Band 7 – Page 4

Algebra, NAP-J4-CA08

Bobby places a disc at (4, −2).

He then moves the disc up 4 units.

What are the coordinates of the new position of the disc?

`text{(8,−2)}`	`(4,2)`	`text{(4,−6)}`	`text{(0,−2)}`

Show Answers Only

`(4,2)`

Show Worked Solution

`(4,2)`

Algebra, NAP-J4-CA07

Ethan writes the sequence:

`7, \ 0.7, \ 0.07, \ 0.007, …`

Describe the rule he uses to write the next number in this sequence.

	`text(add 6.3)`
	`text(subtract 6.3)`
	`text(multiply by 0.01)`
	`text(divide by 0.1)`
	`text(multiply by 10)`
	`text(divide by 10)`

Show Answers Only

`text(divide by 10)`

Show Worked Solution

`7 ÷ 10`	`= 0.7`
`0.7 ÷ 10`	`= 0.07`
`0.07 ÷ 10`	`= 0.007`

`:.\ text(Rule: divide by 10).`

Number, NAP-J4-CA06

Tran is a baker and sells 100 loaves of bread at the markets. Each loaf costs him $2.25 to make.

He sells 80 loaves for $4.95 each.

In the last hour of the market, he sells the last 20 loaves for $2 each.

What is the total profit or loss of the 100 loaves?

`−$5.00`	`$211.00`	`$216.00`	`$436.00`

Show Answers Only

`$211.00`

Show Worked Solution

`text(Total profit/loss)`	`=\ text(sales revenue – costs)`
	`=(80 xx 4.95 + 20 xx 2) – (100 xx 2.25)`
	`= 436 – 225`
	`= $211`

Number, NAP-J4-CA05

Megan has `1/8` cup of sugar.

She needs `1 1/2` cups of sugar for a cake recipe she is using.

How much more sugar does Megan need for the recipe?

`1 1/8\ text(cups)`	`1 1/4\ text(cups)`	`1 3/8\ text(cups)`	`1 5/8\ text(cups)`

Show Answers Only

`1 3/8\ text(cups)`

Show Worked Solution

`text(Sugar needed)`	`= 1 1/2 – 1/8`
	`= 1 3/8\ text(cups)`

Number, NAP-J4-CA02

It takes Cadel 1.6 minutes to ride his bike one full lap around a lake track.

How many laps does Cadel complete in 8 minutes?

`2`	`5`	`12`	`13`

Show Answers Only

`5`

Show Worked Solution

`text(Laps)`	`= 8 ÷ 1.6`
	`= 5\ text(laps)`

Number, NAP-B4-CA15

Jake bought a mobile phone at 25% off the original price.

The original price was $380.

How much did Jake pay for the mobile phone?

`$95`	`$285`	`$342`	`$355`

Show Answers Only

`$285`

Show Worked Solution

`text(Price of mobile)`	`=380 – (text(25%) xx 380)`
	`=380 – 95`
	`=$285`

Number, NAP-B4-CA12

`36 xx`

`= 27`

`1/3`	`3/4`	`4/3`	`3/1`

Show Answers Only

`3/4`

Show Worked Solution

`36 xx n`	`=27`
`:.n`	`=27/36`
	`=3/4`

Measurement, NAP-B4-CA10 SA

What is the size of angle `ABC`?

`text(degrees)`

Show Answers Only

`63^@`

Show Worked Solution

`text(Measure the angle using the inside numbers and use)`

`text(the intervals on the outside to improve accuracy.)`

`angle ABC =63^@`

Number, NAP-B4-NC14

Murray has 36 red plums and 18 purple plums.

What fraction of the plums are red?

`1/36`	`1/3`	`1/2`	`2/3`

Show Answers Only

`2/3`

Show Worked Solution

`text(Fraction of red plums)`	`=text(red plums) / text(total plums)`
	`=36/(36+18)`
	`=36/54`
	`=2/3`

Probability, NAP-B4-NC10

A car dealership contains 12 black, 8 red, 10 blue, 16 silver and 4 white cars.

Walter wears a blindfold and chooses one car at random.

What is the chance that the car is blue?

`1/2`	`1/4`	`1/5`	`1/10`

Show Answers Only

`1/5`

Show Worked Solution

`Ptext{(Blue car)}`	`=\ text(number of blue cars)/text(total number of cars)`
	`=10/50`
	`=1/5`

Algebra, NAP-B4-NC06 SA

The area of the shaded rectangle below is 84 cm².

What is the length of the shaded rectangle?

Show Answers Only

`text(14 cm)`

Show Worked Solution

`text(Let)\ \ d =\ text(length of rectangle)`

`d xx 6`	`=84`
`:. d`	`=84/6`
	`=14\ text(cm)`

Number, NAP-B4-NC05 SA

A number is multiplied by itself and then 12 is added.

The answer is 28.

What is the number?

Show Answers Only

`4`

Show Worked Solution

`text(Reversing the order of operations:)`

`28-12=16`

`sqrt16 = 4`

`text(Check answer:)`

`4 xx 4 +12=28`

`:.\ text(The number is 4.)`

Geometry, NAP-G4-CA05

Which shape below has 2 shaded triangles the same size and shape?

Show Answers Only

Show Worked Solution

Number, NAP-C4-CA11

A lottery prize of $6366 is shared equally among 12 friends.

How much does each person get in dollars and cents?

dollars and

cents

Show Answers Only

`$530.50`

Show Worked Solution

`text(Cash for each person)`

`=6366/12`

`= $530.50`

Measurement, NAP-C4-CA06

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)`

Geometry, NAP-E4-NC09

Milo is drawing the net of this box.

Where should he draw the shape on the box?

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

Show Answers Only

`text(A)`

Show Worked Solution

Number, NAP-F4-NC08

1102 is a tri-square number because

`1^2 + 1^2 + 0^2 = 2`

The next tri-square number after 1102 is

`1104`	`1113`	`1209`	`1126`

Show Answers Only

`1113`

Show Worked Solution

`1^2 + 1^2 + 1^2`	`= 1 + 1 + 1`
	`= 3`

`:. 1113\ text(is the next tri-square number.)`

Geometry, NAP-B1-32

Jude left the factory and turns left on Bop St.

He then turns left immediately and walks straight ahead.

What building does he pass?

`text(school)`	`text(cinema)`	`text(shop)`	`text(cafe)`

Show Answers Only

`text(shop)`

Show Worked Solution

`text(shop)`

Geometry, NAP-G4-NC12

Peter has a rectangular piece of paper.

He folds it along the diagonal `BD`.

After folding, where will point `C` finish?

`D`	`E`	`F`	`G`	`H`

Show Answers Only

`G`

Show Worked Solution

`G`

Measurement, NAP-B2-28

She started gardening at 10:44 am and finished at 12:10 pm.

How long did Jess spend gardening?

`text(36 mins)`	`text(54 mins)`	`text(1 hour 22 mins)`	`text(1 hour 26 mins)`

Show Answers Only

`text(1 hour 26 mins)`

Show Worked Solution

`text(10:44 am to 11:44 am) = 1\ text(hour)`

`text(11:44 am to 12:10 pm) = 26\ text(minutes)`

`:.\ text(1 hour and 26 minutes.)`

Geometry, NAP-B2-26

Mila draws a shape with no parallel sides.

Which shape did Mila draw?

Show Answers Only

Show Worked Solution

Measurement, NAP-B2-22 SA

A rectangular car park is shown below with a perimeter of 70 m.

What is the length of the short side `x`?

`text(metres)`

Show Answers Only

`10\ text(m)`

Show Worked Solution

`text(Perimeter)`	`=25 + 25 + x +x`
`70`	`=50 + 2x`
`:. x`	`=10`

Measurement, NAP-B1-33

It took Will 145 minutes to travel to his grandmother's house.

The time he travelled is closest to

	`1 3/4\ text(hours)`
	`2 1/4\ text(hours)`
	`2 1/2\ text(hours)`
	`2 3/4\ text(hours)`

Show Answers Only

`2 1/2\ text(hours)`

Show Worked Solution

`text(There are 60 minutes in 1 hour.)`

`=> 145\ text(minutes = 2 hours 25 minutes)`

`=>\ text(Closest to)\ 2 1/2\ text{hours (150 minutes)}`

Number and Algebra, NAP-C1-33 SA

A swim centre has 10 boxes of goggles.

Three boxes have 8 pairs of goggles in each box.

The rest have 5 pairs of goggles in each box.

How many pairs of goggles are there altogether?

Show Answers Only

`59`

Show Worked Solution

`text(Total number of goggles)`

`= (3 xx 8) + (7 xx 5)`

`= 24 + 35`

`= 59`

Statistics, NAP-C1-31 SA

Students could pick one activity for their sport.

The table below lists the activities and how many students chose them.

Some students changed activities.

The activities now have an equal number of students.

How many students are now in each team?

Show Answers Only

`8`

Show Worked Solution

`text(Total students)`	`= 6 + 8 + 11 + 7 + 8`
	`= 40`

`text{Numbers in each activity (when equal)}`

`= 40 ÷ 5`

`= 8\ text(students)`

Number and Algebra, NAP-D1-34 SA

Emma wants to make exactly 28 cookies.

How many eggs does she need?

Show Answers Only

`7\ text(eggs)`

Show Worked Solution

`text(2 eggs) -> 8\ text(cookies)`

`text(4 eggs) -> 16\ text(cookies)`

`text(6 eggs) -> 24\ text(cookies)`

`text(7 eggs) -> 28\ text(cookies)`

Number and Algebra, NAP-D1-33 SA

A gold class ticket to the movies costs $16.

A normal ticket to the movies costs three-quarters of a gold class ticket.

What is the cost of three normal tickets?

Show Answers Only

`$36`

Show Worked Solution

`text(C)text(ost of a normal ticket)`

`=3/4 xx $16`

`=$12`

`=>\ text(C)text(ost of 3 normal tickets)`

`=3 xx $12`

`=$36`

Number and Algebra, NAP-D1-32 SA

What number is exactly halfway between 195 and 235?

Show Answers Only

`215`

Show Worked Solution

`text(Each interval is worth 5.)`

`text(Halfway is 4 intervals from each number.)`

`=>\ text(Halfway)`	`= 195 + (4 xx 5)`
	`= 195 + 20`
	`= 215`

Geometry, NAP-D1-28

Which one of these is not the net of a cube?

Show Answers Only

Show Worked Solution

Geometry, NAP-G1-35 SA

This is a map of a pathway through Valentine's school.

Valentine walked along the path from the start to the end.

For about how many metres did Valentine walk west?

metres

Show Answers Only

`40\ text(m)`

Show Worked Solution

`text(Metres travelled west)`

`= 10 + 15 + 10 + 5`

`= 40\ text(m)`

Number and Algebra, NAP-E1-34

5 of plastic cups cost 30 cents.

How many cents does one cup cost?

cents

What is the greatest number of cups that can be bought with exactly $6?

Show Answers Only

`6\ text(cents), 100\ text(cups)`

Show Worked Solution

`text(C)text(ost of 1 cup)`	`= 30 ÷ 5`
	`= 6\ ¢`

`=>\ text(Greatest number of cups)`

`= $6.00 ÷ 6\ ¢`

`= 600\ ¢ ÷ 6\ ¢`

`= 100\ text(cups)`

Number and Algebra, NAP-E1-33 SA

Each new number in this pattern is made by adding together the two numbers before it.

`, 8, 13, 21, 34`

What is the missing number in the pattern?

Show Answers Only

`5`

Show Worked Solution

`8 +`		`= 13`
		`= 13 – 8`
		`= 5`

Number and Algebra, NAP-E1-32 SA

Mr. Lantry asked his students to follow the steps below.

Step 1: Think of an even number between 1 and 10.
Step 2: Halve it.
Step 3: Add twice the number you started with.
Step 4: Multiply by 2.
Step 5: Divide by the number you started with.

What answer should everyone get?

Show Answers Only

`5`

Show Worked Solution

`text{Step 1: Choose 8 (say)}`

`text(Step 2: 8 ÷ 2 = 4)`

`text{Step 3: 4 + (2 × 8) = 20}`

`text(Step 4: 20 × 2 = 40)`

`text(Step 5: 40 ÷ 8 = 5)`

`=>\ text(All numbers should result in an answer of 5.)`

Measurement, NAP-E1-31 SA

This is the sign at a ride at a fun park.

How many centimetres tall is Olaf?

centimetres

Show Answers Only

`text(116 centimetres)`

Show Worked Solution

`text(Olaf’s height)`	`=\ text(1 m 16 cm)`
	`=\ text(116 cm)`

Geometry, NAP-E1-30 SA

Siro makes an object by putting 12 cubes together.

He then paints the object.

He separates each cube again after painting on all sides except where it sits on the ground.

How many cubes have paint on only two faces?

Show Answers Only

`6`

Show Worked Solution

`text(The corner cubes will be painted on 3 sides.)`

`text(The two middle cubes will be pained on 1 side.)`

`=>\ text(The edge cubes not on the corners will each)`

`text(be painted on two sides.)`

`=>\ text(6 cubes have paint only on 2 sides.)`

Number and Algebra, NAP-G1-32 SA

Barry bought a hotdog and a can of soda for lunch.

He payed with a $10 note and got $3 change.

How much did the hotdog cost?

Show Answers Only

`$4.30`

Show Worked Solution

`text(C)text(ost of hotdog and soda)`

`= $10 – $3`

`= $7`

`text(C)text(ost of hotdog)`

`= $7 – $2.70`

`= $4.30`

Geometry, NAP-G1-31

Perry has two blocks.

He joins them to form the solid shape below.

How many edges does the T-shaped object have?

`14`	`15`	`16`	`24`

Show Answers Only

`24`

Show Worked Solution

`text(8 edges on the top face.)`

`text(8 edges on the bottom face.)`

`text(8 edges joining the top and bottom faces.)`

`=> 24\ text(faces in total)`

Number and Algebra, NAP-G1-28 SA

There are 12 children in a year 3 class.

They are split up into 2 groups.

One group has 3 times the number of children as the other group.

How many children are in the larger group?

Show Answers Only

`9`

Show Worked Solution

`text(12 children)`

`text(Splits must be:)`

`text(Group 1 − 3 children)`

`text(Group 2 − 9 children)`

Number and Algebra, NAP-F1-32 SA

Luke and Seb receive pocket money each week.

Luke gets $3 and Seb gets $6.

After 12 weeks, how much more pocket money has Seb received than Luke?

Show Answers Only

`$36`

Show Worked Solution

`text(Strategy one:)`

`text(Seb receives $3 more each week.)`

`:.\ text(After 12 weeks, the extra money)`

`= 12 xx 3`

`= $36`

`text{Strategy two (longer):}`

`text(Seb’s money after 12 weeks)`

`= 12 xx 6`

`= $72`

`text(Luke’s money after 12 weeks)`

`= 12 xx 3`

`= $36`

`:.\ text(Extra)`	`= 72 – 36`
	`= $36`

Number and Algebra, NAP-F1-28 SA

Jonah ran 5 times around a track.

He ran a total of 3000 metres.

Toby ran twice around the same track.

How many metres did Toby run?

Show Answers Only

`1200\ text(metres)`

Show Worked Solution

`text(Length of 1 lap)`	`= 3000 ÷ 5`
	`= 600\ text(metres)`

`text(Metres in 2 laps)`	`= 600 xx 2`
	`= 1200\ text(metres)`

Number and Algebra, NAP-H1-33 SA

Three children were playing a card game.

There were 52 cards. Each child was given 11 cards.

How many cards were left over?

Show Answers Only

`19\ text(cards)`

Show Worked Solution

`text(Cards used)`	`= 3 xx 11`
	`= 33`

`:.\ text(Cards left over)`	`= 52 – 33`
	`= 19`

Measurement, NAP-H1-32

Two pumpkins are weighed on a scale.

The mass of one pumpkin is closest to

`text(2 kg)`	`2 1/2\ text(kg)`	`3 1/2\ text(kg)`	`4 1/2\ text(kg)`	`text(5 kg)`

Show Answers Only

`2 1/2\ text(kg)`

Show Worked Solution

`text(2 pumpkins weigh around 5 kg.)`

`:.\ text(Mass of 1 pumpkin)`	`~~5-:2`
	`~~ 2 1/2\ text(kg)`

Measurement, NAP-I1-32

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-I1-33

Gordon made this number sentence with cards.

Which of these cards will make the number sentence correct?

Show Answers Only

Show Worked Solution

`50-4=46`

Geometry, NAP-H1-34 SA

A building's floor plan is pictured below.

Vlad enters the building through the western door and leaves through the northern door.

What is the smallest number of rooms he must walk through?

Show Answers Only

`5\ text(rooms)`

Show Worked Solution

`5\ text(rooms)`

Statistics, NAP-H1-31 SA

The goals scored by 4 players in a season of water polo were recorded in the graph below.

Will scored 8 goals in the season.

Sam scored 5 goals.

How many more goals did Bilbo score than Ginili?

Show Answers Only

`7\ text(more goals)`

Show Worked Solution

`text(S) text(ince Will scored 8 goals,)`

`= 2\ text(goals)`

`=>\ text(Bilbo scored 10 goals)`

`=>\ text(Ginili scored 3 goals)`

`:.\ text(Bilbo scored 7 more goals than Ginili.)`

Number and Algebra, NAP-C2-24

Camilla designs the following pattern with matchsticks.

How many sticks will Pattern 4 have?

`21`	`27`	`29`	`35`

Show Answers Only

`29`

Show Worked Solution

`text(Each branch end in Pattern 3 will connect to)`

`text(2 more sticks.)`

`:.\ text(Pattern 4 sticks)`	`=13 + (8 xx 2)`
	`=29`

Measurement, NAP-C2-23

Four puppies had their mass measured in their first check-up with the vet.

Which puppy has the greatest mass?

Show Answers Only

Show Worked Solution

`text(Converting all units to grams to compare:)`

`text(Max: 4.4 kg = 4400 grams)`

`text(Jessie: 4300 grams)`

`text(Rocket: 4.05 kg = 4050 grams)`

`text(Barney: 4080 grams)`

`:.\ text(The puppy with the greatest mass is)`

Geometry, NAP-C2-30 SA

This 3D object is made by joining cubes.

It is then lowered into a tin of paint and completely submerged.

When the object is taken back out of the paint tin, how many faces are painted?

Show Answers Only

`18`

Show Worked Solution

`18`

Number and Algebra, NAP-C2-29 SA

Write a number in the box to make this number sentence correct.

`18 + 24 >`

`+ 4`

Show Answers Only

`text{(Any number < 38)}\ + 4`

Show Worked Solution

`18+24`	`=18+20+4`
	`=38+4`
`:.18+24`	`> text{(Any number < 38)}\ + 4`

Measurement, NAP-C2-26

Eva is 4 years old.

Her sister Harriet is exactly 15 months old.

How many months older than Harriet is Eva?

`11`	`25`	`31`	`33`

Show Answers Only

`33\ text(months)`

Show Worked Solution

`text(Age of Eva in months)`

`= 4 xx 12`

`= 48\ text(months)`

`:. 48 – 15 = 33\ text(months)`

Number and Algebra, NAP-F2-33

A soccer match attracted a crowd of 17 221 people.

One third of the people at the match supported the away team.

Which of these is the closest to the number of people at the match who supported the away team?

`500`	`600`	`5000`	`6000`

Show Answers Only

`6000`

Show Worked Solution

`text(One strategy:)`

`1/3 xx 17\ 221`	`~~(18\ 000)/3`
	`~~6000`

Number and Algebra, NAP-F2-31

Andy buys a chocolate bar for 95 cents from the shop.

He has 4 coins in his hand and pays the exact amount.

Which coin is not in Andy's hand?

`text(5 cent)`	`text(10 cent)`	`text(20 cent)`	`text(50 cent)`

Show Answers Only

`text(10 cent)`

Show Worked Solution

`text(4 coins can only make up 95 cents as follows:)`

`1 xx 50\ text(cent)`

`2 xx 20\ text(cent)`

`1 xx 5\ text(cent)`

`:.\ text(Andy doesn’t have a 10 cent.)`

Number and Algebra, NAP-F2-30

Ten people share in a lottery prize of $5650.

They keep $550 each and give the rest to charity.

How much money in total do they have to give to charity?

`$5100`	`$510`	`$150`	`$15`

Show Answers Only

`$150`

Show Worked Solution

`text(Lottery payout to each person)`

`=5650/10`

`=$565`

`:.\ text(Total amount they give to charity)`

`=(565-550) xx 10`

`=$150`

Geometry, NAP-F2-28

Hanse drew four shapes.

Which of these has no line of symmetry?

Show Answers Only

Show Worked Solution

`text(Consider each option:)`

`text(Option 1: 5 lines of symmetry)`

`text(Option 2: 1 line of symmetry)`

`text(Option 3: no lines of symmetry)`

`text(Option 4: 1 line of symmetry)`

Number and Algebra, NAP-F2-27

Which of these expressions has a value that is closest to 5?

	`4 1/4 + 1 1/2`
	`6 1/4 - 1 3/4`
	`7 - 1 1/2`
	`3 3/4 + 1 1/2`

Show Answers Only

`3 3/4 + 1 1/2`

Show Worked Solution

`text(Consider each option:)`

`4 1/4 + 1 1/2 = 5 3/4`

`6 1/4 – 1 3/4 = 4 1/2`

`7 – 1 1/2 = 5 1/2`

`3 3/4 + 1 1/2 = 5 1/4`

`:. 3 3/4 + 1 1/2\ \ text(is closest to 5.)`

Statistics, NAP-F2-22

Camilla asked each student in four year 5 classes if they played soccer.

She recorded the results in the graph below.

Which class had the highest number of students that played soccer?

`text(Class A)`	`text(Class B)`	`text(Class C)`	`text(Class D)`

Show Answers Only

`text(Class A)`

Show Worked Solution

`text(Consider each option:)`

`text(Class A): 8+6=14`

`text(Class B): 10+3=13`

`text(Class C): 4+9=13`

`text(Class D): 11+2=13`

`:.\ text(Class A has the most soccer players.)`

Geometry, NAP-F2-23

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 and Algebra, NAP-E2-35 SA

Kurt, Shane and Harry collect guitars and own 70 guitars between them.

Kurt owns half as many as Shane.

Harry owns four times as many as Kurt.

How many guitars does Kurt own?

Show Answers Only

`10`

Show Worked Solution

`text(Strategy one)`

`text(Try some values for Kurt:)`

`text(If Kurt has 5, Harry has 20, Shane has 10.)`

`=>\ text(i.e. a total of 35 guitars)`

`:.\ text(When Kurt has 10 guitars, there are 70 in total.)`

`text{Strategy two (using algebra)}`

`text(Expressing the information as equations:)`

`K + S + H = 70\ …\ (1)`

`K`	`= 1/2 S`
`=> S`	`= 2K\ …\ (2)`
`H`	`= 4K\ …\ (3)`

`text{Substitute (2) and (3) into (1)}`

`K + 2K + 4K`	`= 70`
`7K`	`= 70`
`K`	`= 10`

`:.\ text(Kurt owns 10 guitars.)`

Number and Algebra, NAP-E2-34 SA

Willy has 8 packets of lollipops.

There are 5 lollipops in each small packet.

There are 12 lollipops in each large packet.

Willy has 6 small packets.

How many lollipops does he have altogether?

Show Answers Only

`54\ text(lollipops)`

Show Worked Solution

`text(S) text(ince Willy has 6 small packets`

`=>\ text(Willy has 2 large packets)`

`:.\ text(Total number of lollipops)`

`= (6 xx 5) + (2 xx 12)`

`=30+24`

`= 54`