MATHEMATICS AND SCIENCE: TEST 3

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INFORMATION FOR QUESTIONS 1 – 3

On this dart board are five different possible scores.

Suppose that three darts are thrown each round,
and that all three land somewhere on the board.
More than one can land on the same score. 5 9
12
3 7

"1' What is the smallest possible total score for a round?

A 3
B 9
C 13
D more than 13

"2' Which one of these total scores for a round is not possible?
A 11
B 12
C 13
D 15

"3' What is the smallest possible total score above 30 for a round?
A 35
B 34
C 33
D less than 33

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 QUESTION 4
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"4' 15 000 people were allowed into a football game, but another 5000 were turned away.
What fraction of the total number of people was turned away?
A one-half
B one-third
C one-quarter
D one-fifth

INFORMATION FOR QUESTION 5

When this magic square is completed, all rows and columns, and the ? 1.50
two major diagonals, have the same total.

2.25 0.25
"5' The number at ? will be
A 0.50 2.00
B 1.00
C 1.25
D 1.75

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INFORMATION FOR QUESTIONS 6 AND 7

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Every triangle in this figure has three circles shaded X
differently. Only three of the circles are shown
shaded. Y
The shading of blank circles is not given.

"6' X will be

A or C or

B D

"7' Y will be

A C

B or D or

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 INFORMATION FOR QUESTIONS 8 AND 9
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Aztec numbers are made up from four single AZTEC NUMBERS

pictures that represent particular numbers in 1 20 400 8000
our number system, as shown in the box.

"8' What number would be represented if two of each picture were present?
A 16 842
B 16 482
C 16 442
D 8 842

"9' What is the smallest number of pictures it would take to represent the number 8765?
A fewer than 25
B 25
C 26
D more than 26

QUESTION 10

"10' A fast-growing plant doubles its height every month. In one year it grows to a height of
12 metres.
How old is a 3-metre plant?
A 10 months
B 8 months
C 6 months
D 3 months

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INFORMATION FOR QUESTIONS 11 – 13

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The table shows oil consumption of the eight biggest oil-using countries.

OIL CONSUMPTION
(million barrels per day)

Australia 0.80 Japan 15.29

China 4.97 Saudi Arabia 11.45
France 2.02 UK 11.71
Germany 2.81 USA 19.6

"11' Which one of the following correctly graphs the figures in the table?
A C Australia
China
France
Germany
Japan
Saudi Arabia
UK
B D USA

"12' How much oil is consumed per year in France?

A 750 barrels C 750 million barrels
B 2 million barrels D 1500 million barrels

"13' Assume Australia’s population is 20 million people.

What is the average daily oil usage per person in Australia?
A 0.04 barrels C 8 barrels
B 0.08 barrels D 16 barrels

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 INFORMATION FOR QUESTIONS 14 AND 15
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Level 1

Level 2 +1 +2 +3

Level 3 +1 +2 +3 +4

"14' If = 5, what is the total value of Level 2?

A 5
B 6
C 15
D 21

"15' If = 0, and the total value of Levels 1, 2 and 3 is 26, what is the value of ?
A 1
B 2
C 3
D more than 3

QUESTION 16

"16' In this sum each different letter stands for a different number. p q r
+ p r q
Two of the numbers are 4 and 9.
r q p
Which one of the following is correct?
A p is 4
B q is 9
C r is 4
D r is 5

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INFORMATION FOR QUESTIONS 17 AND 18

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The bottom layer of this stack of cubes contains sixteen cubes, arranged in a 4 × 4 square.
The two upper layers each contain fewer than sixteen cubes, but there are no holes in the stack (no cubes
above empty spaces).

"17' What is the smallest possible number of cubes in the stack?

A 39
B 37
C 30
D 28

"18' What is the largest possible number of cubes in the stack?

A 37
B 38
C 39
D 40

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 INFORMATION FOR QUESTIONS 19 AND 20
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1 3
5 4

3 9
20 10

V X Y Z

"19' On this number line, what is V?

1 2
A 4 C 5
1 3
B 3 D 10

3
"20' Where would 5 be on this number line?
A X
B Y
C Z
D not at X, Y or Z

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INFORMATION FOR QUESTIONS 21 AND 22

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The Rowe family are visiting Urville Island. They have arrived at Tang by ferry, and are about to hire a
car to travel on day trips to some of the towns on the island, returning to Tang each night.

They want to drive no further than 200 km in a day.

20
Quint
20 Rioli
Pigtown 25 40
25
55 40 Sierra
Yorro
URVILLE ISLAND
32 35
35
Tang
Urville
50

"21' Starting at and returning to Tang, what is the most distant town the Rowe family can visit in a
day?
A Quint
B Yorro
C Urville
D Pigtown

"22' On their last day on Urville Island, the Rowe family will leave Tang and drive to Pigtown, to
catch the ferry home.
Including Tang and Pigtown, what is the greatest number of towns they can visit in the day?
A four
B five
C six
D all seven

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 QUESTION 23
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"23' Brad, Chaz, Dean and Evie go swimming at the same pool. Brad goes every 3 days, Chaz every 6
days and Dean every 7 days. The four all meet up only once every 84 days.
How often does Evie go to the pool if she swims less often than any of the others?
A 8 days.
B 10 days.
C 12 days.
D 14 days.

QUESTION 24

"24' A perfect square number is obtained by multiplying a whole number by itself.

How many perfect square numbers between 10 and 99 have digits that add to a number that is a
perfect square?
A none
B one
C two
D more than two

INFORMATION FOR QUESTION 25

G
Children at a summer camp can take part in any number
of four activities – tennis, horse riding, trampolining and
waterskiing. H I
M
Gabby drew a diagram to represent the children’s choices. Q R
L T N
P S
O
"25' Which region could represent the children taking K J
part in both tennis and horse riding only?
A H
B M
C Q
D T

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INFORMATION FOR QUESTIONS 26 – 28

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Four school houses are competing for the Top House Cup. The points they score for each week are
shown on the graph. Green House’s points for Week 5 have not yet been decided.

40

30

Points
20 Gold
Grey
10
White
Green
0
Week 1 Week 2 Week 3 Week 4 Week 5

"26' At the end of Week 2,

A Grey House had more total points than White House.
B Gold House had more total points than Grey House.
C White House had more total points than Green House.
D Green House had fewer total points than Gold House.

"27' Over the first four weeks, White House’s average weekly score was
A 10 points
B 12.5 points
C 15 points
D 16.67 points

"28' If Green House is to win the Top House Cup, what is the minimum number of points they must
score in Week 5?
A 21
B 26
C 31
D 36

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 INFORMATION FOR QUESTION 29
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"29' The scales shown are balanced. Suppose a ball has four times the mass of one cross.
Which one of the following is true?

A =
B =
C =
D =

INFORMATION FOR QUESTION 30

Three friends, Carmen, Claude and Colin, live along a straight road, as shown below.

The vertical marks are equal distances apart.

CARMEN CLAUDE COLIN

I II III IV

"30' The friends want to have a meeting. At least two of them will walk to the meeting.
The total combined distance they walk will be shortest if they meet at
A I only.
B II only.
C II or III or anywhere in between.
D III only.

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INFORMATION FOR QUESTIONS 31 AND 32

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Different garden plants require different amounts of soil acidity (pH). Some will only grow in soil that
is strongly acidic, others require medium or low acidic conditions.

The graph shows soil acidity requirements for eight types of plant (I, II, ..., VIII).

II

III

IV

VI

VII

VIII

4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5

more acidic less acidic
Soil pH

"31' Which plant can grow in the widest range of soil acidity?
A I C VII
B VI D VIII

"32' Delia wants to grow plants II, III, IV and VI in the same garden.
Which soil pH would be satisfactory?
A 6.9
B 7.1
C 7.3
D no pH would suit all the plants

END OF TEST 3

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