Band 9 – Page 2

Number, NAP-A3-NC25

A garden centre sells a potting mix made up of soil, manure and sand.

Soil makes up `3/4` of the mix and manure makes up `1/6` of the mix.

What fraction of the potting mix is sand?

`1/12`	`4/10`	`5/12`	`3/7`

Show Answers Only

`1/12`

Show Worked Solution

`text(Sand)`	`= 1 – (3/4 + 1/6)`
	`= 1 – (9/12 + 2/12)`
	`= 1/12`

Measurement, NAP-A3-CA31

2 kilometres and 80 metres is the same as

`text(280 km)`	`text(2.08 km)`	`text(2008 m)`	`text(2.80 m)`

Show Answers Only

`text(2.08 km)`

Show Worked Solution

`text(2 km + 80 m)`

`= 2000\ text(m + 80 m)`

`= 2080\ text(m)`

`= 2.08\ text(km)`

Number, NAP-A3-CA29

Mary has 60 books and splits them into four categories.

This table shows the percentage of each category.

How many sport books does Mary have?

`2`	`18`	`20`	`30`

Show Answers Only

`18`

Show Worked Solution

`text(30% of 60 books are sport books.)`

`:.\ text(Number of sport books)`	`= 30text(%) xx 60`
	`= 18\ text(books)`

Number, NAP-A3-CA28

A school has 360 students.

The ratio of boys to girls is 4 to 6.

How many boys attend the school?

`90`	`144`	`216`	`240`

Show Answers Only

`144`

Show Worked Solution

`text(One strategy)`

`text(Ratio is 10 parts split 4 : 6)`

`1/10 xx 360 = 36`

`⇒\ text(Ratio can also be expressed:)`

`4 xx 36:`	`6 xx 36`
`144:`	`216`

`:. 144\ text(boys attend the school.)`

Number, NAP-A3-CA27 SA

Patrick uses 25 litres of water every minute when he has a shower.

Kate uses 150 litres of water when she has a bath.

How many less litres of water does Patrick use in a `5 1/2` minute shower than Kate's bath?

litres

Show Answers Only

`12.5\ text(litres)`

Show Worked Solution

`text(Patrick water usage)`

`= 5.5 xx 25`

`= 137.5\ text(litres)`

`:.\ text(Less usage)`	`= 150 – 137.5`
	`= 12.5\ text(litres)`

Geometry, NAP-A3-CA26

What is the size of the angle marked `x°` in this diagram?

`100°`	`110°`	`120°`	`170°`

Show Answers Only

`110°`

Show Worked Solution

`text(From diagram, other interior angle)`

`= 180° – 120°`

`= 60°`

`:. x`	`= 60 + 50`
	`= 110°`	`(text(exterior angle equals the)` `text{sum of interior opposites})`

Geometry, NAP-A3-CA25

This is a map of mountains in a national park.

Tony is at the Hillary Lodge facing East. He turns 225° in a clockwise direction.

Which mountain is Tony now facing?

`text(Mt Black Dog)`	`text(Mt Ellis)`	`text(Mt Blart)`	`text(Mt Can Can)`

Show Answers Only

`text(Mt Blart)`

Show Worked Solution

`text(Mt Blart)`

Number, NAP-A3-CA24

A hockey stick is on sale, reduced from $220 to $165.

What percentage discount has been applied?

`text(25%)`	`text(33%)`	`text(45%)`	`text(55%)`

Show Answers Only

`text(25%)`

Show Worked Solution

`text(Discount)`	`= text(reduction)/text(original price) xx 100`
	`= ((220 – 165))/220 xx 100`
	`= 25text(%)`

Geometry, NAP-A3-NC29

This object was made by gluing identical cubes together.

This is a view from the front.

Which drawing shows a view from the right side?

Show Answers Only

Show Worked Solution

Number, NAP-A3-NC28

What is the answer to `8.8 ÷ 0.4`?

0.022	0.22	2.2	22

Show Answers Only

`22`

Show Worked Solution

`8.8 ÷ 0.4`	`= 88 ÷ 4`
	`=22`

Number, NAP-A4-NC27

Pamela has these four number cards.

Which two cards have the same value?

Show Answers Only

Show Worked Solution

`9^2`	`= 9xx9`
	`=81`
`3^4`	`= 3 xx 3 xx 3 xx 3`
	`= 81`

`:. 9^2 and 3^4\ \ text(have the same value.)`

Algebra, NAP-A4-NC26

The graph of `y = 2x-3` will be drawn on this grid.

Which two points will the straight line pass through?

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

Show Answers Only

`A and C`

Show Worked Solution

`text(Solution 1)`

`y = 2x-3\ text(passes through)\ (0, -3)`

`text(with a gradient of 2.)`

`:. A and C`

`text(Solution 2)`

`A(-1, -5), \ B(1, -5), \ C(3, 3), \ D(-2, 1)`

`=>\ text(Only)\ A and C\ text(satisfy the equation)`

`\ \ y = 2x-3.`

Algebra, NAP-A4-NC25

In a set of five consecutive whole numbers, the largest number is given the value `h`.

The smallest number in the set has a value of

`h + 4`	`5 - h`	`h - 5`	`h - 4`

Show Answers Only

`h – 4`

Show Worked Solution

`text(Numbers in descending order are:)`

`h , h – 1, h – 2, h – 3, h – 4`

`:.\ text(Smallest number is)\ \ h – 4`

Probability, NAP-A4-NC24

Peter's fitness coach runs fitness drills so that the participants are exercising intensely for 20 seconds and then resting for 30 seconds.

What is the probability that Peter is resting at any single point in time during the session?

0.2	0.3	0.5	0.6

Show Answers Only

`0.6`

Show Worked Solution

`P`	`= text(time resting)/text(total time of session)`
	`= 30/(20+30)`
	`= 0.6`

Number, NAP-A4-NC21

What is the answer to `8.8 ÷ 0.4`?

0.022	0.22	2.2	22

Show Answers Only

`22`

Show Worked Solution

`8.8 ÷ 0.4`	`= 88 ÷ 4`
	`=22`

Measurement, NAP-A4-CA30 SA

Clancy needs to paint all sides of a triangular prism.

The area of each triangular face is 12 cm².

What is the total area Clancy needs to paint?

cm²

Show Answers Only

`78\ text(cm²)`

Show Worked Solution

`text(Total Area)`	`= (2 xx 12) + 2 xx (3 xx 5) + (8 xx 3)`
	`= 78\ text(cm²)`

Geometry, NAP-A4-CA26

This is a map of mountains in a national park.

Tony is at the Hillary Lodge facing East. He turns 225° in a clockwise direction.

Which mountain is Tony now facing?

`text(Mt Black Dog)`	`text(Mt Ellis)`	`text(Mt Blart)`	`text(Mt Can Can)`

Show Answers Only

`text(Mt Blart)`

Show Worked Solution

`text(Mt Blart)`

Geometry, NAP-A4-CA25

A traffic light is 2.4 m tall. Its shadow from a nearby floodlight is 3 m long.

What is the height of the floodlight?

`text(3.6 m)`	`text(3.8 m)`	`text(4.0 m)`	`text(4.2 m)`

Show Answers Only

`text(4.0 m)`

Show Worked Solution

`text(Triangles are similar,)`

`text(S)text(ince similar triangles have sides in)`

`text(similar ratios:)`

`h/5`	`= 2.4/3`
`:. h`	`= (5 xx 2.4)/3`
	`= 4\ text(metres)`

Algebra, NAP-A4-CA24 SA

The number of rabbits, `P`, that live on an island is estimated by the rule.

`P = (3/2 M)^2 + 2` where `M` is the number of months rabbits have lived on the island.

How many rabbits are estimated to live on the island after 6 months.

rabbits

Show Answers Only

`83`

Show Worked Solution

`text(Estimated number of rabbits)`

`= (3/2 xx 6)^2 + 2`

`= 81 + 2`

`= 83`

Algebra, NAP-A4-CA23 SA

Kelly uses this rule to work out the next number in a pattern.

The first three numbers of the pattern are: 9, 51, 303, …

What is the fifth number in his pattern?

Show Answers Only

`10\ 887`

Show Worked Solution

`text(4th number)`	`= 6 xx 303`
	`= 1815`

`text(5th number)`	`= 6 xx 1815`
	`= 10\ 887`

Statistics, NAP-A4-CA22

Malcolm will travel by bus for 18 days during November.

A daily ticket will cost him $7.40 and a monthly ticket will cost him $109.80.

What is Malcolm's average daily saving on days he travels by bus if he buys a monthly ticket?

`$1.30`	`$6.10`	`$23.40`	`$125.80`

Show Answers Only

`$1.30`

Show Worked Solution

`text(C)text(ost of daily tickets)`

`= 18 xx 7.40`

`= $133.20`

`text(Monthly ticket saving)`

`= 133.20 – 109.8`

`= $23.40`

`:.\ text(Average daily saving)`

`= 23.40/18`

`= $1.30`

Number, NAP-B4-NC27

A tennis racquet costs $95.

A tax of 10% is added to the price.

Which calculation will give the new price?

`95 + 10`	`95 + 0.1`	`95 xx 0.1`	`95 xx 1.1`

Show Answers Only

`95 xx 1.1`

Show Worked Solution

`text(New price)`	`=95 + (10text{%} xx 95)`
	`=95 + 0.1 xx 95`
	`=95 xx 1.1`

Algebra, NAP-B4-NC26

Which of these points lies on the straight line joining the points `(4, 6)` and `(16, 12)`?

`(3, 3)`	`(5, 5)`	`(6, 7)`	`(10, 9)`

Show Answers Only

`(6, 7)`

Show Worked Solution

`text(Gradient)`	`= (y_2 – y_1)/(x_2 – x_1)`
	`= (12 – 6)/(16 – 4)`
	`= 6/12`
	`= 1/2`

`text(Equation of straight line)`

`m = 1/2,\ text(through)\ (4, 6),`

`y – 6`	`= 1/2 (x – 4)`
`y`	`= 1/2 x + 4`

`text(Consider)\ (6, 7):`

`7`	`= 1/2 xx 6 + 4`
	`= 7`

`:. (6, 7)\ text(lies on the line)`

Number, NAP-B4-NC25

Furby has no petrol in his car.

He buys $63 worth of petrol at $1.25 per litre.

His car uses 7 litres of petrol per 100 km travelled.

Which calculation gives the number of kilometres travelled before Furby's tank is empty again?

	`63 ÷ 1.25 xx 7 ÷ 100`
	`63 ÷ 1.25 ÷ 7 xx 100`
	`63 xx 1.25 ÷ 7 ÷ 100`
	`63 xx 1.25 xx 7 xx 100`

Show Answers Only

`63 ÷ 1.25 xx 7 ÷ 100`

Show Worked Solution

`text(Number of kilometres)`

`=\ text{(number of litres}) xx text{(km per litre)}`

`= (63 ÷ 1.25) xx (7 ÷ 100)`

`= 63 ÷ 1.25 xx 7 ÷ 100`

Algebra, NAP-B4-NC24

Ogi owns the most marbles among his friends. He owns

4 times the number Chris owns,
12 times the number Alison owns and
32 times the number Matt owns.

About how many times more marbles does Chris own than Matt?

`8`	`28`	`36`	`128`

Show Answers Only

`8`

Show Worked Solution

`text(Let)\ \ O`	`=\ text(number of Ogi’s marbles)`
`C`	`=\ text(number of Chris’ marbles etc …)`

`text(Expressing the information given as equations:)`

`O`	`= 4C`
`O`	`= 32M`
`:. 4C`	`= 32M`
`C`	`= 8M`

`:.\ text(Chris owns 8 times more marbles than Matt.)`

Geometry, NAP-B4-CA27 SA

In the figure below, the lines `p` and `q` are parallel.

What is the value of `x`?

Show Answers Only

`x=110`

Show Worked Solution

`x^@`	`= 75 + 35`
	`= 110^@`

Measurement, NAP-B4-CA25

A yoyo at the end of a string moves through a quarter circle, as shown below.

The string is 70 cm long.

The curved distance the yoyo has travelled is closest to

`text(80 cm)`	`text(90 cm)`	`text(100 cm)`	`text(110 cm)`

Show Answers Only

`110`

Show Worked Solution

`text(Distance)`	`= 1/4 xx 2pir`
	`= 1/4 xx 2 xx pi xx 70`
	`= 109.95…`
	`~~ 110\ text(cm)`

Geometry, NAP-B4-CA23

This is a map of the road a bus uses to travel from the bus depot to the beach and back again.

The map is to scale.

The total distance the bus travels on this route is 1800 metres.

What is the scale of the map?

`text(1 unit = 36 m)`	`text(1 unit = 42 m)`	`text(1 unit = 45 m)`	`text(1 unit = 50 m)`

Show Answers Only

`36`

Show Worked Solution

`text(Total grid units travelled = 50)`

`:.\ text(S)text(cale)`	`= 1800/50`
	`= 36\ text{m (to 1 unit)}`

Algebra, NAP-B4-CA26

What is the value of `6 + 2x - x^2` when `x = −3`?

`−9`	`3`	`9`	`21`

Show Answers Only

`−9`

Show Worked Solution

`6 + 2x – x^2`	`= 6 + 2(−3) – (−3)^2`
	`= 6 – 6 – 9`
	`= −9`

Algebra, NAP-B4-CA24 SA

The daily energy requirement, `E` (kilojoules), for a person of mass `m` (kilograms) is calculated using the rule `E = 7m + 7300`.

For Elijah, `E = 7755`

What is Elijah's mass?

kilograms

Show Answers Only

`65`

Show Worked Solution

`7755`	`= 7m + 7300`
`7 m`	`= 455`
`m`	`= 455/7`
	`= 65\ text(kilograms)`

Geometry, NAP-B4-CA22

The distance on the map from Hill End to Rouse Hill along the road is 5 cm.

How long will it take to walk from Hill End to Rouse Hill along the road at a speed of 6 kilometres per hour?

	1 hour 15 minutes
	1 hour 25 minutes
	12 hours 5 minutes
	12 hours 30 minutes

Show Answers Only

`text(1 hour 15 minutes)`

Show Worked Solution

`text(Distance)`	`= 5 xx 1500`
	`= 7500\ text(m)`
	`= 7.5\ text(km)`

`:.\ text(Walk Time)`	`= 7.5/6`
	`= 1.25\ text(hours)`
	`= 1\ text(hour 15 minutes)`

Number, NAP-J3-NC06

`8 + (17 - 5 xx 3 + 2) =`

What number does

represent?

`62`	`46`	`12`	`0`

Show Answers Only

`12`

Show Worked Solution

`8 + (17 – 5 xx 3 + 2)`	`=`	?
`8 + (17-15+2)`	`=`	?
`8 + 4`	`=`	?
`12`	`=`	?

Number, NAP-J3-CA38 SA

Josh and Elyse own a shed business.

They charge $3350 to build a shed.

They pay 4 workers $42 per hour for 7 hours each to construct the shed.

The materials used for the shed cost $1125.

The remaining money is divided equally between Josh and Elyse.

How much will they each receive?

Show Answers Only

`$524.50`

Show Worked Solution

`text(Shed sale price = $3350)`

`text(Labour cost)`	`= 4 xx 7 xx 42`
	`= $1176`

`text(Materials cost = $1125)`

`text(Remaining money)`	`= 3350 – (1176 + 1125)`
	`= $1049`

`:.\ text(Amount each received)`	`= 1049/2`
	`= $524.50`

Measurement, NAP-J3-CA34 SA

Penelope made a shape using 6 identical squares.

What is the perimeter of the shape?

centimetres

Show Answers Only

`108`

Show Worked Solution

`text(Length of 1 side)`	`=27/3`
	`=9\ text(cm)`

`:.\ text(Perimeter)`

`= (10 xx 9) + (4 xx 4.5)`

`= 90 + 18`

`= 108\ text(cm)`

Geometry, NAP-J3-CA29

This shape is reflected across the line and then rotated 90° clockwise.

Which image shows the appearance of the shape after these transformations?

Show Answers Only

Show Worked Solution

`text(After reflection)`

`text(After rotation)`

Number, NAP-J3-CA27

Which number sentence is correct when = 8

	12 × = 96 ÷
	7 × = 448 ÷
	5 × = 384 ÷
	3 × = 24 ÷

Show Answers Only

`7 xx 8 = 448 ÷ 8`

Show Worked Solution

`7 xx 8`	` = 448 ÷ 8`
`56`	`=56`

Geometry, NAP-A3-NC27

Tom drew this shape on grid paper.

Which one of the shapes below when joined to Tom's shape without an overlap, will not make isosceles triangle?

Show Answers Only

Show Worked Solution

Number, NAP-J4-NC06

`8 + (17 - 5 xx 3 + 2) =`

What number does

represent?

`62`	`46`	`12`	`0`

Show Answers Only

`12`

Show Worked Solution

`8 + (17 – 5 xx 3 + 2)`	`=`	?
`8 + 4`	`=`	?
`12`	`=`	?

Number, NAP-J4-CA33 SA

Cassie opens a savings account and deposits $900 into it.

She makes no more deposits and earns simple interest on her original deposit at 3.5% each year.

How much interest will Cassie earn after 4 years?

Show Answers Only

`$126`

Show Worked Solution

`text(Interest earned)`	`=Prn`
	`= 900 xx 3.5/100 xx 4`
	`= $126`

Measurement, NAP-J4-CA31

Each morning Joel walks for 25 minutes from his home to Gateshead Station.

He then travels by train to Newie Station.

From Newie Station, Joel then walks for 24 minutes to the beach for a surf.

What is the latest time Joel can leave home to arrive at the beach by 7:00?

`06:15`	`06:00`	`05:55`	`05:50`	`05:45`

Show Answers Only

`05:50`

Show Worked Solution

`text(Working backwards from arriving at the beach at 07:00,)`

`07:00\ text(less 24 minutes walking = 06:36)`

`text(1st train to arrive before 06:36 leaves Gateshead at 06:15.)`

`:.\ text{Joel must leave at 05:50 (25 minutes before 06:15).}`

Algebra, NAP-J4-CA32

A reception area has pillars that are `x` cm wide and the gap between pillars is `y` cm.

If the reception area has 12 pillars on one side, the length of that side can be represented by which expression?

`11(x + y)`	`12(x + y)`	`12x + y`	`12xy`	`12x + 11y`

Show Answers Only

`12x + 11y`

Show Worked Solution

`text(The length of the side)`

`=\ text(width of 12 pillars + width of 11 gaps)`

`= 12x + 11y`

Number, NAP-J4-CA30 SA

Willy buys 16 lollipops for $5.60.

Wonka buys 30 lollipops at the same cost per lollipop.

How much more does Wonka pay than Willy?

Show Answers Only

`$4.90`

Show Worked Solution

`text(C)text(ost of 1 lollipop) = 5.60/16 = $0.35`

`text(C)text(ost of 30 lollipops) = 30 xx 0.35 = $10.50`

`:.\ text(Extra that Wonka pays)`

`= 10.50 – 5.60`

`= $4.90`

Geometry, NAP-J4-CA27

This shape is reflected across the line and then rotated 90° clockwise.

Which image shows the appearance of the shape after these transformations?

Show Answers Only

Show Worked Solution

`text(After reflection)`

`text(After rotation)`

Statistics, NAP-J4-CA24 SA

Sixty Year 9 students were surveyed about their pets.

32 owned a dog
21 owned a cat
15 didn't have a dog or a cat

The diagram is missing some information.

How many students own both a dog and a cat?

Show Answers Only

`8`

Show Worked Solution

`text(S)text(ince 32 students own a dog,)`

`text(Number that own a dog and a cat)`

`= 32 – 24`

`= 8`

`(text(this can also be done similarly)`

`text{with cats})`

Measurement, NAP-J4-CA23

Guy is placing door casing on the top and both sides of 2 doors, as pictured below.

How many metres of door casing does he need?

`text(4.63 m)`	`text(6.74 m)`	`text(9.26 m)`	`text(67.4 m)`

Show Answers Only

`text(6.74 m)`

Show Worked Solution

`text(Metres of door casing needed)`

`= (2110 xx 2) + 2520`

`= 6740\ text(mm)`

`= 6.74\ text(m)`

Algebra, NAP-J4-CA22

Leo drew a straight line through the points (0, 5) and (3, −2) as shown in the diagram below.

What is the gradient of the line that Leo drew?

`7/3`	`3/7`	`−3/7`	`−7/3`

Show Answers Only

`−7/3`

Show Worked Solution

`text(Gradient)`	`= (y_2 – y_1)/(x_2 – x_1)`
	`= (5 – (−2))/(0 – 3)`
	`= −7/3`

Number, NAP-J4-CA18

The weight of a banana is 0.1246 kg.

What is the weight of the banana rounded to the nearest hundredth of a kilogram?

`text(0.12 kg)`	`text(0.13 kg)`	`text(0.124 kg)`	`text(0.125 kg)`

Show Answers Only

`text(0.12 kg)`

Show Worked Solution

`text(Nearest hundredth – look at the first)`

`text(3 decimal places and round to 2.)`

`:. 0.12\ text(kg)`

Number, NAP-C4-CA25

Harry sold one schnitzel wrap every 4 minutes at a surfing competition.

At this rate, how many minutes would it take to sell $320 worth of schnitzel wraps?

	`text(25 minutes)`
	`text(50 minutes)`
	`text(80 minutes)`
	`text(200 minutes)`

Show Answers Only

`text(200 minutes)`

Show Worked Solution

`text(Total wraps sold)`	`= 320 ÷ 6.40`
	`= 50`

`:.\ text(Minutes to sell $320 worth)`

`= 50 xx 4`

`= 200\ text(minutes)`

Number, NAP-C4-CA24

This graph shows the cost of a tow truck that charges a flat fee plus a cost per kilometre.

The expression to calculate the cost is

	`40 + (6 xx text{kilometres towed)}`
	`40 + (10 xx text{kilometres towed)}`
	`40 + (16.6 xx text{kilometres towed)}`
	`40 + (100 xx text{kilometres towed)}`

Show Answers Only

`40 + (10 xx text{kilometres towed)}`

Show Worked Solution

`text{The flat fee is $40 (i.e. the cost for 0 km).}`

`text(Each kilometre towed increases the cost of the)`

`text(tow truck by $10.)`

`40 + (10 xx text{kilometres towed)}`

Geometry, NAP-C4-CA23 SA

Brett drew the shape below using rectangles and straight lines.

What is the value of `x`?

`text(degrees)`

Show Answers Only

`164^@`

Show Worked Solution

`text(Using the right angle property of the rectangles,)`

`90^@ – 74^@ = 16^@`

`text(Vertically opposite angles are equal,)`

`:. x^@`	`= 180 – 16`
	`= 164^@`

Algebra, NAP-C4-CA22

Richard is ascending in a hot air balloon.

The temperature drops by the same amount every 50 metres that Richard ascends.

At ground level the temperature is 31°C.

At a height of 600 metres, the temperature is –5°C.

What is the air temperature at a height of 200 metres?

`text(16°C)`	`text(18°C)`	`text(19°C)`	`text(22°C)`

Show Answers Only

`text(19°C)`

Show Worked Solution

`text(There are)\ 12 xx 50\ text(m distances in 600 m.)`

`text(Temperature drop each 50 m)`

`= {31 – (-5)}/12`

`= 36/12`

`= 3°`

`:.\ text(Temperature at 200 m)`

`= 31 – (4 xx 3)`

`= 19\ text(°C)`

Number, NAP-C4-CA19

Pamela looks at the price of four sunscreens.

Which sunscreen is the cheapest per litre?

`text(Sun)`	`text(Sport)`	`text(Block)`	`text(Wet)`

Show Answers Only

`text(Sport sunscreen)`

Show Worked Solution

`text(Sun)\ =1090/1200 = 0.91\ text(c/mL)`

STRATEGY: Finding the cost per mL is much more efficient in answering this question than finding the cost per litre.

`text(Sport)\ =540/600 = 0.9\ text(c/mL)`

`text(Block)\ =475/500 = 0.95\ text(c/mL)`

`text(Wet)\ =740/750 = 0.99\ text(c/mL)`

`:.\ text(Sport sunscreen is the cheapest per litre.)`

Algebra, NAP-C4-CA18

A plumber calculates the price of a job using a service fee and an amount per hour.

This table shows some of the job prices.

How are the jobs calculated?

	$60 service fee + $35 per hour
	$60 service fee + $70 per hour
	$58 service fee + $72 per hour
	$58 service fee + $36 per hour

Show Answers Only

`text($58 service fee)\ +\ text($36 per hour)`

Show Worked Solution

`text(Testing Option 4 equation with the table values:)`

`130`	`= 58 + 2 xx 36`
`202`	`= 58 + 4 xx 36`
`274`	`= 58 + 6 xx 36`
`346`	`= 58 + 8 xx 36`

`:.\ text($58 service fee)\ +\ text($36 per hour)`

Algebra, NAP-E4-CA25 SA

Bill creates a pattern of branches and nodes on a computer.

Bill continued the pattern until the shape had 3279 branches.

How many nodes did the shape have?

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`1093\ text(nodes)`

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`text(Pattern shows that:)`

`text(Number of branches)/text(Number of nodes)\ = 3/1 = 12/4 =3`

`=>\ text(If there are 3279 branches,)`

`:.\ text(Number of nodes)`	`= 3279 -: 3`
	`= 1093\ text(nodes)`

Algebra, NAP-G4-NC25 SA

The table below shows the relationship between the width of a tree's trunk in centimetres and how old it is in months.

If this pattern continues, how old would you expect a tree with a 4.5 cm wide trunk to be?

months

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`30`

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`text(Continuing the pattern,)`

`text(24 months) => 4 1/8`

`text(26 months) => 4 1/4`

`text(28 months) => 4 3/8`

`text(30 months) => 4 1/2`

Geometry, NAP-B2-35 SA

Lisa builds this 3D object for a playground with cubes.

She paints all faces of the object, including the base.

How many cubes are painted on exactly 2 faces?

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`9`

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`text(9 cubes will be painted on exactly 2 faces.)`

`text{(the shaded cubes below will be the ones}`

`text{with exactly 2 faces painted.)}`

Number and Algebra, NAP-B2-37 SA

The number of soccer players in France is 11.67 million.

The number of soccer players in Spain is 7.83 million.

How many more soccer players are in France than in Spain?

million

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`3.84\ text(million)`

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`11.67\ text(million) – 7.83\ text(million)`

`=3.84\ text(million)`

Number and Algebra, NAP-B2-36

Penny has 5 birds that each eat 30 grams of bird food a day.

She has 6kg of bird food.

How many days will her bird food last for?

`4\ text(days)`	`20\ text(days)`	`40\ text(days)`	`200\ text(days)`

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`40\ text(days)`

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`text(Bird food consumption per day)`

`=5 xx 30`

`= 150\ text(g)`

`:.\ text(Number of days the bird food will last)`

`= 6\ text(kg) -: 150\ text(g)`

`= 6000 -: 150`

`= 40\ text(days)`

Geometry, NAP-B1-35 SA

Barry stacked some cubes and made this solid object.

How many cubes are in Barry's object altogether?

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`26`

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`text(Looking at each layer)`

`text(Bottom layer)`	`= 13\ text(cubes)`
`text(2nd layer)`	`= 7\ text(cubes)`
`text(3rd layer)`	`= 4\ text(cubes)`
`text(Top layer)`	`= 2\ text(cubes)`

`=>\ text(Total cubes used)`

`= 13 + 7 + 4 + 2`

`= 26`

Statistics, NAP-F1-35 SA

Brett made a graph showing all the coins in his money box.

How much money does Brett have in coins?

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`$8.30`

Show Worked Solution

`text(Total of Brett’s money)`

`= 2 xx $1 + 8 xx 50¢ + 6 xx 20¢ + 4 xx 10¢ + 14 xx 5¢`

`= $2 + $4 + $1.20 + 40¢ + 70¢`

`= $8.30`