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]
Trang 1Middle Primary Division
Questions 1 to 10, 3 marks each
1. How many dots are on the plate?
2. Jill had 15 grapes She ate 5 How many are left?
3. This grid gives the position of different
shapes For example, a ♢ is in position
Trang 2MP 2
5. On this spinner, which shape are you
most likely to spin?
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
12345678910
11 12
7. The graph below shows the number of pets owned by the students in
a Year 4 class
02468
Cats Dogs Fish Rabbits
Pets in Year 4
How many pets does this class have altogether?
Trang 4MP 4
Questions 11 to 20, 4 marks each
11. Cianna is stringing beads for a necklace, starting with two roundbeads, then a square bead, and then repeating this pattern of threebeads
She finished her necklace with a round bead, which happens to be the18th round bead How many square beads are on her necklace?
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?
(A) 20 (B) 25 (C) 27 (D) 30 (E) 45 5
54
Trang 5MP 5
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
15. John wrote his name on his book Martha said he wrote with a blackpen Aaron said it was a brown pencil Frankie said it was a blackcrayon If each of John’s friends were half right, what did he reallyuse 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 5
Subtract2
Multiply
by 3
Is thisgreaterthan 50?
Selectthisanswer
Yes
No
Trang 619. Simon has some 24 cm long strips Each
strip is made from a different number of
equal-sized tiles
Simon took 1 tile from each strip to
make a new strip How long is the new
strip?
(A) 18 cm (B) 20 cm (C) 23 cm
(D) 24 cm (E) 33 cm
Trang 7MP 7
20. 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?
1
Questions 21 to 25, 5 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 theremainder went to his grandson How much money did his grandsonreceive?
(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 with39?
Trang 8How many glue sticks balance with how many erasers?
(A) 3 glue sticks with 8 erasers
(C) 1 glue stick with 6 erasers
(B) 3 glue sticks with 50 erasers(D) 3 glue sticks with 17 erasers(E) 7 glue sticks with 23 erasers
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. Jill has three large piles of coins: 10c, 20c and 50c In how manydifferent ways can she make one dollar?
Trang 9MP 9
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 wholenumbers to get a total of 12 For instance, 1 + 5 + 6 = 12 is one waybut 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 theproduct
Of all the ways to do this, what is the largest possible product?
30. 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?
Trang 18Middle Primary Division
Questions 1 to 10, 3 marks each
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
1J
Trang 19MP 2
5 Lincoln went to buy some fruit at the school canteen He bought 4apples which cost 30 cents each How much did the 4 apples cost?(A) 60c (B) 80c (C) $1.00 (D) $1.20 (E) $1.60
6 Five dice were rolled, and the results were
35
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
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 wholeschool excursion?
Trang 20MP 3
9 Which of these shapes are pentagons?
(A) all of the shapes (B) shape 3 only (C) shapes 3 and 4
(D) shapes 1 and 3 (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 tostart with?
Questions 11 to 20, 4 marks each
11 Which of the shaded areas below is the largest?
12 Helen is adding some numbers and gets the total 157 Then she realisesthat she has written one of the numbers as 73 rather than 37 Whatshould the total be?
(A) 110 (B) 121 (C) 124 (D) 131 (E) 751
Trang 21MP 4
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?
If this special packet contained 24 biscuits, how many biscuits would
be in the normal packet?
15 Greg sees a clock in the mirror, where it looks
like this What is the actual time?
(D) 6:50 (E) 7:10
12
16 Jonathan made this shape with rectangular
cards 2 cm long and 1 cm wide
What is the perimeter of the shape?
(A) 6 cm (B) 12 cm (C) 18 cm
(D) 24 cm (E) 36 cm
Trang 22(A) Monday (B) Tuesday (C) Thursday (D) Friday (E) Saturday
19 In the 4 by 4 square shown, I am filling in
the 16 small squares with the numbers 1, 2,
3 and 4 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 do the two squares marked ∗ add to?
*
*
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?
Trang 23MP 6
Questions 21 to 25, 5 marks each
21 This shape can be folded up to make a
Trang 24MP 7
24 I have a rectangular block of cheese that I can cut
into 12 identical 1 cm cubes, with none left over
How many differently-shaped blocks of cheese could
I have started with?
(A) 2 (B) 3 (C) 4 (D) 5 (E) 6
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?
1 2 3 4 5 6 7 8 9 10
11 12
For questions 26 to 30, shade the answer as a whole numberfrom 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 In a three-digit number, one of the digits is 7 and the difference tween any two of the digits is 4 or less
be-What is the smallest this number could be?
Trang 25MP 8
27 Julie has 5 steps up to her classroom, where
step 5 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 3 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 andFido is the youngest Fido is 10 years younger than Bob, and none ofthe 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?
30 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?
Trang 35注意：
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Individual students, nonprofit libraries, or schools are permitted to make fair use of the papers and its
solutions Republication, systematic copying, or
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Trang 36Middle Primary 1
Middle Primary Division
Questions 1 to 10, 3 marks each
1. How many eggs are in these
4. A bowl has 8 peaches After the children take one
each, there is one peach left How many children
are there?
5. A Runnyball team has 5 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
1 2 3 4 5 6 7 8
Player
Trang 37Middle 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?
r r
Which boy owns a dog?
(A) Alex (B) Chris (C) Finn
(D) Jo (E) Teejay
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) 4 blocks east, 3 blocks north
(B) 3 blocks west, 4 blocks north
(C) 4 blocks west, 2 blocks north
(D) 3 blocks east, 2 blocks north
(E) 2 blocks north, 2 blocks south 1st Avenue
2nd Avenue
3rd Avenue 4th Avenue 5th Avenue
N
E
Trang 38Middle Primary 3
10. Jake is playing a card game, and
these are his cards
Elena chooses one card from Jake at
Questions 11 to 20, 4 marks each
11. In Jacqui’s puzzle, a number is put in
Trang 3914. 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
=+
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) 5 cents
17. 27 identical cubes are used to make this
Trang 40Middle Primary 5
18. Meena has a $50 gift voucher to spend in a toyshop, but they won’tgive change from the voucher Here is a short list of toys she wouldlike She tried to spend as much of the $50 as possible
If she buys no more than one of each toy, how much of the voucherwill not get used?
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 isunfolded, what will it look like?
Trang 41Middle 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 shewalks
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 inthe car?
Questions 21 to 25, 5 marks each
21. In my dance class, 14 students are taller than Bob, and 12 are shorterthan Alice Four students are both shorter than Alice and taller thanBob How many students are in my dance class?
22. My sister and I are playing a game where she picks two countingnumbers and I have to guess them When I tell her a number, shemultiplies my number by her first number and then adds her secondnumber
When I say 15, she says 50 When I say 2, she says 11
If I say 6, what should she say?
23. A year 6 student saved 100 cents in 5 days, each day saving 5 centsmore than the previous day How many cents did she save on the fifthday?
(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?
Trang 42it is turned, the two red sides are always opposite, and cannot matchSquare 1.
How many different squares could she build?
For questions 26 to 30, shade the answer as a whole number from 0 to 999 in the space provided on the answer sheet.
Questions 26–30 are worth 6, 7, 8, 9 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
Trang 43Middle 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 ofboys 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 3 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?