SEAMO X 2022 — Paper C — Grade 5–6

Evaluate $2023.25\times2024.75-2021.25\times2026.75$.

At $5{:}00$ pm Mink wonders when the hour and minute hands will be equally distant from the number five on opposite sides. Find the time.

Find the units digit of $2+2\times3+2\times3^2+\cdots+2\times3^{10}$.

Arrange $5^{273},2^{728},3^{455}$ in ascending order.

Evaluate $2022\left(\frac1{2\times4}+\frac1{4\times6}+\cdots+\frac1{2020\times2022}\right)$.

Removing one black marble gives black:red ratio $9:7$. Replacing it and removing one red marble gives $7:5$. How many more black marbles than red were originally in the box?

Use each of $+,-,\times,\div$ once in $10\square10\square10\square10\square10$ to obtain the smallest result. Negative integers are allowed. Find the result.

Find the remainder when $7^{2022}+8^{2022}$ is divided by three.

Regular hexagon $ABCDEF$ has printed area $108\text{ cm}^3$. Find the area of shaded triangle $ABX$ formed by diagonals $AC,BF$.

Mink cycles from home at $8{:}08$ am at constant speed. Her brother follows on a motorcycle eight minutes later, catches her four km from home, returns immediately, then leaves again and catches her eight km from home. When is the second catch?

In the problem’s NBA season scenario, each team plays sixty-six matches, with at most one per day, three in any four days, five in any seven days, and eight in any thirteen days. The season starts December twenty-six. How many days does it last?

Given $\angle ABC=\angle ACB$, $\angle ADC=\angle DAC$, and $\angle DAB=21^\circ$, find $\angle ABC$.

Two bottles of saline have concentrations $8\%$ and $5\%$. Mixing their full contents gives $6.2\%$. In a second experiment, one quarter of the first and one sixth of the second are mixed. Find the new concentration.

Find the sum of all digits of $111111111\times999999999$.

Isosceles triangle $PAB$ is inside square $ABCD$ of side six cm, with $PA=PB=5$ cm and diagonal $AC$. Find shaded area $PAC$.