SEAMO X 2021 — Paper B — Grade 3–4

A new operation follows $3\star4=5$, $5\star6=19$, $4\star7=17$. Find $2\star3$.

Find the area of the quadrilateral with the dimensions shown.

Evaluate $1\div(2\div3)\div(3\div4)\div(4\div5)\div(5\div6)$.

Evaluate $\frac1{1\times4}+\frac1{4\times7}+\frac1{7\times10}+\cdots+\frac1{16\times19}$.

How many triangles are in the figure?

How many ways can $23$ be expressed as a sum of three odd numbers?

Five nested squares have side lengths $5,4,3,2,1$ cm. Find the total shaded area.

Each of bags $A,B$ contains $8$ black and $8$ red marbles. Jerry moves $4$ black marbles from $A$ to $B$. What is the minimum number he must transfer from $B$ back to $A$, without looking, to guarantee at least $8$ black marbles in $A$ again?

The sequence begins $1,3,4,7,1,8,9,7,6,\ldots$. From the third term onward, each is the units digit of the sum of the preceding two. Find the sum of the first $40$ terms.

A square is embedded in a right triangle. The hypotenuses of the two shaded triangles are $86$ cm and $47$ cm. Find the total shaded area.

A strip of width $3$ cm is cut from a square as shown. The remaining area is $180\text{ cm}^2$. Find the square’s side.

At a party, two children share one can of soft drink, three share one pack of potatoes, and four share one tub of fruit jelly. They consume $52$ items altogether. How many children are there?

One hundred soldiers stand in a line. From the left they call $1,2,3,1,2,3,\ldots$; then from the right they call $1,2,3,4,1,2,3,4,\ldots$. How many call $3$ twice?

Evaluate $20202021\times20212020-20202020\times20212021$.

An escalator moves upward at constant speed. Peter walks at $20$ steps per minute and reaches the top in $3$ minutes; Jane walks at $12$ steps per minute and takes $4$ minutes. How many steps long is the escalator?