SASMO 2015 Primary 5 (Grade 5) Contest

Question 1

An operator $\heartsuit$ acts on two numbers as follows: $3\heartsuit2=61$, $5\heartsuit3=152$, $6\heartsuit1=65$, $9\heartsuit4=365$. What is $7\heartsuit5$?

1. 230
2. 235
3. 302
4. 352
5. None of the above

Question 2

Fill in the blank: 2 tens 5 ones more than ___ is 4 tens 3 ones.

1. 18
2. 28
3. 58
4. 68
5. None of the above

Question 3

Find the missing term in the sequence $1,8,27,64,\_\_,216$.

1. 81
2. 100
3. 125
4. 149
5. 281

Question 4

Find the smallest whole number between 1 and 100 that is divisible by 12 and by 18.

1. 24
2. 36
3. 48
4. 54
5. 72

Question 5

If the five-digit number $123N5$ is divisible by 9, find $N$.

1. 2
2. 4
3. 5
4. 7
5. 9

Question 6

An equilateral triangle is cut into four pieces and rearranged to form a square. If the square has side 13 cm and the triangle has height 17 cm, find the side length of the triangle, correct to the nearest whole number.

1. 18 cm
2. 19 cm
3. 20 cm
4. 21 cm
5. 22 cm

Question 7

$2^4$ means 2 multiplied by itself 4 times. Find the last digit of $5^{10}$.

1. 0
2. 1
3. 5
4. 6
5. None of the above

Question 8

In a soccer tournament, 12 teams play against each other twice. How many games are there altogether?

1. 24
2. 66
3. 78
4. 132
5. 156

Question 9

A perfect-square year is a year that is a perfect square. When is the next perfect-square year?

1. 2016
2. 2020
3. 2025
4. 2116
5. None of the above

Question 10

A ruler, pencil, eraser and sharpener lie in a row. The sharpener is next to neither the ruler nor the eraser. The pencil is not third. The eraser is neither first nor last. What is the order from first to last?

1. Pencil, eraser, ruler, sharpener
2. Sharpener, eraser, ruler, pencil
3. Pencil, eraser, sharpener, ruler
4. Pencil, ruler, eraser, sharpener
5. Sharpener, pencil, eraser, ruler

Question 11

A big rectangle is made of 4 identical small rectangles. If the longer side of a small rectangle is 20 cm, find the area of the big rectangle.

1. 600 cm²
2. 800 cm²
3. 2015 cm²
4. 3200 cm²
5. Not enough information

Question 12

Which statements are correct? A: $8+(0\div2015)=8$. B: $8+(2015\div0)=8$. C: $8+(0\times2015)=8$.

1. Only C
2. Only B and C
3. Only A and C
4. All three
5. None of the above

Question 13

Numbers $x$ and $y$ satisfy $3\le x\le6$ and $8\le y\le10$. Find the least possible value of $y-x$.

1. 0
2. 2
3. 3
4. 5
5. None of the above

Question 14

A palindromic whole number reads the same forward and backward. How many 3-digit palindromic numbers are there?

1. 19
2. 90
3. 100
4. 900
5. None of the above

Question 15

Simplify $\frac{1}{2+\frac34}$.

1. $\frac49$
2. $\frac4{11}$
3. $1\frac14$
4. $2\frac34$
5. None of the above

Question 16

Cheryl wants to cut $4$ cm by $3$ cm rectangular cards from a $30$ cm by $22$ cm sheet. Find the greatest number of cards that can be cut.

Question 17

The product of two numbers is 100. Neither number has 10 as a factor. Find their sum.

Question 18

A circle and a triangle are drawn on a flat surface. What is the greatest number of regions that can be formed?

Question 19

A train travels at 60 km/h and is 100 m long. Find the time for it to pass completely through a 1-km tunnel.

Question 20

How many rectangles are there in a $3\times3$ square grid? A square is also a rectangle.