
 
 
Show Answers Only

Show Worked Solution

`text(Money bag is heavier than the gold bar.)`

`text(Bowling ball is the same mass as the money bag)`

`=>\ text(Bowling ball is heavier than gold)`

`text(Lead weight is heavier than the bowling ball)`

`=>\ text(Lead weight is the heaviest of all items)`

Measurement, NAP-D2-16

Bob had a mini tennis court in his backyard, as shown in the diagram below.
 

 

 
What is the area of the mini tennis court?

 
 `6\ text(square metres)`
 
 `12\ text(square metres)`
 
 `24\ text(square metres)`
 
 `48\ text(square metres)`
Show Answers Only

`24\ text(m²)`

Show Worked Solution

`text(The mini tennis court has dimensions:)\ \ 4 xx 6.`

`:.\ text(Area)` `= 4 xx 6`
  `= 24\ text(m²)`

Measurement, NAP-I2-15

Banjo started with 475 millilitres of water in a flask.

After he poured some of the water into a cup, the level of water in the flask is pictured below.
 

  
How much water did Banjo pour into the cup?

`text(50 millilitres)` `text(75 millilitres)` `text(100 millilitres)` `text(400 millilitres)`
 
 
 
 
Show Answers Only

`text(75 millilitres)`

Show Worked Solution

`text(Volume of water poured into the cup)`

`=475 – 400`

`= 75\ text(millilitres)`