corner piece edge piece interior piece (two straight sides at right angles) (one straight side) (no straight sides).. We treat two shapes as the same if one is a rotation of the other, w[r]
(1)Upper Primary Division
Questions to 10, marks each 1. What does the digit in 2015 represent?
(A) one (B) ten (C) one hundred (D) one thousand (E) ten thousand
2. What is the value of 10 twenty-cent coins?
(A) $1 (B) $2 (C) $5 (D) $20 (E) $50
3. What temperature does this thermometer show?
(A) 25◦ (B) 38◦ (C) 27◦
(D) 32◦ (E) 28◦
15 20 25 30 ◦C
4. Which number you need in the box to make this number sentence true?
19 + 45 = 20 +
(A) 34 (B) 44 (C) 46 (D) 64 (E) 84
5. Which number has the greatest value?
(2)UP
6. The perimeter of a shape is the distance around the outside Which of these shapes has the smallest perimeter?
(A) (B) (C)
(D) (E)
7. The class were shown this picture of many dinosaurs They were asked to work out how many there were in half of the picture
• Simon wrote ì 10. ã Carrie wrote ì 12. ã Brian wrote 10ì12ữ2. ã Remy wrote 10ữ2ì12.
Who was correct?
(A) All four were correct (B) Only Simon (C) Only Carrie (D) Only Brian (E) Only R´emy
8. In the diagram, the numbers 1, 3, 5, and are placed in the squares so that the sum of the numbers in the row is the same as the sum of the numbers in the column
The numbers and are placed as shown What could be the sum of the row?
(A) 14 (B) 15 (C) 12 (D) 16 (E) 13
(3)UP
9. To which square should I add a counter so that no two rows have the same number of counters, and no two columns have the same number of counters?
(A) A (B) B (C) C (D) D (E) E
A
B C
D E
10. A half is one-third of a number What is the number?
(A) three-quarters (B) one-sixth (C) one and a third (D) five-sixths (E) one and a half
Questions 11 to 20, marks each
11. The triangle shown is folded in half three times without unfolding, making another triangle each time
Which figure shows what the triangle looks like when unfolded?
(A) (B) (C) (D) (E)
12. If L = 100 and M = 0.1, which of these is largest?
(4)UP
13. You want to combine each of the shapes (A) to (E) shown below separately with the shaded shape on the right to make a rectangle
You are only allowed to turn and slide the shapes, not flip them over The finished pieces will not overlap and will form a rectangle with no holes
For which of the shapes is this not possible?
(A) (B) (C)
(D) (E)
14. A plumber has 12 lengths of drain pipe to load on his ute He knows that the pipes won’t come loose if he bundles them so that the rope around them is as short as possible How does he bundle them?
(A) (B) (C)
(D) (E)
15. The numbers to are placed in the circles so that each side of the triangle has a sum of 10 If is placed in the circle shown, which number is in the shaded circle?
(A) (B) (C)
(D) (E)
(5)UP
16. Follow the instructions in this flow chart
Start with Subtract Multiply by Is this greater than 50? Select this answer Yes No
(A) 57 (B) 63 (C) 75 (D) 81 (E) 84
17. A square piece of paper is folded along the dashed lines shown and then the top is cut off
The paper is then unfolded Which shape shows the unfolded piece?
(A) (B) (C) (D) (E)
18. Sally, Li and Raheelah have birthdays on different days in the week beginning Sunday August No two birthdays are on following days and the gap between the first and second birthday is less than the gap between the second and third Which day is definitely not one of their birthdays?
(A) Monday (B) Tuesday (C) Wednesday
(6)UP
19. A square of side length cm is placed alongside a square of side cm
3 cm
5 cm
What is the area, in square centimetres, of the shaded part?
(A) 22.5 (B) 23 (C) 23.5 (D) 24 (E) 24.5
20. A cube has the letters A, C, M, T, H and S on its six faces Here are two views of this cube
C
M
A
A
M
T
Which one of the following could be a third view of the same cube?
(A)
M
H
T
(B)A
C
T
(C)
T S
C
(D)H
T
A
(E) (7)UP
Questions 21 to 25, marks each
21. A teacher gives each of three students Asha, Betty and Cheng a card with a ‘secret’ number on it Each looks at her own number but does not know the other two numbers Then the teacher gives them this information
All three numbers are different whole numbers and their sum is 13 The product of the numbers is odd Betty and Cheng now know what the numbers are on the other two cards, but Asha does not have enough information What number is on Asha’s card?
(A) (B) (C) (D) (E)
22. In this multiplication, L, M and N are different digits What is the value of
L + M + N ?
(A) 13 (B) 15 (C) 16
(D) 17 (E) 20
L L M
× M
N M M
23. A scientist was testing a piece of metal which contains copper and zinc He found the ratio of metals was parts copper to parts zinc Then he melted this metal and added 120 g of copper and 40 g of zinc into it, forming a new piece of metal which weighs 660 g What is the ratio of copper and zinc in the new metal?
(8)UP
24. Jason had between 50 and 200 identical square cards He tried to arrange them in rows of but had one left over He tried rows of and then rows of 6, but each time he had one card left over Finally, he discovered that he could arrange them to form one large solid square How many cards were on each side of this square?
(A) (B) (C) 10 (D) 11 (E) 12
25. Eve has $400 in Australian notes in her wallet, in a mixture of 5, 10, 20 and 50 dollar notes
As a surprise, Viv opens Eve’s wallet and replaces every note with the next larger note So, each $5 note is replaced by a $10 note, each $10 note is replaced by a $20 note, each $20 note is replaced by a $50 note and each $50 note is replaced by a $100 note
Eve discovers that she now has $900 How much of this new total is in $50 notes?
(A) $50 (B) $100 (C) $200 (D) $300 (E) $500
For questions 26 to 30, shade the answer as a whole number from to 999 in the space provided on the answer sheet. Question 26 is marks, question 27 is marks, question 28 is
8 marks, question 29 is marks and question 30 is 10 marks.
26. Alex is designing a square patio, paved by putting bricks on edge using the basketweave pattern shown
(9)UP
27. There are many ways that you can add three different positive whole numbers to get a total of 12 For instance, + + = 12 is one way but + + = 12 is not, since 2, and are not all different
If you multiply these three numbers, you get a number called the product
Of all the ways to this, what is the largest possible product?
28. I have watches with a 12 hour cycle One gains minutes a day and the other loses minutes a day If I set them at the correct time, how many days will it be before they next together tell the correct time?
29. A 3× flag is divided into six squares, as shown. Each square is to be coloured green or blue, so that every square shares at least one edge with another square of the same colour
In how many different ways can this be done?
30. The squares in a 25 × 25 grid are painted black or white in a spiral pattern, starting with black at the centre ∗ and spiralling out
The diagram shows how this starts How many squares are painted black?
(10)(11)(12)(13)(14)(15)(16)(17)(18)Upper Primary Division
Questions to 10, marks each
1 Which number is 20 more than 17?
(A) (B) 27 (C) 37 (D) 217 (E) 2017
2 How many 200 g apple pies will weigh kg?
(A) (B) 20 (C) 50 (D) 80 (E) 200
3 Five dice were rolled, and the results were as shown
What fraction of the dice showed a two on top? (A) (B) (C) (D) (E)
4 At the camping shop, Jane bought a rucksack for $55 and a compass for $20
How much change did she get from $100?
(19)UP
5 Which of these shapes are pentagons?
1
4
(A) all of the shapes (B) shape only (C) shapes and
(D) shapes and (E) none of the shapes
6 Mitchell lives km from school Naomi lives times as far from school as Mitchell Olivia lives km closer to school than Naomi How far does Olivia live from school?
(A) km (B) km (C) 15 km (D) 13 km (E) 21 km
7 Helen is adding some numbers and gets the total 157 Then she realises that she has written one of the numbers as 73 rather than 37 What should the total be?
(A) 110 (B) 121 (C) 124 (D) 131 (E) 751
8 In the year 3017, the Australian Mint recycled its coins to make new coins
Each 50c coin was cut into six triangles, six squares, and one hexagon The triangles were each worth 3c and the squares were each worth 4c
How much should the value of the hexagon be to make the total still worth 50c?
3 c 4c 3c 4c 3c 4c c 4c
3c 4c 3c
4c
?
(20)UP
9 Felicity has a combination lock for her bike like the one below It has the numbers to on each tumbler
It clicks every time she moves the tumblers one number forward or back, including a click as the tumbler moves between and
She found the lock in the position 9–0–4 shown Her combination is 5–8–7 9
What is the least number of clicks needed to get the lock to her com-bination?
(A) 20 (B) 18 (C) 17 (D) (E)
10 Which number multiplied by itself is equal to times 20?
(A) 10 (B) 20 (C) 25 (D) 100 (E) 120
Questions 11 to 20, marks each 11 Greg sees a clock in the mirror, where it looks
like this What is the actual time?
(A) 4:10 (B) 4:50 (C) 5:10
(D) 6:50 (E) 7:10
12
12 In these two number sentences
+ + + = 12
+ + + = 20
what is the value of ?
(21)UP
13 In this sum, each of the letters X, Y and Z represents a different digit Which digit does the letter X represent?
(A) (B) (C) (D) (E)
X X
X Y
Y X Z
+
14 A maths student made the following pattern:
1 1
2 2
3 4
4 8
5 11 15 16 15 11
The numbers down the sides of the pattern increase by and each of the other numbers is found by adding the two numbers above it What will be the sum of all the numbers on the next line in this pattern?
(A) 128 (B) 138 (C) 148 (D) 158 (E) 168
15 The school bought 18 boxes of primary school paint for $900 Each box had a number of bottles, each worth $2.50 How many bottles were in each box?
(A) 15 (B) 20 (C) 45 (D) 50 (E) 125
16 One year in June, there were four Wednesdays and five Tuesdays On which day was the first of June?
(A) Monday (B) Tuesday (C) Thursday (D) Friday (E) Saturday
17 What percentage of this shape is shaded?
(A) 40% (B) 48% (C) 50%
(22)UP
18 At 10 am the school flagpole cast a shadow m long Next to the flagpole, the 0.5 m tap cast a shadow of 0.3 m
How tall is the flagpole in metres?
(A) (B) (C)
(D) 10 (E) 12 ?
0.5 m
6 m 0.3 m
19 This shape can be folded up to make a cube
Which cube could it make?
(A) (B) (C)
(D) (E)
20 The area of the large rectangle is 300 square metres It is made up of four identical smaller rectangles What is the width of one of the small rectangles in metres?
(23)UP
Questions 21 to 25, marks each
21 Which one of the patterns below would be created with these folds and cuts?
(A) (B) (C) (D) (E)
22 The whole numbers from to are to be placed in the seven circles in the diagram In each of the three triangles drawn, the sum of the three numbers is the same
Two of the numbers are given What is X + Y ?
(A) (B) (C)
(D) (E)
7
Y X
4
23 A square ABCD with a side of cm is joined with a smaller square EF GC with a side of cm as shown
What is the area of the shaded shape BDF E?
(A) 12 cm2 (B) 14 cm2 (C) 16 cm2 (D) 18 cm2 (E) 24 cm2
(24)UP
24 In this year of 2017, my family is in its prime: I am 7, my brother is 5, my mother is 29 and my father is 31 All of our ages are prime numbers
What is my father’s age the next year that my family is in its prime, when all of our ages are again prime?
(A) 37 (B) 41 (C) 43 (D) 47 (E) 61
25 A triangular prism is to be cut into two pieces with a single straight cut What is the smallest possible total for the combined number of faces of the two pieces?
(A) (B) (C)
(D) 10 (E) 11
For questions 26 to 30, shade the answer as a whole number from to 999 in the space provided on the answer sheet Question 26 is marks, question 27 is marks, question 28 is
8 marks, question 29 is marks and question 30 is 10 marks
26 Two rectangles overlap to create three regions, each of equal area The orig-inal rectangles are cm by 15 cm and 10 cm by cm as shown The sides of the smaller shaded rectangle are each a whole number of centimetres
What is the perimeter of the smaller shaded rectangle, in centimetres?
6
15
10
(25)UP
27 Jonathan made a tower with rectan-gular cards cm long and cm wide, where each row has one more card than the row above it
The perimeter of a tower with levels is 18 cm, as shown
What will be the perimeter of a tower with 10 levels, in centimetres?
28 All of the digits from to are used to form two 5-digit numbers What is the smallest possible difference between these two numbers?
29 A jigsaw piece is formed from a square with a combination of ‘tabs’ and ‘slots’ on at least two of its sides
Pieces are either corner, edge or interior, as shown
corner piece edge piece interior piece (two straight sides at right angles) (one straight side) (no straight sides)
We treat two shapes as the same if one is a rotation of the other, without turning it over How many different shapes are possible?
30 A 3×3 grid has a pattern of black and white squares. A pattern is called balanced if each × subgrid contains exactly two squares of each colour, as seen in the first example
The pattern in the second example is unbalanced be-cause the bottom-right 2× subgrid contains three white squares
Counting rotations and reflections as different, how many balanced 3× patterns are there?
balanced
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