Australian Mathematics Competition - 2012 - Middle Primary - Grade 3 & 4 - Questions and Solutions

Problem 1:

The value of \(48-25\) is
(A) 63
(B) 17
(C) 27
(D) 13
(E) 23

Problem 2:

The area, in square metres, of the rectangle below is

(A) 9
(B) 10
(C) 12
(D) 14
(E) 16

Problem 3:

In which order would you place the following cards to make the largest 5-digit number?

(A) PQR
(B) QRP
(C) QPR
(D) PRQ
(E) RQP

Problem 4:

What should we get if we add one tenth, one hundredth and two thousandths?
(A) 112
(B) 1.12
(C) 300
(D) 0.112
(E) 0.13

Problem 5:

Mary's soccer team wins a game by two goals. Between them the two teams scored 8 goals. How many goals did Mary's team score?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 8

Problem 6:

Which of these spinners would be more likely to spin a rabbit?

Problem 7:

What is the perimeter, in metres, of the shape

below?

(A) 9
(B) 12
(C) 15
(D) 18
(E) none of these

Problem 8:

The digits of 2012 can be arranged to make several 4-digit numbers (the first digit of a 4-digit number cannot be zero). The difference between the largest and the smallest of these is
(A) 2012
(B) 1202
(C) 1122
(D) 1180
(E) 1188

Problem 9:

Mary colours in a honeycomb tessellation of hexagons. If hexagons share a common edge, she paints them in different colours.

What is the smallest number of colours she needs?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6

Problem 10:

Sentries marked \(S\) guard the rows and columns they are on. Sentries marked \(T\) guard

diagonally. How many squares are unguarded?
(A) 1
(B) 3
(C) 5
(D) 7
(E) 8

Problem 11:

Sam is 12 years old and Tom is 7 years old. When the sum of their ages is 45 , how old will Tom be?
(A) 15
(B) 19
(C) 20
(D) 25
(E) 27

Problem 12:

The net shown is folded to make a cube. Which face is opposite the face marked O ?
(A) J
(B) K
(C) L
(D) M
(E) N

Problem 13:

Three standard dice are rolled and the numbers on the top faces are added together.

How many different totals are possible?
(A) 15
(B) 16
(C) 18
(D) 24
(E) 36

Problem 14:

A garden stake is used to support a small tree. 90 cm of the stake is above the ground and one-third of the stake is below the ground. How long is the stake?
(A) 135 cm
(B) 120 cm
(C) 93 cm
(D) 90 cm
(E) 30 cm

Problem 15:

The square shown is a magic square. This means that the sum of all rows, columns and diagonals are the same. What is the value of \(R\) ?
(A) 8
(B) 9
(C) 12
(D) 13
(E) 16

Problem 16:

Adrian is watching a 90 -minute movie. His computer indicates that the movie is seven-tenths of the way through. How long is there still to play?
(A) 25 minutes
(B) 27 minutes
(C) 37 minutes
(D) 63 minutes
(E) 90 minutes

Problem 17:

Michael threw 8 darts at the dartboard shown.

All eight darts hit the dartboard. Which of the following could have been his total score?
(A) 22
(B) 37
(C) 42
(D) 69
(E) 76

Problem 18:

Five students, Cam, Franco, Adrian, Trent and Xavier line up in order of age from youngest to oldest. Cam is next to Adrian in the line while Franco and Trent are not next to each other. Who cannot be in the middle of the line?
(A) Cam
(B) Franco
(C) Adrian
(D) Trent
(E) Xavier

Problem 19:

Alex placed 9 number cards and 8 addition symbol cards on the table as shown.

Keeping the cards in the same order he decided to remove one of the addition cards to form a 2-digit number. If his new total was 99, which 2-digit number did he form?
(A) 32
(B) 43
(C) 54
(D) 65
(E) 76

Problem 20:

Ann thinks of a two-digit number and notices that the first digit is one more than twice the second digit. How many different numbers could she have thought of?
(A) 1
(B) 2
(C) 3
(D) 5
(E) 6

Problem 21:

Five towns are joined by roads, as shown in the diagram.

How many ways are there of travelling from town \(P\) to town \(T\) if no town can

be visited more than once?
(A) 3
(B) 5
(C) 6
(D) 7
(E) 9

Problem 22:

Mike is one year older than his brother and one year younger than his sister. When all three ages are multiplied together the result is 504. What is the sum of their ages?
(A) 17
(B) 16
(C) 21
(D) 24
(E) 36

Problem 23:

One of the mischief makers in a class decided to play a prank by glueing together some \(1 \times 1 \times 1\) blocks to form a solid cube. If he used 64 blocks to make the cube and needed to put glue on every face that was to be touching another face, how many faces were glued?
(A) 176
(B) 216
(C) 240
(D) 264
(E) 288

Problem 24:

Jasdeep plays a game in which he has to write the numbers 1 to 6 on the faces of a cube. However, he loses a point if he puts two numbers which differ by 1 on faces which share a common edge. What is the least number of points he can lose?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4

Problem 25:

Twelve points are marked on a square grid as shown.

How many squares can be formed by joining 4 of these

points?
(A) 5
(B) 6
(C) 9
(D) 11
(E) 13

Problem 26:

A \(5 \times 5 \times 5\) cube has a \(1 \times 1 \times 5\) hole cut through from one side to the opposite side, a \(3 \times 1 \times 5\) hole through another and a \(3 \times 1 \times 5\) hole through the third as shown in the diagram.

How many \(1 \times 1 \times 1\) cubes are removed in this process?

Problem 27:

The difference between two numbers is 42 . If five is added to each of them, the larger number becomes three times the smaller number. What is the larger number at the start?

Problem 28:

A rectangular tile has a perimeter of 24 cm . When Sally places four of these tiles in a row to create a larger rectangle, she finds the perimeter is double the perimeter of a single tile. What would be the perimeter of the rectangle formed by adding another 46 tiles to make a row of 50 tiles?

Problem 29:

How many ways are there of walking up a set of 7 stairs if you can take one or two steps at a time?

Problem 30:

A rhombus-shaped tile is formed by joining two equilateral triangles together. Three of these tiles are

combined edge to edge to form a variety of shapes as in the example given.

How many different shapes can be formed? (Shapes which are reflections or rotations

of other shapes are not considered different.)