NUMeraCymelbabastow.weebly.com/uploads/9/8/9/4/9894393/yr9p_cn2012.pdf · 7 © ACARA 2012 YEAR 9 NUMeraCy (CalCUlatOr allOWeD) 11 The opening hours of a post office are shown on this

9year

2012

Use 2B or HB pencil only

© Australian Curriculum, Assessment and Reporting Authority, 2012

0:40 Time available for students to complete test: 40 minutes

SeSSION 1

NUMeraCy CalCUlatOr allOWeD

Do not write on this page.

3

© ACARA 2012

YEAR 9 NUMeraCy (CalCUlatOr allOWeD)

3

PraCtICe QUeStIONS

P1 50, 100, 150, 200, 250, ?

Which number comes next in this sequence?

251 260 300 350

P2 Write a number in the box to make this number sentence correct.

6 + 4 =

4

© ACARA 2012


1 An airline bought 6 new planes for a total cost of $721.5 million. Each plane cost the same amount.

How much did each plane cost?

$120.25 million$360.75 million$715.5 million

$4329 million

2 The map shows the different directions four cars are travelling.

A B C

D

North

Which car is travelling south-east?

Car A Car B Car C Car D

3 Martina asked students in her class where they were born. She used the data to draw this graph.

Region of birth

AustralasiaAsiaEuropeAfricaOther

Where were about a quarter of the students born?

Australasia Asia Europe Africa

5

© ACARA 2012


4 These are three pictures of the same sculpture.

The sculpture is in the shape of

a rectangle and a circle.a rectangle and a sphere.a prism and a circle.

a prism and a sphere.

5 Lee wants to bake 7 cakes. Each cake needs 4 eggs. He has no eggs so he goes to the shop. The shop sells eggs in cartons of 6.

How many cartons of eggs does Lee need?

2 4 5 7

6 Every day Jim drives 20 kilometres to work. On Monday his average speed was 80 kilometres per hour. On Tuesday his average speed was only 20 kilometres per hour.

How many more minutes did it take Jim to drive to work on Tuesday than Monday?

15 45 60 75

6

© ACARA 2012


7 Which of these numbers is closest in value to 221272 ?

0.5 0.6 0.7 0.8 1.2

8 Which arrow is pointing to the approximate position of 800 on a number line?

20 40 30 50 80 100 300 500

9 Which shape has 25 shaded?

10 This flowchart shows the rules for a number game.

Inputnumber

Outputnumber

Is thenumber

odd?

yes

no

Add 3 to thenumber

Divide the number by 2

The output number is 16.

What are two possible values for the input number?

8 and 13 8 and 19 13 and 32 19 and 32

7

© ACARA 2012


11 The opening hours of a post office are shown on this sign.

How many hours each week is the post office open?

60 70 84 98

12 Alicia has a bag of jelly beans. 30% of the jelly beans are red. She takes a blue jelly bean from the bag and eats it. Without looking, she takes another jelly bean from the bag.

What is the chance that this jelly bean is red?

less than 30%equal to 30%greater than 30%

13 Tiles of two shapes are used to cover a floor.

The basic shapes used in designing the tiles are identical rectangles and semicircles.

Which of the following statements is true about these two tile shapes?

They have the same area and the same perimeter.They have different areas but the same perimeter.They have the same area but different perimeters.

They have different areas and different perimeters.

8

© ACARA 2012


14 Mike sells cars. His weekly salary, S dollars, is calculated using this rule:

S = 500 + 0.02V

where V is the total value in dollars of the cars he sells that week. Last week, the total value of the cars Mike sold was $120 000.

What was Mike’s salary last week?

$740 $1205 $2900 $6000 $24 000

15 Which of the following equations is not true for all positive values of y?

y2 = y × 20 = y – yy + y = 2 × y

1 = y ÷ y

16 Tim takes 72 paces to walk across the school yard. His pace is 90 centimetres long. Lara’s pace is 80 centimetres long.

How many paces does Lara take to walk across the school yard?

62 64 81 82 100

17 Sarah is painting a wall using three colours.

She paints 13 of the wall blue,

14 of the wall green and the rest yellow.

What fraction of the wall does she paint yellow?

1012

512

57

712

27

9

© ACARA 2012


18 Sally collected some data from her class. She used the data to draw this graph on her computer. She accidentally removed all the labels.

Which kind of data could Sally be showing on her graph?

Horizontal axis Vertical axis

Favourite colour Number of studentsHand span HeightGender Height

Shoe size Number of students

19 Nina is making a line of tiles on a wall. The tiles come in 6 designs and she always puts the tiles in the same order. The picture shows the start of her line of tiles.

Each tile costs $3.50 and she uses $112 worth of tiles.

Which of these is the last tile in her line of tiles?

20 200 = 1000 − n4

What is the value of n ?

50 200 800 3200 4800

10

© ACARA 2012


21 The sum of three angles around a point is 360°. Two of these angles are acute angles.

What must the third angle be?

an acute anglean obtuse anglea straight angle

a reflex angle

22 Starting at point P, Dave walks around this swimming pool. He starts by heading north.

In which direction is he heading when he is 23 of the

distance around?

west south-west south south-east

23 Jason uses these formulas to calculate how the money in his bank account grows.

Year1 = $1000, Year2 = Year1 + Year1

10 , Year3 = Year2 + Year2

10 , Year4 = Year3 + Year3

10

What is the value of Year4 ?

$

24 Paul and Gary both bought a quantity of the same type of olives at a shop. Gary bought half the quantity of olives that Paul bought. The total cost of Gary’s and Paul’s olives was $14.85.

How much did Gary’s olives cost?

$

North

P

11

© ACARA 2012


25 Erica used a computer to make a pattern of triangles.

Number of black triangles 1 3 9 27 81 243 …

Number of white triangles 0 1 4 13 40 121 …

Erica continued the pattern until the shape had 6561 black triangles.

How many white triangles did the shape have?

26 Steve had a rectangular piece of paper that was 90 cm long and 60 cm wide. He cut the paper into right-angled triangles the same size and shape as this one.

12 cm

6 cm

There are no pieces of the paper left over.

How many of these triangles did he cut the paper into?

50 75 100 150

27 A gardener plants 50 seeds from the same packet into three pots.

This table shows the number of seeds planted and the percentage of seeds that sprouted.

Pot label Number of seeds planted Percentage that sprouted

A 12 75%

B 20 50%

C 18 50%

What percentage of the seeds from the packet sprouted?

%

12

© ACARA 2012


28 Shauna plotted five points on this square grid.

J

K

L

Point K is 28 millimetres from point L. Shauna adds a sixth point, M, so that the arrangement of points has one line of symmetry.

How far is point M from point J?

millimetres

29 A teacher is showing a picture on a screen. The picture is 12 cm by 8 cm. The screen is 2.4 m by 2 m.

The teacher enlarges the image on the screen so it is as big as possible without distorting its proportions.

What are the dimensions (in cm) of the enlarged picture?

cm by cm

30 When 4 people meet and each shakes hands once with everybody else there is a total of 6 separate handshakes.

This formula gives the total number of handshakes (H) when a group of N people meet.

H = 0.5N(N – 1)

For what value of N does H = 300?

13

© ACARA 2012


31 This is the net of a cube.

The cube has a volume of 343 cubic millimetres.

What is the length of the net in millimetres?

millimetres

32 The diagram shows two views of a prism on a grid.

Each square on the grid has an area of one square centimetre. The vertical edges of the prism are 3 centimetres high.

What is the volume of the prism in cubic centimetres?

cubic centimetres

StOP – eND OF teSt

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length

9year

2012

Use 2B or HB pencil only

© Australian Curriculum, Assessment and Reporting Authority, 2012

0:40 Time available for students to complete test: 40 minutes

SeSSION 2

NUMeraCy NON-CalCUlatOr

2

© ACARA 2012

YEAR 9 NUMeraCy (NON-CalCUlatOr)

1 The picture shows five stacks of $2 coins.

How much money is there in total?

$10 $16 $20 $22

2 Helen paid $1.19 for 7 prints at the camera shop.

How much did she pay for each print?

$0.11 $0.17 $1.12 $1.26

3 Luke walks to school every day. The distance from his home to school is 1.5 kilometres.

Luke leaves home and walks 500 metres towards school.

What fraction of the distance to school has he walked?

15

14

13

12

4 Sharon bought 3 fruit buns and 4 bread rolls at the bakery.

The buns cost 80 cents each. The rolls cost 40 cents each.

How much did Sharon pay?

$1.20 $3.60 $4.00 $4.80 $8.40

3

© ACARA 2012


5 Joan is making a pattern with sticks. She continues adding sticks as shown.

Step 1 Step 2 Step 3 Step 6

… ?

6 sticks 11 sticks 16 sticks … ? sticks

How many sticks will Joan need to make Step 6 of her pattern?

30 31 32 33

6 Which of these designs looks identical after a quarter turn?

7 Which expression is equal to 5b3 ?

8 × b15 × b5 × b × b × b5 + b + b + b5 × 5 × 5 × b × b × b

4

© ACARA 2012


8 This graph shows the price per tonne of crops grown in a country.

800700600500400300200100

0

canolawheatbarley

Crop prices

Date (quarters of the year)

Price (dollars

per tonne)

Q1 Q1 Q1 Q1Q2 Q2 Q2 Q2Q3 Q3 Q3 Q3Q4 Q4 Q4 Q4

2006 2007 2008 2009

For several quarters, the price of barley was greater than the price of wheat. In one of those quarters, the price of canola fell below $500 per tonne.

Which quarter was this?

2006 Q3 2007 Q1 2007 Q2 2007 Q3

9 Rita is drawing the net of this box.

Where should Rita put this symbol on the net?

5

© ACARA 2012


10 Dean uses the same rule to change each into a .

2 43 7

7 19

Which of these rules did Dean use?

=

× 1 + 2

=

× 2 + 5

=

× 3 – 2

=

× 4 – 5

11 Terry bought 7 boxes of pencils. In total this was 84 pencils.

Which equation correctly shows n as the average number of pencils in each box?

84 × 7 = n84 − 7 = nn ÷ 7 = 84n × 7 = 84

12 A standard six-sided dice is rolled.

Which of the following events has a probability less than 1?

rolling a number greater than 0rolling a number less than or equal to 7rolling a number greater than or equal to 1rolling a number greater than or equal to 6

6

© ACARA 2012


13 Joe filled this empty bucket with water from a tap.

First the water ran from the tap slowly. Then the water ran quickly until the bucket was nearly full. As the water reached the top of the bucket, he turned the tap off.

Which graph best shows how the depth of water in the bucket changed?

depthof

water

time

depthof

water

time

depthof

water

time

depthof

water

time

14 To make a syrup, 3 cups of water must be used for every 4 cups of sugar.

How many cups of water are needed for 6 cups of sugar?

1.5 cups 4.5 cups 5 cups 8 cups

15 Sam leaves home at 10:35 am to go to a movie. The movie starts at 12:20 pm.

How much time does Sam have before the movie starts?

1 hour and 45 minutes

1 hour and 55 minutes2 hours and 15 minutes2 hours and 25 minutes

16 Which one of these is equal to 3 57

?

8 ÷ 7 15 ÷ 7 21 ÷ 7 26 ÷ 7 35 ÷ 7

7

© ACARA 2012


17 Which of these multiplications gives the greatest value?

0.031 × 100 0.132 × 10 0.312 × 0.1 0.0003 × 1000

18 35 × ? = 14

Which fraction is ? equal to?

25

57

27

15

19 Bindi made 36 muffins. Some of the muffins were apple and some were pear. Both kinds of muffins looked the same.

Tegan took a muffin. She had a 1 in 9 chance of taking a pear muffin.

How many apple muffins did Bindi make?

20 Which one of these shapes has diagonals that cross at right-angles?

8

© ACARA 2012


21

How many edges does this prism have?

7 12 15 19 21

22 This table shows the cost of planting a crop in paddocks of different areas.

area of paddock (hectares) 20 40 60 80 100

cost of planting crop ($) 1600 3200 4800 6400 8000

Complete the rule so that it agrees with the values in the table.

cost of planting crop = × area of paddock

23 A positive number n is multiplied by 4, then 20 is added.

Which of the following operations would give the same result?

Adding 20 to n, then multiplying by 4.

Adding 4 to n, then multiplying by 20.Adding 4 to n, then multiplying by 5.Adding 5 to n, then multiplying by 4.

24 In a school library there are 1000 books. 450 of the books are fiction and the rest are non-fiction.

What is the ratio of fiction to non-fiction books in the library?

9 : 11 9 : 10 9 : 20 9 : 13

9

© ACARA 2012


25 Dale is a beekeeper. The mass of 500 millilitres of Dale’s honey is 700 grams.

How many litres is 3.5 kilograms of Dale’s honey?

litres

26 This table shows Jack’s results for a two-day canoe race.

time(hours:minutes:seconds)

Day 1 7:57:54

Day 2 6:59:56

What was Jack’s total time for the two-day race?

13:56:50 13:116:110 14 :17:10 14 :57:50

27 Sarah bought two full bags of sand. Both bags had the same amount of sand in them.

After she used 14 of one bag of sand, she had a total of 35 kilograms of sand left.

How many kilograms of sand were in one full bag?

kilograms

28 Write the answer to this division in the box.

12.24 ÷ 0.12 =

10

© ACARA 2012


29 This diagram shows a common tiling pattern that uses squares and octagons.

The dotted lines show that the area of each octagon is a multiple of the area of each square.

The area of each octagon is 175 cm2.

What is the side length of each square?

cm

30 Jerry made this paper fan.

base

a

He used 10 identical isosceles triangles.

When the fan is open, its base forms a straight line.

How many degrees is the angle marked a ?

degrees

11

© ACARA 2012


31 Kyle has some wooden blocks the same as the one shown.

3 cm 2 cm

1 cm

He stacks them face to face to make a solid cube.

What is the smallest possible volume of the cube?

cubic centimetres

32 This symbol is made from two circles and two lines. The circles have the same centre, C.

60°

P A

B

Q

C

The radius of the small circle is 34

the radius of the large circle.

The angle between the two lines is 60°. The arc AB is 16 mm.

What is the length of the arc PQ in millimetres?

mm

StOP – eND Of teSt

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NUMeraCymelbabastow.weebly.com/uploads/9/8/9/4/9894393/yr9p_cn2012.pdf · 7 © ACARA 2012 YEAR 9 NUMeraCy (CalCUlatOr allOWeD) 11 The opening hours of a post office are shown on this