SASMO 2014 Primary 4 (Grade 4) Contest

Find the missing term in the following sequence: $1,4,9,16,\_\_,36$.

Find the smallest whole number between 1 and 100 that is divisible by 5 and by 7.

A frog fell into a drain that was 20 cm deep. After one hour, it gathered enough energy to jump 6 cm, but it then slid down 4 cm. If it continued in this manner after every hour, how many hours would it take to get out of the drain?

The diagram shows a circle with centre $O$ and radius 5 cm. $OABC$ is a rectangle. What is the length of $AC$?

A textbook is opened at random. To what pages is it opened if the product of the facing page numbers is 420?

A shop sells sweets where every 3 sweet wrappers can be exchanged for one more sweet. Kelvin has enough money to buy only 19 sweets. What is the biggest number of sweets that he can get from the shop?

A clock takes 6 seconds to make 3 chimes. Assuming that the rate of chiming is constant and the duration of each chime is negligible, how long does the clock take to make 4 chimes?

The diagram shows a square divided into four rectangles. If the sum of the perimeters of the four rectangles is 32 cm, find the area of the square.

Alvin, Betty and Cheryl scored a total of 2014 points during a competition. Betty scored 271 points less than Alvin. Betty scored 3 times as many points as Cheryl. How many points did Betty score?

When the five-digit number $76N43$ is divided by 9, the remainder is 5. Find $N$.

The diagram shows a rectangle with its two diagonals. What fraction of the rectangle is shaded?

Each figure is formed by surrounding one row of black squares with white squares, as shown. In which figure will there be 2014 white squares?

Find the total number of squares in a $4\times4$ square grid.

How many digits are there before the fifteenth 7 in the following number?

$37337333733337333337\ldots$

A box contains 30 coloured pens: 15 blue, 10 red and 5 black. Alice takes some pens from the box without looking at their colours. What is the least number of pens she must take so that she has at least 8 pens of the same colour?

In the following alphametic, all different letters stand for different digits. Find the four-digit sum $PEEL$.

$$AM+LAP=PEEL$$

A teacher has a bag of sweets for her class. If she gave 4 sweets to each student, she would have 82 sweets left. If she gave 9 sweets to each student, she would have 2 sweets left. How many students and how many sweets are there?

When Amy, Betty and Cheryl eat out, each orders either beef or chicken.

(a) If Amy orders beef, Betty orders chicken.

(b) Either Amy or Cheryl orders beef, but not both.

(c) Betty and Cheryl do not both order chicken.

Who could have ordered beef yesterday and chicken today?

What are the last three digits of the sum

$$1+11+111+\cdots+\underbrace{111\ldots111}_{70\text{ digits}}?$$

The diagram shows 9 points. Draw 4 consecutive line segments (the starting point of each new segment must coincide with the endpoint of the previous segment) to pass through all 9 points.