SEAMO self-study edition 2027; not an official 2027 paper. Original source years are retained. 25 questions, 90 minutes; Q1–10: 3 points, Q11–20: 4 points, Q21–25: 6 points, total 100. Original response types and all subparts are preserved. Verified is an editorial convention; source defects, necessary assumptions and unresolved mathematical uncertainty are disclosed.
It is known that $m,n,p$ are positive integers, where $m\lt n\lt p$. If $2^m+2^n+2^p=2336$, find $m$.
Given that $a,b,c$ are positive real numbers and $a+b+c=1$, evaluate the following expression by choosing the correct option:
$$\sqrt{4a+1}+\sqrt{4b+1}+\sqrt{4c+1}.$$
Let $k$ be a real number. Find the least value of $k$ such that the following inequality is correct:
$$\sqrt{x-2}+\sqrt{7-x}\le k.$$
Interpretation for this practice: the inequality must hold for every real $x$ for which both radicals are defined, namely $2\le x\le7$. The source leaves this quantifier implicit.
If $7.03^3=347.428927$, then $0.703^3$ is equal to what?
Original printed options:
(A) 0.034728927
(B) 0.34728927
(C) 3.4728927
(D) 0.0034728927
(E) 0.00034728927
Source correction: none of the five printed options equals the exact result. All original options are retained for comparison; enter the exact numerical value instead of a letter.
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 $m+n$.
Practice assumptions: the results of the two matches are independent, and m/n is written in lowest terms with positive integers m and n. These conditions are implicit, not expressly stated in the source.
How many distinct integers are there among the following numbers?
$$\left\lfloor\frac{1^2+1}{100}\right\rfloor,\left\lfloor\frac{2^2+2}{100}\right\rfloor,\left\lfloor\frac{3^2+3}{100}\right\rfloor,\ldots,$$
$$\left\lfloor\frac{100^2+100}{100}\right\rfloor.$$
Here $\lfloor a\rfloor$ denotes the greatest integer less than or equal to $a$.
$ABCD$ is a square of side length 10 cm. $E$ and $F$ are the midpoints of $BC$ and $AB$, respectively. Find the area of $\triangle GDC$ in $\mathrm{cm}^2$, where $G$ is the intersection of $DE$ and $FC$ shown in the original figure.
The integer $N$ is formed by writing all integers from 1001 to 1021 consecutively, that is, $N=100110021003\ldots1021$. Find the greatest power of 3 that is a factor of $N$.
Mr. Woodley paid 650,000 dollars for two commercial properties. A year later, the market value of the first property rose by 20%, while that of the second dropped by 25%. The two properties then had the same market value. What was the market value of the first property at first?
