Band 6 – Page 21

Measurement, NAP-D3-NC09

How much more water is needed to fill the jug to 2 L?

`text(400 mL)`	`text(500 mL)`	`text(600 mL)`	`text(1500 mL)`

Show Answers Only

`text(500 mL)`

Show Worked Solution

`text(Volume of water in jug)`

`= 1.5\ text(L)`

`:.\ text(Extra water to be added)`

`= 2.0 – 1.5`

`= 0.5\ text(L)`

`= 500\ text(mL)`

Measurement, NAP-D3-NC08

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)`

Number, NAP-E3-CA11

Davis wants to make 7 pavlovas.

Each pavlova needs 7 eggs. He has no eggs so he goes to the shop.

The shop sells eggs in cartons of 12.

How many cartons of eggs does Davis need to buy?

`3`	`4`	`5`	`7`

Show Answers Only

`5`

Show Worked Solution

`text(Number of eggs needed)`

`= 7 xx 7`

`= 49`

`:.\ text(Number of cartons needed)`

`=49/12`

`= 4.083…`

`=5\ text(cartons)`

Geometry, NAP-E3-CA09

A gymnast does a move where she makes 3 full somersaults and lands back on her feet.

By how many degrees has the gymnast rotated her body in this move?

`270^@`	`540^@`	`720^@`	`1080^@`

Show Answers Only

`1080^@`

Show Worked Solution

`text(One somersault rotates)\ 360^@.`

`:.3\ text(somersaults)`	`= 3 xx 360^@`
	`= 1080^@`

Geometry, NAP-E3-CA08

A sculpture is pictured from 3 different angles below:

The sculpture is in the shape of

	a rectangle and a circle.
	two spheres.
	a cylinder and a circle.
	a cylinder and a sphere.

Show Answers Only

`text(A cylinder and a sphere.)`

Show Worked Solution

`text(A cylinder and a sphere.)`

Measurement, NAP-E3-CA03

A neighbourhood soccer oval is marked out with the dimensions shown below.

What is the area of the field?

	`298\ text(square metres)`
	`2842.75\ text(square metres)`
	`5261.25\ text(square metres)`
	`8123.25\ text(square metres)`

Show Answers Only

`5261.25\ text(m²)`

Show Worked Solution

`text(Area of the soccer field)`

`= 57.5 xx 91.5`

`= 5261.25\ text(m²)`

Number, NAP-B3-NC08 SA

A number is multiplied by itself and then 9 is added.

The answer is 18.

What is the number?

Show Answers Only

`3`

Show Worked Solution

`text(Reversing the order of operations:)`

`18-9=9`

`3 xx 3 = 9`

`text(Check answer:)`

`3 xx 3 +9=18`

`:.\ text(The number is 3.)`

Geometry, NAP-B3-NC07 SA

Jeff folds this net to make a rectangular prism.

Which face is opposite of `D`?

Show Answers Only

`F`

Show Worked Solution

`F`

Measurement, NAP-B3-NC06

Which container has the least liquid?

Show Answers Only

Show Worked Solution

Geometry, NAP-B3-NC04

Johnny cuts a paper shape in half.

The shape of each half is a

`text(hexagon)`	`text(pentagon)`	`text(trapezium)`	`text(kite)`

Show Answers Only

`text(pentagon)`

Show Worked Solution

`text(pentagon)`

Number and Algebra, NAP-B3-NC03

Which one of these has the same value as `14 xx 2`?

`10 + 4 + 2`	`10 xx 2 + 4`	`10 xx 2 + 2`	`10 xx 2 + 8`

Show Answers Only

`10 xx 2 + 8`

Show Worked Solution

`14 xx 2`	`=28`
`10 xx 2 +8`	`=20 +8`
	`=28`

Statistics, NAP-C3-CA09

This table shows the number of people who visited a war memorial on weekdays over 4 weeks.

Which day had the greatest total attendance over the 4 weeks?

`text(Monday)`	`text(Tuesday)`	`text(Wednesday)`	`text(Thursday)`

Show Answers Only

`text(Tuesday)`

Show Worked Solution

`text(One strategy:)`

`text(At a glance, Thursday and Friday numbers look low.)`

`=>\ text(Checking total attendances on the 1st 3 days:)`

`text(Monday = 226)`

`text(Tuesday = 266)`

`text(Wednesday = 234)`

`:.\ text(Greatest total attendance on Tuesday.)`

Geometry, NAP-C3-CA08

This is part of the map of Hunter Street.

Jo Jo lives at number 2 which is the 1st house on the East side.

What is the number of the 16th house on Hunter Street on the east side?

`8`	`16`	`32`	`36`

Show Answers Only

`32`

Show Worked Solution

`text(1st house on East side is number 2.)`

`text(2nd house on East side is number 4.)`

`vdots`

`:.\ text(16th house on East side is number 32.)`

Measurement, NAP-C3-CA07

What is the best estimate for the mass of this basketball?

`60\ text(grams)`	`600\ text(grams)`	`6\ text(kilograms)`	`60\ text(kilograms)`

Show Answers Only

`600\ text(grams)`

Show Worked Solution

`600\ text(grams)`

Number, NAP-C3-CA06 SA

Geoffrey buys 4 peaches and 1 watermelon from a fresh fruit market.

How much does Geoffrey pay altogether?

Show Answers Only

`$4.60`

Show Worked Solution

`text(Total payment)`	`= (4 xx 0.75) + 1.60`
	`= 3.00 + 1.60`
	`= $4.60`

Measurement, NAP-F3-CA12

Michael cut a diagonal into a rectangular piece of wood.

What is the missing length?

`23\ text(cm)`	`22\ text(cm)`	`19\ text(cm)`	`17\ text(cm)`

Show Answers Only

`22\ text(cm)`

Show Worked Solution

`text(Let)\ \ d=\ text(the unknown length)`

`d+38`	`=45 + 15`
`:. d`	`=60 – 38`
	`=22\ text(cm)`

Number, NAP-F3-CA08

The shaded area on this graph shows how much of a computer file has loaded.

What percentage of the file has loaded?

`text(65%)`	`text(70%)`	`text(75%)`	`text(80%)`

Show Answers Only

`text(75%)`

Show Worked Solution

`text(Total number of bars) = 20`

`text(Number of black bars) = 15`

`:.\ text(Percentage loaded)`	`= 15/20`
	`=0.75`
	`=75text(%)`

Geometry, NAP-F3-CA04

This diagram is the net of a

	square pyramid
	triangular pyramid
	triangle
	triangular prism

Show Answers Only

`text(square pyramid)`

Show Worked Solution

`text(square pyramid)`

Measurement, NAP-E3-NC13

Tenzing started his trek at 5:30 am.

He arrived at his destination `14 1/2` hours later.

At what time did he arrive at his destination?

`7:30\ text(pm)`	`8:00\ text(pm)`	`9:30\ text(pm)`	`10:00\ text(pm)`

Show Answers Only

`text(8:00 pm)`

Show Worked Solution

`text(One strategy:)`

`5:30\ text(am plus)\ 14 1/2\ text(hours)`	`=\ text(5:30 pm plus)\ 2 1/2\ text(hours)`
	`=\ text(8:00 pm)`

Geometry, NAP-E3-NC10

Which of these designs looks identical after a quarter turn?

Show Answers Only

Show Worked Solution

Geometry, NAP-E3-NC09

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)`

Number, NAP-F3-CA10

The number 0.67 is between

	`0.06 and 0.6`
	`0.6 and 1`
	`6 and 7`
	`60 and 70`

Show Answers Only

`0.6 and 1`

Show Worked Solution

`0.6 and 1`

Algebra, NAP-F3-CA07

The rule below results in the following table.

What is the missing number in the table?

`107`	`207`	`214`	`249`

Show Answers Only

`207`

Show Worked Solution

`2 xx 100+7`	`=200+7`
	`=207`

Measurement, NAP-F3-CA06

Two sides of a triangle measure 6 cm and 12 cm.

Which one of these statements about the length of the third side is true?

	Its length is 6 cm.
	Its length is less than 6 cm.
	Its length is greater than 18 cm.
	Its length is greater than 6 cm but less than 18 cm.

Show Answers Only

`text(Its length is greater than 6 cm but less than 18 cm.)`

Show Worked Solution

`=>\ text(One side of a triangle cannot be longer than)`

`text(the sum of the 2 other sides.)`

`=>\ text(One side of a triangle cannot be shorter than)`

`text(the difference between the other 2 sides.)`

`:.\ text(Its length is greater than 6 cm but less)`

`text(than 18 cm)`

Number, NAP-F3-CA05

Freddie watches television for 5 hours each day.

What fraction of the day is Freddie not watching television?

`5/17`	`19/5`	`19/24`	`24/19`

Show Answers Only

`19/24`

Show Worked Solution

`text(Hours not watching television)`

`= 24 – 5 = 19\ text(hours)`

`:.\ text(Fraction not watching television) = 19/24`

Geometry, NAP-F3-CA03

There are seven cubes in this 3D puzzle.

The puzzle is completely dipped into orange paint.

When the cubes are separated, how many faces will be orange?

`42`	`28`	`27`	`26`	`10`

Show Answers Only

`28`

Show Worked Solution

`28`

Geometry, NAP-F3-NC12

Kimoko cut a regular pentagon into several identical pieces with no paper left over.

Which of these could be the shape of the pieces?

Show Answers Only

Show Worked Solution

`text(A pentagon can be made up of 5 isosceles)`

`text(triangles as shown below.)`

`:.\ text(The shape of the pieces could only be:)`

Geometry, NAP-F3-NC11

4 angles are labelled on the triangle pictured below.

Which angle is closest in size to 45°?

`A`	`B`	`C`	`D`

Show Answers Only

`A`

Show Worked Solution

`text(Angles)\ B and C\ text(are closer to 90°.)`

`text(Angle)\ D\ text(is obtuse.)`

`text(Angle)\ A\ text(looks close to half a right angle.)`

`:.\ text(Angle)\ A`

Geometry, NAP-F3-NC10

Simon looked at a stack of cubes from the direction of the arrow, shown in the diagram below.

Which is Simon's view of the cubes?

Show Answers Only

Show Worked Solution

Number, NAP-F3-NC08

Manou placed an apple pie into his oven.

The 1st measurement of the apple pie's temperature was − 4°C.

Twenty minutes later, a second temperature reading was taken, which measured 21°C.

What was the change in temperature between the two measurements?

decrease of 25°C	decrease of 17°C	increase of 25°C	increase of 17°C

Show Answers Only

`text(increase of)\ 25^@text(C)`

Show Worked Solution

`text(Change in temperature)`	`=21-(-4)`
	`=25^@ text(C)`

`:.\ text(An increase of 25°C.)`

Probability, NAP-F3-NC07

Tony can spin an arrow on any of the spinners below.

Which spinner gives Tony the best chance of landing on a number 2?

Show Answers Only

Show Worked Solution

`Ptext{(spinning a 2)} = 2/4=1/2`

`text(All other spinners have less than 50% chance.)`

Number, NAP-F3-NC05

A circle is divided into 5 equal areas and labelled, as shown in the diagram below.

What percentage of the circle's area has been labelled with an odd number?

`text(3%)`	`text(15%)`	`text(30%)`	`text(40%)`	`text(60%)`

Show Answers Only

`text(60%)`

Show Worked Solution

`text(S)text(ince all areas are equal,)`

`text(Percentage labelled with an odd number)`

`=text(odd sections)/text(total sections)`

`=3/5`

`=60text(%)`

Measurement, NAP-G3-NC14

The flask pictured below can hold up to 100 mL of water.

How much water is in the flask?

`60\ text(mL)`	`70\ text(mL)`	`80\ text(mL)`	`90\ text(mL)`

Show Answers Only

`text(80 mL)`

Show Worked Solution

`text(Flask is filled until the 60 mL mark.)`

`text(Flask is half filled between 60-100 mL marks.)`

`:.\ text(Volume of water in the flask)`

`=60 + (1/2 xx 40)`

`=80\ text(mL)`

Number, NAP-G3-NC11

The Park Run is a 5 kilometre fun run.

Paul completes the Park Run in 40 minutes.

Iris runs at the same speed as Paul.

How long will it take her to run 3 kilometres?

`text(24 minutes)`	`text(28 minutes)`	`text(32 minutes)`	`text(38 minutes)`

Show Answers Only

`text(24 minutes)`

Show Worked Solution

`text(Time taken for Iris to run 3 kilometres)`

`=3/5 xx 40`

`= 24\ text(minutes)`

Geometry, NAP-G3-NC10

Which object is a prism?

Show Answers Only

Show Worked Solution

Number, NAP-G3-NC09

Patrick poured one quarter of a litre of milk into his glass.

How many millilitres did Patrick pour into his glass?

	`25`
	`250`
	`750`
	`4000`
	`5000`

Show Answers Only

`250\ text(ml)`

Show Worked Solution

`text(Volume poured)`	`= 1/4 xx 1000`
	`= 250\ text(ml)`

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-NC07

Which of these patterns fits the rule, "Double the previous number and add 4"?

	`3, 4, 5, 6, 9, …`		`2, 8, 14, 20, 26, …`
	`3, 6, 12, 24, 48, …`		`2, 8, 20, 44, 92, …`

Show Answers Only

`2, 8, 20, 44, 92 …`

Show Worked Solution

`2, 8, 20, 44, 92 …`

Statistics, NAP-G3-NC06

Gavin measured the temperature every 3 hours from 6:00 am to 3:00 pm.

Which graph shows Gavin's results?

Show Answers Only

Show Worked Solution

Geometry, NAP-G3-NC05

Andre placed one block on top of another block.

This is a drawing of the front view and the side view.

Which of these is a correct top view?

Show Answers Only

Show Worked Solution

Number, NAP-G3-NC03

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`

Geometry, NAP-G3-CA12

Which of these is not a net of a square pyramid?

Show Answers Only

Show Worked Solution

Geometry, NAP-G3-CA10

Daniel is at the Racoon Ridge Inn.

Which of these directions should Daniel follow to get to Darlington?

	Go north-east to York, then turn left.
	Go north-west to York, then turn left.
	Go north-east to York, then turn right.
	Go north-west to York, then turn right.

Show Answers Only

`text(Go north-east to York, then turn right.)`

Show Worked Solution

`text(Go north-east to York, then turn right.)`

Number, NAP-G3-CA09

Penny has $5.

Chocolate bars cost $1.80.

How many chocolate bars can Penny buy?

`2`	`3`	`5`	`9`

Show Answers Only

`text(2 chocolate bars)`

Show Worked Solution

`text(Strategy 1)`

`2 xx $1.80`	`= $3.60`
`3 xx $1.80`	`= $5.40`

`text(Strategy 2)`

`5/1.80 = 2.77…\ \ text{(round down)}`

`:.\ text(Penny can only buy 2.)`

Number, NAP-G3-CA07

Jeet bought 4 pineapples and 3 mangos.

He used this calculation to work out the total cost

3 × 3.99 + 4 × 2.70

How much did one pineapple cost?

`$2.70`	`$3`	`$3.99`	`$4`

Show Answers Only

`$2.70`

Show Worked Solution

`text(S)text(ince 4 pineapples were bought,)`

`text(the cost of one is $2.70.)`

Probability, NAP-G3-CA05

Shane rolls a standard 6-sided dice once.

Which of the following is Shane most likely to roll?

	a number less than 3
	a number greater than 2
	an even number
	the number 3 or 4

Show Answers Only

`text(a number greater than 2)`

Show Worked Solution

`text(Consider the probability of each option:)`

`P\ text{(a number less than 3)} = 2/6`

`P\ text{(a number greater than 2)} = 4/6`

`P\ text{(an even number)} = 1/2`

`P\ text{(3 or 4)} = 2/6`

`:.\ text(A number greater than 2 is most likely.)`

Number, NAP-H3-NC12

The second world war finished in 1945.

Approximately how many years ago did it finish?

`60`	`70`	`80`	`90`

Show Answers Only

`80`

Show Worked Solution

`text(1945 plus 80 years is 2025.)`

`=>\ text(The closest approximation is 80 years.)`

Geometry, NAP-H3-NC11

Banjo drew a net drawing of a rectangular prism.

One of the prism's faces is drawn incorrectly.

Which face did he draw incorrectly?

`A`	`B`	`C`	`D`

Show Answers Only

`D`

Show Worked Solution

`D`

Geometry, NAP-H3-NC10

Some tiles are missing from this pattern of tiles.

When complete the pattern has two lines of symmetry.

Which of these could be the missing part of the pattern?

Show Answers Only

Show Worked Solution

Probability, NAP-H3-NC09

Two standard dice are rolled at the same time and the two numbers are added up.

Which total is most likely?

`2`	`3`	`4`	`7`

Show Answers Only

`7`

Show Worked Solution

`text(A total of 7 is most likely.)`

`text{Note that a 7 can occur in the following ways:}`

`(6,1), (1,6), (5,2), (2,5), (4,3) or (3,4)`

`text(No other option given has as many)`

`text(combinations.)`

Number, NAP-H3-NC08 SA

The baseball game had a crowd of 3000 fans.

Two thirds of the fans wore a cap.

How many fans did not wear a cap?

Show Answers Only

`1000`

Show Worked Solution

`text(Fans with no cap)`	`= 1/3 xx 3000`
	`= 1000`

Geometry, NAP-H3-NC07

Tony draws a triangle in a semi-circle and labels 4 angles as shown below.

Which angle is closest in size to a right-angle?

`A`	`B`	`C`	`D`

Show Answers Only

`B`

Show Worked Solution

`B`

Algebra, NAP-H3-NC06

The table below has a pattern. The top and bottom numbers are connected by a rule.

What is the top number when the bottom number is 28?

`5`	`7`	`12`	`17`

Show Answers Only

`7`

Show Worked Solution

`text(Top number × 4 = Bottom number)`

`text(Top number × 4 = 28)`

`:.\ text(Top number = 7)`

Number, NAP-H3-NC05

Nick had a $10 note only.

At the service station, he bought 5 iceblocks that cost $1.20 each.

How much change should he get?

`$4.00`	`$4.50`	`$6.00`	`$8.80`

Show Answers Only

`$4.00`

Show Worked Solution

`text(Change)`	`= 10 – (5 xx 1.20)`
	`= 10 – 6`
	`= $4.00`

Algebra, NAP-H3-CA20

An unknown number is added to 6.

The result is multiplied by 3 to give an answer of 12.

Which of these is the unknown number?

`− 3`	`− 2`	`2`	`30`

Show Answers Only

`−2`

Show Worked Solution

`text(Working backwards:)`

`text(S)text(ince 4 is multiplied by 3 to make 12,)`

`=>\ text(unknown + 6 = 4)`

`:.\ text(Unknown number = − 2)`

Number, NAP-H3-CA10

A candy box contains 6 white chocolate bars and 11 dark chocolate bars.

About what percentage of the candy in the box are white chocolate bars?

`6text(%)`	`35text(%)`	`58text(%)`	`65text(%)`

Show Answers Only

`35text(%)`

Show Worked Solution

`text(Percentage of white chocolate bars)`

`=6/17`

`=35text{% (nearest %)}“

Geometry, NAP-H3-CA09

This is Albert's left glove.

Albert's right glove is a mirror image of his left glove.

Which of these is Albert's right glove?

Show Answers Only

Show Worked Solution

Statistics, NAP-H3-CA08

A local triathlon club gathers data on its members and displays it in a graph below.

How many members in the triathlon club are 50 or younger?

`7`	`9`	`14`	`18`	`21`

Show Answers Only

`21`

Show Worked Solution

`text(Number of members 50 or younger)`

`=5+9+7`

`=21`

Number, NAP-H3-CA07

Which one of these numbers is a factor of 34?

`3`	`4`	`17`	`68`

Show Answers Only

`17`

Show Worked Solution

`17`

Probability, NAP-H3-CA05

Bonny draws the number 1 or 2 on a group of disks, pictured below.

One disk is chosen at random.

What is the chance the disk has a 2 drawn on it?

`1/3`	`5/15`	`5/18`	`13/18`

Show Answers Only

`5/18`

Show Worked Solution

`text(Fraction with a “2”)`	`= text(Number of 2’s) / text(Total circles)`
	`=5/18`