Upper Primary Division
Questions 1 to 10, 3 marks each 1. What does the digit 1 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 do 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?
(A) 1.3 (B) 1.303 (C) 1.31 (D) 1.301 (E) 1.131
UP 2
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 6 ×10.
• Carrie wrote 5 ×12.
• Brian wrote 10×12÷2.
• R´emy wrote 10÷2×12.
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, 7 and 9 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 3 and 7 are placed as shown. What could be the sum of the row?
(A) 14 (B) 15 (C) 12 (D) 16 (E) 13
7 3
UP 3
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, 4 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?
(A) L+M (B) L×M (C) L÷M (D) M ÷L (E) L−M
UP 4
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 1 to 6 are placed in the circles so that each side of the triangle has a sum of 10. If 1 is placed in the circle shown, which number is in the shaded circle?
(A) 2 (B) 3 (C) 4
(D) 5 (E) 6
1
UP 5
16. Follow the instructions in this flow chart.
Start with 5
Subtract 2
Multiply by 3
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 2 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
(D) Thursday (E) Friday
UP 6
19. A square of side length 3 cm is placed alongside a square of side 5 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 A M
A M T
Which one of the following could be a third view of the same cube?
(A)
M H
T
(B)A T
C
(C)T S
C
(D)H T
A
(E)S M C
UP 7
Questions 21 to 25, 5 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) 9 (B) 7 (C) 5 (D) 3 (E) 1
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 5 M
23. A scientist was testing a piece of metal which contains copper and zinc. He found the ratio of metals was 2 parts copper to 3 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?
(A) 1 part copper to 3 parts zinc (B) 2 parts copper to 3 parts zinc (C) 16 parts copper to 17 parts zinc (D) 8 parts copper to 17 parts zinc (E) 8 parts copper to 33 parts zinc
UP 8
24. Jason had between 50 and 200 identical square cards. He tried to arrange them in rows of 4 but had one left over. He tried rows of 5 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) 8 (B) 9 (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 0 to 999 in the space provided on the answer sheet.
Question 26 is 6 marks, question 27 is 7 marks, question 28 is 8 marks, question 29 is 9 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.
She has 999 bricks she can use, and designs her patio to be as large a square as possible.
How many bricks does she use?
UP 9
27. There are many ways that you can add three different positive whole numbers to get a total of 12. For instance, 1 + 5 + 6 = 12 is one way but 2 + 2 + 8 = 12 is not, since 2, 2 and 8 are not all different.
If you multiply these three numbers, you get a number called the product.
Of all the ways to do this, what is the largest possible product?
28. I have 2 watches with a 12 hour cycle. One gains 2 minutes a day and the other loses 3 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 3×2 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?
∗
Upper Primary Division
Questions 1 to 10, 3 marks each
1. Which number is 20 more than 17?
(A) 3 (B) 27 (C) 37 (D) 217 (E) 2017
2. How many 200 g apple pies will weigh 4 kg?
(A) 2 (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) 3
4 (B) 1
2 (C) 2
3 (D) 2
5 (E) 3
5
4. At the camping shop, Jane bought a rucksack for $55 and a compass for $20.
How much change did she get from $100?
(A) $25 (B) $35 (C) $45 (D) $55 (E) $65
UP 2
5. Which of these shapes are pentagons?
1 2 3
4 5
(A) all of the shapes (B) shape 3 only (C) shapes 3 and 4 (D) shapes 1 and 3 (E) none of the shapes
6. Mitchell lives 4 km from school. Naomi lives 3 times as far from school as Mitchell. Olivia lives 3 km closer to school than Naomi. How far does Olivia live from school?
(A) 9 km (B) 3 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?
3c
4c 4c 3c 3c 4c
3c
4c
3c 4c 3c 4c
?
(A) 3c (B) 8c (C) 18c (D) 20c (E) 43c
UP 3
9. Felicity has a combination lock for her bike like the one below. It has the numbers 0 to 9 on each tumbler.
It clicks every time she moves the tumblers one number forward or back, including a click as the tumbler moves between 9 and 0.
She found the lock in the position 9–0–4 shown. Her combination is 5–8–7.
0 8
9
1 9
0
5 3
4
What is the least number of clicks needed to get the lock to her com- bination?
(A) 20 (B) 18 (C) 17 (D) 9 (E) 7
10. Which number multiplied by itself is equal to 5 times 20?
(A) 10 (B) 20 (C) 25 (D) 100 (E) 120
Questions 11 to 20, 4 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 ?
(A) 1 (B) 2 (C) 3 (D) 4 (E) 5
UP 4
13. In this sum, each of the letters X, Y and Z represents a different digit. Which digit does the letter X represent?
(A) 1 (B) 4 (C) 5 (D) 7 (E) 9
X X X Y Y X Z
+
14. A maths student made the following pattern:
1 1 1
2 2 2 2
3 4 4 4 3
4 7 8 8 7 4
5 11 15 16 15 11 5
The numbers down the sides of the pattern increase by 1 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%
(D) 52% (E) 66%
UP 5
18. At 10 am the school flagpole cast a shadow 6 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) 3 (B) 5 (C) 8
(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?
(A) 2 (B) 5 (C) 8 (D) 10 (E) 12
UP 6
Questions 21 to 25, 5 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 1 to 7 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) 5 (B) 6 (C) 7
(D) 8 (E) 9
7
Y X
4
23. A square ABCD with a side of 6 cm is joined with a smaller square EF GC with a side of 4 cm as shown.
What is the area of the shaded shapeBDF E?
(A) 12 cm2 (B) 14 cm2 (C) 16 cm2 (D) 18 cm2 (E) 24 cm2
D
A B
C G
E F
6 4
UP 7
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) 6 (B) 8 (C) 9
(D) 10 (E) 11
For questions 26 to 30, shade the answer as a whole number from 0 to 999 in the space provided on the answer sheet.
Question 26 is 6 marks, question 27 is 7 marks, question 28 is 8 marks, question 29 is 9 marks and question 30 is 10 marks.
26. Two rectangles overlap to create three regions, each of equal area. The orig- inal rectangles are 6 cm by 15 cm and 10 cm by 9 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
9
UP 8
27. Jonathan made a tower with rectan- gular cards 2 cm long and 1 cm wide, where each row has one more card than the row above it.
The perimeter of a tower with 3 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 0 to 9 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 2 ×2 subgrid contains exactly two squares of each colour, as seen in the first example.
The pattern in the second example isunbalanced be- cause the bottom-right 2×2 subgrid contains three white squares.
Counting rotations and reflections as different, how many balanced 3×3 patterns are there?
balanced
unbalanced
