SEAMO 2022 — Paper D — Grade 7–8

Compare (i) $2^{329}$ and (ii) $5^{141}$. Which statement is true?

A bell chimes whenever the hands of a standard twelve-hour clock form a $180^\circ$ angle. How many chimes occur from one midnight to the next?

If $7.03^3=347.428927$, find $0.703^3$.

Integers $m\gt n$ satisfy $m+n=20,m^2+n^2=328$. Find $m^2-n^2$.

Evaluate $\sum_{k=1}^{2021}\frac{2022}{k(k+1)}$.

Find the smallest positive integer k such that $2^{91}+k$ is divisible by one hundred twenty-seven.

The six-digit integer $\overline{abcdef}$ satisfies $\overline{fabcde}=5\overline{abcdef}$. Find a+b+c+d+e+f.

A sphere’s radius increases five percent. Find its volume’s percentage increase, to one decimal place. Use $V=4\pi r^3/3$.

Two independent football matches each have equally likely win, draw and loss. The probability of at least one draw is m/n. Find m+n.

Positive integers x,y are less than ten and satisfy $2^x9^y=\overline{2x9y}$. Find x+y.

Solve $\log_x(2x^2-7x+12)=2$.

Solve $1+\sin\theta-2\cos^2\theta=0$ for $0^\circ\le\theta\le90^\circ$.

Find the last two digits of $9^{2022}$.

In the cryptarithm $MATH+MATH=HABIT$, different letters represent distinct digits. Find B.

If $x^2-10x+1=0$, find $x^4+x^{-4}$.

Evaluate $\frac{16}{345678^2-345674\times345682}$.

In triangle ABC, $AB=AC$. D is on AC and E on AB, with $AD=DE=BE$ and $BD=BC$. Find angle A.

Given $a=\sqrt6-2,b=2\sqrt2-\sqrt6$, which statement is true?

Count integers n from one through $2022$ for which $1^n+2^n+3^n+4^n+5^n$ is divisible by five.

Which expression is greatest?