SASMO 2015 Primary 6 (Grade 6) Contest

Question 1

Fill in the blank: 6 tens 9 ones greater than 7 is the same as 1 ten 6 ones less than ____.

1. 46
2. 60
3. 76
4. 92
5. None of the above

Question 2

The diagram shows how an equilateral triangle can be cut into four pieces and rearranged to form a square. If the side of the square is 16 cm and the height of the triangle is 21 cm, find the side length of the triangle, correct to the nearest whole number.

1. 22 cm
2. 23 cm
3. 24 cm
4. 25 cm
5. 26 cm

Question 3

An operator $\diamond$ acts on two numbers as shown: $3\diamond2=65$, $5\diamond3=158$, $6\diamond1=67$, $9\diamond4=3613$. What is $7\diamond5$?

1. 1235
2. 1335
3. 3512
4. 3513
5. None of the above

Question 4

$3^4$ means 3 multiplied by itself 4 times. Find the last digit of $6^{10}$.

1. 0
2. 1
3. 6
4. 8
5. None of the above

Question 5

Find the missing term in the sequence $2,5,10,17,\square,37$.

1. 23
2. 24
3. 26
4. 27
5. 29

Question 6

A perfect square year is a year whose number is a perfect square. When was the previous perfect square year?

1. 1764
2. 1849
3. 1936
4. 2012
5. None of the above

Question 7

If the five-digit number $2345N$ is divisible by 6, find $N$.

1. 0
2. 2
3. 4
4. 6
5. 8

Question 8

How many rectangles are there in a $4\times4$ square grid? Note: a square is also a rectangle.

1. 70
2. 90
3. 100
4. 110
5. None of the above

Question 9

The height of a man is 150 cm, correct to the nearest centimetre. What is the lowest possible height of the man?

1. 149 cm
2. 149.4 cm
3. 149.5 cm
4. 149.9 cm
5. None of the above

Question 10

Simplify $\displaystyle\frac{1}{2+\frac{3}{4+\frac56}}$.

1. $\frac{2}{33}$
2. $\frac{29}{76}$
3. $2\frac{1}{12}$
4. $2\frac{18}{29}$
5. None of the above

Question 11

A palindromic number is a whole number that reads the same forward and backward. How many four-digit palindromic numbers are there?

1. 19
2. 90
3. 100
4. 9000
5. None of the above

Question 12

A bag contains some sweets that can be divided equally among 3, 4, 6 or 7 children with no remainder. What is the smallest possible number of sweets?

1. 42
2. 84
3. 168
4. 504
5. None of the above

Question 13

Given that $xyz=2015$, where $x,y,z$ are whole numbers and $x<y<z$, how many possible triples $(x,y,z)$ are there?

1. 1
2. 4
3. 5
4. 27
5. None of the above

Question 14

Daniel wants to cut $3$ cm by $2$ cm rectangular cards from a $50$ cm by $19$ cm rectangular sheet. Find the greatest number of cards that can be cut.

1. 144
2. 150
3. 158
4. 159
5. None of the above

Question 15

A train travels at 90 km/h and is 300 m long. Find the time taken for the train to pass completely through a 4.5 km tunnel.

1. 3 min
2. 3 min 2 s
3. 3 min 12 s
4. 3 min 20 s
5. None of the above

Question 16

The product of two numbers is 1000. Neither number has 10 as a factor. Find the difference between the two numbers.

Question 17

Given that $4!=4\times3\times2\times1$, find the number of consecutive zeros at the end of $14!$.

Question 18

Jerry drives 2000 km during a trip. He rotates the four tyres on the car and one spare so that each tyre is used for the same distance. How many kilometres are covered by each tyre?

Question 19

Jane is at a junction with four roads to her friend's house. Four passersby make the statements shown in the source. If only one passerby tells the truth, on which road does Jane's friend live?

Question 20

The diagram shows a rectangle divided into three smaller rectangles and a square. If the perimeter of the unshaded rectangle is 48 cm and the square area is 36 cm², find the total area of the shaded rectangles.