Locus Bureau | US 32406

Numeracy practice assessment

Apply mathematics and statistics in a range of everyday situations.

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This practice is untimed. It contains the same 34 items as the review paper, presented one at a time.

Each item has an optional reference panel with expected evidence and alignment notes. It does not mark or score your work.

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Question 1

Community library

1(a)

A study room is booked from 2:35 pm until 4:10 pm.

How many minutes is the booking?

minutes

Question 1

Community library

1(b)

The diagram shows a rectangular reading corner and circular floor cushions at the same scale. The cushions must lie flat inside the reading corner without overlapping.

What is the greatest number of cushions that fit on the floor?

cushions

Question 1

Community library

1(c)

The plan of a reading room uses the scale 1 cm represents 2 m. On the plan, the room is a rectangle 4.5 cm long and 3 cm wide.

What is the real floor area of the room, in square metres?

m²

Question 1

Community library

1(d)

A class returns 28 books. The average mass of each book is 0.42 kilograms.

What is the estimated total mass of the books, in kilograms?

kg

Question 1

Community library

1(e)

The graph shows visits to the library from January to June. A board report says, ‘Library visits increased every month from January to June.’

Line graph of library visits from January to June.

Do you agree with the report? Use at least three months and numbers from the graph to explain your answer.

Question 1

Community library

1(f)

The table shows how many books fit on identical shelves.

Book capacity by number of shelves
Shelves	Book capacity
2	56
4	112
6	168
8	224

Which rule gives the book capacity from the number of shelves?

(i)Add 28 to the number of shelves(ii)Multiply the number of shelves by 28(iii)Multiply the number of shelves by 56(iv)Subtract the number of shelves from 224

Question 1

Community library

1(g)

A library trolley has a maximum load of 20 kilograms. There are 48 books with an average mass of 0.43 kilograms each.

Using the average mass as an estimate, can all 48 books be moved in one load? Explain your answer.

Question 2

Weekend market

2(a)

Mandarins cost $4.75 per kilogram. A bag has a mass of 2.8 kilograms.

How much does the bag cost?

$

Question 2

Weekend market

2(b)

A drink is mixed using 3 cups of concentrate for every 5 cups of water.

How many cups of concentrate are needed for 7.5 cups of water?

cups

Question 2

Weekend market

2(c)

A small jar of tomato relish is 280 g and costs $4.90. A large jar is 420 g and costs $6.93. A sign says, ‘The large jar is better value.’

Is the sign correct? Use the weights and prices to explain your answer.

Question 2

Weekend market

2(d)

A rectangular market stall is 3.2 m long and 2.5 m wide. A ground sheet needs to cover the stall area plus 15% extra.

What area of ground sheet is needed, in square metres?

m²

Question 2

Weekend market

2(e)

A prize jar contains 9 blue tokens, 6 green tokens and 5 orange tokens. One token is chosen without looking.

What is the chance of choosing a green token? Give your answer as a percentage.

%

Question 2

Weekend market

2(f)

A vendor says, ‘Logo B is Logo A after a 180° rotation.’

Is the vendor correct? Explain using the direction of the arrow and the position of the dot.

Question 3

Household water

3(a)

A rectangular rainwater tank has internal dimensions 1.5 m by 0.8 m by 0.75 m. One cubic metre equals 1,000 litres.

Rectangular rainwater tank with its three dimensions labelled.

How many litres does the tank hold when full?

litres

Question 3

Household water

3(b)

A shower uses 7.5 litres of water per minute. Three people each take an 8-minute shower.

How many litres of water are used altogether?

litres

Question 3

Household water

3(c)

An old toilet uses 9 litres for each flush. A replacement uses 6 litres for each flush.

What is the percentage reduction in water used per flush? Round to the nearest whole percent.

%

Question 3

Household water

3(d)

The chart shows monthly rainfall. A notice says, ‘Rainfall was higher in every autumn month, March to May, than in either January or February.’

Column chart of monthly rainfall from January to June.

Is the notice correct? Use values from the chart to explain your answer.

Question 3

Household water

3(e)

A full tank contains 900 litres. A household plans to use 75 litres each day. The rule V = 900 - 75d gives the volume V, in litres, left after d days.

How many litres are left after 6 days?

litres

Question 3

Household water

3(f)

A household has 750 litres of stored water. It expects to use 110 litres each day. No rain is forecast for 7 days.

Is there enough stored water for all 7 days? Show how you worked out your answer.

Question 3

Household water

3(g)

A second rainwater tank holds 5,000 litres when full. The gauge shows the water in it now.

How many more litres are needed to fill this tank?

litres

Question 4

Coastal walk

4(a)

The map shows five marked locations. The first coordinate is read along the horizontal axis.

Coordinate map with five labelled locations and a compass. — Grid data: A is at (1, 4), B at (2, 2), C at (4, 3), D at (3, 5), and E at (5, 1). The route arrow runs from B to C.

Which letter is at coordinate (4, 3)?

Question 4

Coastal walk

4(b)

On a printed route map, the walking route measures 7.2 cm. The scale is 1 cm represents 1.5 km.

What is the real route distance, in kilometres?

km

Question 4

Coastal walk

4(c)

A walker travels 10.8 km at an average speed of 4.5 km per hour.

How many minutes does the walking take?

minutes

Question 4

Coastal walk

4(d)

Use the same map. A walker travels in a straight line from B to C.

Which direction best describes the path from B to C?

Question 4

Coastal walk

4(e)

A park notice gives a 3 in 10 chance of rain. A phone forecast gives a 35% chance. A walker says, ‘Those forecasts are about the same.’

Do you agree? Explain using a fraction, decimal or percentage.

Question 4

Coastal walk

4(f)

The walk starts at 9:25 am. The walking time is 2 hours 24 minutes, and the group also takes a 35-minute break.

What time does the group finish?

time

Question 4

Coastal walk

4(g)

Sediment builds up at a steady rate of 1 centimetre every 40 years. The diagram is drawn to scale.

A cliff cross-section has unequal sediment layers and a 1 metre scale bar. The centres of the shell and fish markers are 3.0 metres apart vertically. — The shell-marker centre is exactly three scale-bar lengths above the fish-marker centre. The scale bar represents 1 metre.

About how many years separate the shell marker and the fish marker?

years

Question 5

Beach clean-up

5(a)

Volunteers collect 180 items. Two-fifths of the items are plastic.

How many plastic items are collected?

items

Question 5

Beach clean-up

5(b)

The dot plot shows the mass of nine bags collected by one group.

Dot plot of collected-bag masses from 1.2 to 2.0 kilograms. — Data values: one bag at 1.2 kg, two at 1.4 kg, three at 1.6 kg, two at 1.8 kg, and one at 2.0 kg.

Which statement is correct?

(i)The median mass is 1.4 kg(ii)The range of the masses is 1.0 kg(iii)The most common mass is 1.6 kg(iv)Half of the bags are heavier than 2.0 kg(v)The graph shows 10 bags

Question 5

Beach clean-up

5(c)

Another group fills 8 sacks. The average mass of each sack is 2.35 kg.

What is the total mass of the sacks, in grams?

g

Question 5

Beach clean-up

5(d)

The chart shows the 180 collected items by material. An organiser says, ‘More than half of all items were plastic or metal.’

Column chart of collected items by material.

Is the organiser correct? Use numbers from the chart to explain your answer.

Question 5

Beach clean-up

5(e)

Two of the last 10 planned clean-up events were cancelled because of unsafe weather.

Based on these results, what is the estimated chance that the next event is cancelled? Give your answer as a percentage.

%

Question 5

Beach clean-up

5(f)

A collection box is a cube. Four possible nets are shown.

Four arrangements of six squares labelled A to D.

Which net will fold to make the cube?

(i)A(ii)B(iii)C(iv)D

Question 5

Beach clean-up

5(g)

Volunteers photograph a piece of driftwood next to a standard cleaning bucket.

A 30-centimetre-high cleaning bucket stands beside a fully visible piece of driftwood at the same depth. The driftwood appears about three and a half bucket heights long.

About how long is the driftwood, in centimetres?

cm

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Numeracy practice assessment

How many minutes is the booking?

Evidence and alignment

Expected evidence

Marking decision

What is the greatest number of cushions that fit on the floor?

Evidence and alignment

Expected evidence

Marking decision

What is the real floor area of the room, in square metres?

Evidence and alignment

Expected evidence

Marking decision

What is the estimated total mass of the books, in kilograms?

Evidence and alignment

Expected evidence

Marking decision

Do you agree with the report? Use at least three months and numbers from the graph to explain your answer.

Evidence and alignment

Expected evidence

Marking decision

Which rule gives the book capacity from the number of shelves?

Evidence and alignment

Expected evidence

Marking decision

Using the average mass as an estimate, can all 48 books be moved in one load? Explain your answer.

Evidence and alignment

Expected evidence

Marking decision

How much does the bag cost?

Evidence and alignment

Expected evidence

Marking decision

How many cups of concentrate are needed for 7.5 cups of water?

Evidence and alignment

Expected evidence

Marking decision

Is the sign correct? Use the weights and prices to explain your answer.

Evidence and alignment

Expected evidence

Marking decision

What area of ground sheet is needed, in square metres?

Evidence and alignment

Expected evidence

Marking decision

What is the chance of choosing a green token? Give your answer as a percentage.

Evidence and alignment

Expected evidence

Marking decision

Is the vendor correct? Explain using the direction of the arrow and the position of the dot.

Evidence and alignment

Expected evidence

Marking decision

How many litres does the tank hold when full?

Evidence and alignment

Expected evidence

Marking decision

How many litres of water are used altogether?

Evidence and alignment

Expected evidence

Marking decision

What is the percentage reduction in water used per flush? Round to the nearest whole percent.

Evidence and alignment

Expected evidence

Marking decision

Is the notice correct? Use values from the chart to explain your answer.

Evidence and alignment

Expected evidence

Marking decision

How many litres are left after 6 days?

Evidence and alignment

Expected evidence

Marking decision

Is there enough stored water for all 7 days? Show how you worked out your answer.

Evidence and alignment

Expected evidence

Marking decision

How many more litres are needed to fill this tank?

Evidence and alignment

Expected evidence