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 p[r]
(1)Middle Primary Division
Questions to 10, marks each 1. How many dots are on the plate?
(A) 10 (B) 12 (C) 13
(D) 14 (E) 15
2. Jill had 15 grapes She ate How many are left?
(A) (B) (C) (D) 10 (E) 11
3. This grid gives the position of different shapes For example, a ♢ is in position B4
Which shape is in position D2?
(A) ♢ (B) ⊕ (C) ♡
(D) ⊙ (E) △
1 A B C D ⊕ ♡ ♡ ⊙ △ ♢ ⊙ ⊙ ⊕ ♡ △ ♡ ⊕ △
(2)MP
5. On this spinner, which shape are you most likely to spin?
(A) N (B) (C) ⋆
(D) ♠ (E) •
⋆ N
•
• ♠
6. What time is shown on this clock? (A) twelve o’clock
(B) a quarter to nine (C) a quarter past three (D) a quarter past twelve (E) three o’clock
1 10 11 12
7. The graph below shows the number of pets owned by the students in a Year class
0
Cats Dogs Fish Rabbits Pets in Year 4
How many pets does this class have altogether?
(3)MP
8. 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
9. How many by rectangles will fit exactly into an by rectangle?
(A) 14 (B) 28 (C) 36
(D) 56 (E) 63
10. Five swimmers were in a 50 m race The time each swimmer took to finish the race is shown in this graph Who won the race?
Time in seconds
0 10 20 30 40
Ivan Henry Franco Ethan George
(4)MP
Questions 11 to 20, marks each
11. Cianna is stringing beads for a necklace, starting with two round beads, then a square bead, and then repeating this pattern of three beads
She finished her necklace with a round bead, which happens to be the 18th round bead How many square beads are on her necklace?
(A) 10 (B) 12 (C) 18 (D) (E)
12. 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)
13. When complete, each row, column and diagonal in this diagram has a sum of 15 What is the sum of the numbers in the shaded squares?
(5)MP
14. 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
15. John wrote his name on his book Martha said he wrote with a black pen Aaron said it was a brown pencil Frankie said it was a black crayon If each of John’s friends were half right, what did he really use to write his name?
(A) a brown pen (B) a brown crayon (C) a brown pencil (D) a black pen (E) a black pencil
16. Follow the instructions in this flow chart
Start with Subtract Multiply by Is this greater than 50? Select this answer Yes No
(6)MP
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. Rod had fewer than 100 blocks When he made five equal rows, he had one block left over With four equal rows, he had one block left over With nine equal rows, there were no blocks left over How many blocks did he have?
(A) 18 (B) 49 (C) 81 (D) 91 (E) 99
19. Simon has some 24 cm long strips Each strip is made from a different number of equal-sized tiles
Simon took tile from each strip to make a new strip How long is the new strip?
(7)MP
20. 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)
1
Questions 21 to 25, marks each
21. Grandpa had $400 in his wallet He gave half the money to his wife From what was left, he then gave one-quarter to his son Half of the remainder went to his grandson How much money did his grandson receive?
(A) $50 (B) $125 (C) $100 (D) $200 (E) $75
22. The numbers 40, 19, 37, 33, 12, 25, 46, 18, 39, 21 are matched in pairs so that the sum of each pair is the same Which number is paired with 39?
(A) 19 (B) 33 (C) 21 (D) 18 (E) 25
(8)MP
24. Molly is thinking of a number Twice her number take away seven is the same as her number plus five What is her number?
(A) 19 (B) 17 (C) 15 (D) 12 (E) 10
25. Tom borrowed some items from the stationery cupboard He found that glue sticks weigh the same as staplers, and that staplers weigh the same as 20 erasers
iGlo o iGlo o iGlo o iGlo o iGlo o
How many glue sticks balance with how many erasers? (A) glue sticks with erasers
(C) glue stick with erasers
(B) glue sticks with 50 erasers (D) glue sticks with 17 erasers (E) glue sticks with 23 erasers
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.
(9)MP
27. A newspaper open on the table had page 42 opposite page 55 because someone had removed some pages from the centre What is the number of the last page of the news-paper?
28. 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?
29. 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?
30. 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
(10)(11)(12)(13)(14)(15)(16)(17)(18)Middle Primary Division
Questions to 10, marks each
1 The value of + + + is
(A) 10 (B) 19 (C) 37 (D) 208 (E) 2017
2 Jillian has her 9th birthday in 2017 In which year was she born?
(A) 2006 (B) 2007 (C) 2008 (D) 2009 (E) 2010
3 What is the value of the in 213?
(A) 0.02 (B) 0.2 (C) (D) 20 (E) 200
4 The squirrel’s tree is on square L3
To get there from square K1, the squirrel must move
(A) two squares right and one square down (B) one square left and two squares down (C) three squares left and two squares down (D) three squares right and one square down (E) one square right and two squares down
1
J
2
K
3
L
4
(19)MP
5 Lincoln went to buy some fruit at the school canteen He bought apples which cost 30 cents each How much did the apples cost?
(A) 60c (B) 80c (C) $1.00 (D) $1.20 (E) $1.60
6 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)
7 Zara was cycling She came to a T-intersection in the road where she saw this sign
The road to Smithton passes through Marytown
How many kilometres is it from Marytown to Smithton?
Smithton 23 km Marytown 15 km
Janesville 28 km
(A) (B) 13 (C) 38 (D) 43 (E) 51
8 Riverside Primary School has 235 staff and students Each bus can fit 50 people What is the least number of buses they need for a whole school excursion?
(20)MP
9 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
10 Fred gave half of his apples to Beth, and then half of what was left to Sally, leaving him with just one apple How many did he have to start with?
(A) 12 (B) (C) (D) (E)
Questions 11 to 20, marks each
11 Which of the shaded areas below is the largest?
(A) (B) (C) (D) (E)
12 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?
(21)MP
13 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 ?
(A) 3c (B) 8c (C) 18c (D) 20c (E) 43c
14 At the supermarket Ashan noticed that her favourite biscuits were on special, with one-third extra for free in the packet
If this special packet contained 24 biscuits, how many biscuits would be in the normal packet?
(A) 12 (B) 16 (C) 18 (D) 20 (E) 32
15 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
16 Jonathan made this shape with rectangular cards cm long and cm wide
What is the perimeter of the shape?
(A) cm (B) 12 cm (C) 18 cm
(22)MP
17 In these two number sentences
+ + + = 12
+ + + = 20
what is the value of ?
(A) (B) (C) (D) (E)
18 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
19 In the by square shown, I am filling in the 16 small squares with the numbers 1, 2, and so that each row and each column has one of each of these numbers I have filled in some of the squares as shown What the two squares marked ∗ add to?
(A) (B) (C)
(D) (E)
1
4
2 *
*
20 On these scales, two of the cubes balance with three of the balls
How many cubes need to be added to the right-hand side to make the scales bal-ance?
(A) (B) (C)
(23)MP
Questions 21 to 25, marks each
21 This shape can be folded up to make a cube
Which cube could it make?
(A) (B) (C)
(D) (E)
22 How many three-digit numbers contain only the digits and 3, and each of them at least once?
(A) (B) (C) (D) (E) 32
23 Which one of the patterns below would be created with these folds and cuts?
(24)MP
24 I have a rectangular block of cheese that I can cut into 12 identical cm cubes, with none left over How many differently-shaped blocks of cheese could I have started with?
(A) (B) (C) (D) (E)
25 A clockface can be divided with two straight lines into three regions so that the sum of the numbers in each region is the same What is this sum?
(A) 20 (B) 22 (C) 24
(D) 26 (E) 28
1 10 11 12
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 marks, question 29 is marks and question 30 is 10 marks
26 In a three-digit number, one of the digits is and the difference be-tween any two of the digits is or less
(25)MP
27 Julie has steps up to her classroom, where step is the floor of the classroom
Each day she tries to think of a different way of climbing up these steps She does not have to touch each step, but the biggest distance she can reach is steps
How many different ways are there of going up the steps?
28 Zhipu has an unusual construction set, consisting of square tiles which only connect together if they are joined with half a side touching That is, the corner of one connects with the midpoint of the other, as in the diagram
In how many ways can he connect three tiles? (Two arrangements are not different if they can be rotated or reflected to look the same.)
29 Old Clarrie has three dogs The oldest is Bob, next comes Rex and Fido is the youngest Fido is 10 years younger than Bob, and none of the dogs are the same age
When Clarrie adds their ages together they come to 28 years When Clarrie multiplies their ages together, he gets a number What is the smallest that this number could be?
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(36)Middle Primary 1
Middle Primary Division
Questions to 10, marks each
1. How many eggs are in these cartons?
(A) 12 (B) 15 (C) 16 (D) 18 (E) 21
2. Which one of the following is the largest number?
(A) 401 (B) 410 (C) 14 (D) 140 (E) 44
3. Which of the following is equal to m?
(A) cm (B) 30 cm (C) 300 cm (D) 3000 cm (E) 36 cm
4. A bowl has peaches After the children take one each, there is one peach left How many children are there?
(A) (B) (C)
(D) (E)
5. A Runnyball team has players.
This graph shows the number of goals each player scored in a tournament Who scored the second-highest number of goals?
(A) Ali (B) Beth (C) Caz
(D) Dan (E) Evan
1
Ali Beth Caz Dan Evan
Goals
Player
(37)Middle Primary 2
6. The next counting number after 1089 is
(A) 1090 (B) 10810 (C) 1910 (D) 1900 (E) 1009
7. These cards were dropped on the table, one at a time
In which order were they dropped?
(A) 4r Ar 5r 3r 2r (B) Ar 4r 5r 3r 2r (C) 2r 4r Ar 3r 5r (D) Ar 2r 3r 4r 5r (E) 2r 3r 4r 5r Ar
r A r A r r r r r 4 r 4 r r r r r r 5 r 5 r r r r 3 r 3 r r r 2 r 2 r
8. The table shows the pets six children own
Which boy owns a dog?
(A) Alex (B) Chris (C) Finn (D) Jo (E) Teejay
Cat Dog Fish
Girls Chris Jo Sam
Boys Teejay Finn Alex
9. Sophia is at the corner of 1st Street and 1st Avenue Her school is at the corner of 4th Street and 3rd Avenue
To get there, she walks
(A) blocks east, blocks north (B) blocks west, blocks north (C) blocks west, blocks north (D) blocks east, blocks north
(E) blocks north, blocks south 1st Avenue
2nd Avenue 3rd Avenue 4th Avenue 5th Avenue 1st Street 2nd Street 3rd Street 4th Street S E N W S N E
(38)Middle Primary 3
10. Jake is playing a card game, and these are his cards
Elena chooses one card from Jake at random
Which of the following is Elena most
likely to choose? r
A r A r J r J r ♣ ♣ ♣ ♣ 4 ♣ 4 ♣ r r
r rrr r
r r 9 r 9 r ♠ ♠ ♠ 3 ♠ 3 ♠ K ♠ K ♠ ♣ ♣ ♣ ♣ ♣ ♣ ♣ 7 ♣ 7 ♣
(A) a heart (r) (B) a diamond (q) (C) a spade (♠)
(D) a picture card (J, Q or K) (E) an even-numbered card
Questions 11 to 20, marks each 11. In Jacqui’s puzzle, a number is put in
each box
In each circle, the four numbers must add to 13
Which number goes in the top box?
(A) (B) (C)
(D) (E)
?
5 3
1
12. Noah follows the instructions in this flow chart What number does he end with?
Start with Subtract Multiply by Greater
than 100? End
No Yes
(A) 120 (B) 150 (C) 200 (D) 225 (E) 250
(39)Middle Primary 4
13. On this number line, where would the number
2 be?
0 A B C D E
(A) A (B) B (C) C (D) D (E) E
14. When Bessie puts a mirror next to her calculator, the digits some-times spell words in the mirror Which number spells ‘BESSIE’ in the mirror?
(A) 315538 (C) 832213
(B) 835513 (D) 815312
(E) 312238 0 . = +
1 2 3 −
4 5 6 ì
7 8 9 ữ
0 . = + 1 2 3 − 4 5 6 × 7 8 9 ÷
15. Looking at this view of four dice, how many dots cannot be seen?
(A) 21 (B) 28 (C) 32 (D) 36 (E) 45
16. A pencil costs 25 cents and a ruler costs 80 cents
With $5 I bought one ruler and as many pencils as I could afford What change did I get?
(A) 25 cents (B) 20 cents (C) 15 cents (D) 10 cents (E) cents
17. 27 identical cubes are used to make this × × cube
How many more are needed to make a × × cube?
(A) (B) 25 (C) 27
(D) 36 (E) 37
(40)Middle Primary 5
18. Meena has a $50 gift voucher to spend in a toyshop, but they won’t give change from the voucher Here is a short list of toys she would like She tried to spend as much of the $50 as possible
$24 $14 $6 $39
If she buys no more than one of each toy, how much of the voucher will not get used?
(A) $1 (B) $3 (C) $5 (D) $7 (E) $9
19. A square piece of paper is folded twice along its diagonals, as shown in the diagram Two corners are then cut off When the paper is unfolded, what will it look like?
(A) (B) (C)
(D) (E)
(41)Middle Primary 6
20. It takes Preeti 30 minutes to walk to school
Sometimes she goes on her bike and she cycles twice as fast as she walks
Occasionally, her mother takes her in the car, which goes three times as fast as her bike How many minutes does it take to get to school in the car?
(A) (B) (C) (D) 10 (E) 15
Questions 21 to 25, marks each
21. In my dance class, 14 students are taller than Bob, and 12 are shorter than Alice Four students are both shorter than Alice and taller than Bob How many students are in my dance class?
(A) 22 (B) 24 (C) 26 (D) 28 (E) 30
22. My sister and I are playing a game where she picks two counting numbers and I have to guess them When I tell her a number, she multiplies my number by her first number and then adds her second number
When I say 15, she says 50 When I say 2, she says 11 If I say 6, what should she say?
(A) 23 (B) 27 (C) 35 (D) 41 (E) 61
23. A year student saved 100 cents in days, each day saving cents more than the previous day How many cents did she save on the fifth day?
(A) 20 cents (B) 25 cents (C) 30 cents (D) 40 cents (E) 50 cents
24. A cube has the letters A, M, C, D, E and F on its six faces Two different views of the cube are shown
I place the cube on the table so that the front shows C If I look at the back of the cube, what will I see?
D AC A E
F
(A) D (B) E (C) F (D) E (E) F
(42)Middle Primary 7
25. Shirley has six pieces of her construction kit: two red, two blue and two green She wants to build a square using four of the pieces
Shirley considers Square below to be the same as Square 2, since the colours match once Square is turned over and rotated However she considers Square to be different from Square 1, since no matter how it is turned, the two red sides are always opposite, and cannot match Square Red Red Blue Green Square Green Blue Red Red Square Red Blue Red Green Square
How many different squares could she build?
(A) (B) (C) 12 (D) 16 (E) 18
For questions 26 to 30, shade the answer as a whole number from to 999 in the space provided on the answer sheet. Questions 26–30 are worth 6, 7, 8, and 10 marks, respectively.
26. At my local greengrocer, you take a ticket from the machine and wait until your number is called The roll of tickets goes from 000 up to 999 When I was there last week with my neighbour, we took two tickets in a row and our two numbers added to 777
What was the next ticket number after ours?
TA
KE A TI C K E T
(43)Middle Primary 8
27. There are 390 children at a summer camp
One-third of the number of girls is equal to one-half of the number of boys How many girls are there?
28. How many of the numbers from 100 to 999 have exactly one zero digit?
29. A tower is built from exactly 2019 equal rods Starting with rods as a triangular base, more rods are added to form a regular octahedron with this base as one of its faces The top face is then the base of the next octahedron
The diagram shows the construction of the first three octahedra
How many octahedra are in the tower when it is finished?
30. John is one year older than his wife Mary They have three children, whose ages are two years apart
The product of John and Mary’s ages is less than 2019 The product of the three children’s ages is also less than 2019
Next year both these products will be greater than 2020 This year, what is the sum of all five ages?