SEAMO 2026 Paper D SET 1 – Self-practice

Which of the following statements has a larger value? Compare $(i)=\underbrace{2\times2\times\cdots\times2}_{329\text{ factors}}$ and $(ii)=\underbrace{5\times5\times\cdots\times5}_{141\text{ factors}}$.

Each time the hands of a standard 12-hour clock form a 180° angle, a bell chimes once. From midnight today until midnight tomorrow, how many chimes will be heard?

If $7.03^3=347.428927$, then $0.703^3$ is equal to

Let $m,n$ be integers with $m\gt n$. Suppose $m+n=20$ and $m^2+n^2=328$. Find $m^2-n^2$.

Find the sum $\frac{2022}{1\times2}+\frac{2022}{2\times3}+\frac{2022}{3\times4}+\cdots+\frac{2022}{2021\times2022}$.

Find the smallest positive integer $k$ such that $2^{91}+k$ is divisible by 127.

Let $\overline{abcdef}$ be a 6-digit integer such that $\overline{fabcde}$ is 5 times $\overline{abcdef}$. Find $a+b+c+d+e+f$.

If the radius of a sphere increases by 5%, what is the corresponding percentage increase in its volume, corrected to 1 decimal place? [Volume of sphere $=\frac43\pi r^3$.]

A football match can be won, drawn or lost with equal probability. A school plays 2 matches each week. The probability that at least one match is drawn that week is $m/n$. Find $m+n$, where $m,n$ are coprime positive integers.

Find positive integers $x,y$, with $x\lt 10,y\lt 10$, satisfying $2^x9^y=\overline{2x9y}$. Find $x+y$.

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

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

The last two digits of $9^{2022}$ are

In the cryptarithm below, each letter represents a unique digit. What digit is represented by B? $\overline{MATH}+\overline{MATH}=\overline{HABIT}$.

If $x^2-10x+1=0$, find $x^4+\frac1{x^4}$.

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

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

Given $a=\sqrt6-2$ and $b=2\sqrt2-\sqrt6$, then

How many integers n between 1 to 2022 are there such that $1^n+2^n+3^n+4^n+5^n$ is divisible by 5?

Which of the following expressions has the greatest value?