SEAMO 2022 — Paper B — Grade 3–4

Five numbers have average $7$. One is changed to $9$, making the new average $8$. What was that number originally?

What is the $100$th number in $1,4,7,10,\ldots$?

In the pentagon, $\angle A=90^\circ$. Find $\angle B+\angle C+\angle D+\angle E$.

A square number is a number multiplied by itself, such as $1\times1=1$, $2\times2=4$, $3\times3=9$. Find the first square number greater than $2022$.

Find the perimeter of the figure shown.

A two-digit number is ascending if its units digit is greater than its tens digit, for example $12,56,39,27$. How many two-digit ascending numbers are there?

Mdm Jones distributes $20$ rice dumplings and $25$ apple pies to her neighbours. She has $2$ dumplings left but is short of $2$ pies. How many neighbours receive the food?

Find the possible pairs $(A,B)$ in $\overline{7A36B}$ so that this five-digit number is divisible by both $5$ and $9$.

$ABCD$ is a rectangle of area $40\text{ cm}^2$. Point $H$ lies on $AD$, while $E,F,G$ are the midpoints of $AB,BC,CD$. Find the total shaded area.

A car leaves $A$ and a motorcycle leaves $B$ simultaneously, travelling in the same direction. At $60\text{ km/h}$ the car catches the motorcycle in $5$ hours; at $70\text{ km/h}$ it catches it in $3$ hours. Find the motorcycle’s speed.

The solid consists of three layers of $2\text{ cm}\times2\text{ cm}\times2\text{ cm}$ cubes. Find the total area of exposed surfaces on the top and sides.

There are $48$ books on three shelves. Candy moves $8$ books from the top to the middle, then $6$ from the middle to the bottom. The shelves then have equal numbers. How many books were originally on the top shelf?

How many consecutive digits $1$ occur in the product of the number with $2022$ digits all $8$ and the number with $2022$ digits all $9$?

The area of a circle is $\pi r^2$, where $\pi=22/7$ and $r$ is the radius. Find the shaded area in the quadrant of radius $7\text{ cm}$.

Students $A,B,C,D,E$ occupy the top five ranks. Their guesses are: $A$: $B$ is second, $C$ fifth; $B$: $D$ second, $E$ fourth; $C$: $E$ first, $A$ fifth; $D$: $C$ second, $B$ third; $E$: $D$ third, $A$ fourth. Each student has exactly one correct statement. Who is first?

The number $37$ can be expressed as a sum of distinct prime numbers, for example $3+5+29$ or $2+5+7+23$. How many such sums are possible?

Starting on $1$ January $2022$, $A$ works three days then rests one day. $B$ works five days then rests two days. $C$ covers days on which both are off. How many days does $C$ work in $2022$?

Find the remainder when $666666$ is divided by $13$.

Find the number of shortest paths from $A$ to $B$.

It is now $5$ pm. How many minutes later will the hour and minute hands first lie at equal angular distances on opposite sides of the number $5$?