SEAMO X 2022 — Paper B — Grade 3–4

It is $7$ am. How many minutes until the clock hands first form a straight line?

How many digits occur before the first $9$ in $1,1,2,1,1,2,3,2,1,1,2,3,4,3,2,1,\ldots$?

Insert $\times,\div,+,-$, once each, into $13\square13\square13\square13\square13$ to maximise its value. Encode them as $1,2,3,4$ respectively; for example $\times,\div,+,-$ is code $1234$.

Evaluate $99^2+198+1^2$.

Define $m\oplus n=m+(m+1)+(m+2)+\cdots+(m+n)$. Evaluate $4\oplus7$.

Evaluate $\frac1{1\times2\times3}+\frac1{2\times3\times4}+\frac1{3\times4\times5}+\cdots+\frac1{98\times99\times100}$.

Find the sum of all digits in $999999\times999999$. Avoid tedious multiplication.

Elaine and Florence leave their houses simultaneously, walking towards each other at $72$ and $48\text{ m/min}$ respectively. They meet $32$ metres from the midpoint between the houses. Find the distance between the houses.

A month has five Saturdays, three of whose dates are even. What weekday is the $10$th?

Find the number of paths from $A$ to $B$ in the diagram, following the indicated directions.

In triangle $ABC$ of area $21\text{ cm}^2$, $D,E,F$ are the midpoints of $AF,BD,CE$ respectively. Find the area of triangle $DEF$.

Find the last two digits of $3^{2022}$, the product of $2022$ factors of $3$.

$ABCD$ is a square of area $50\text{ cm}^2$. Points $E,F,G,H$ are side midpoints as shown. Find the shaded square’s area.

Whole numbers $a,b,c$ satisfy $a+b+c=16$ and $9a+8b+6c=135$. Find $2a+b-c$.

A drink uses $25$ g of concentrated syrup and $100$ ml water. Lina drinks half, then adds $36$ ml water. How much syrup must she add to restore the original sweetness?