Printed positive marks are preserved per question. The source uses different blank-answer and incorrect-answer rules by section, including an optional bonus penalty; the import does not reproduce that complete official scoring scheme.
$O$ is the centre of a circle with diameter $AB$. Points $C,D$ lie on the circumference as shown. Given $\angle ACB=90^\circ$, $\angle OAD=59^\circ$ and $DO\parallel AC$, find $\angle ABC$.
A composite number is a positive integer expressible as a product of two or more smaller positive integers greater than 1. For example, $20=2\times10$ is composite, but 3 is not. Exactly one of 2345, 23456, 234567, 2345678, 23456789 is not composite. Which one?
In Part I of the Thailand Mathematics Contest (TMC), each of questions 1–12 has exactly one correct choice among A–E. A correct answer earns 4 points, a blank earns 1 point, and an incorrect answer earns 0. Marking more than one choice earns 0. Students should choose one choice or leave it blank. What is the probability that Jack gets nonzero points on question 6?
Let $a>0$. Consider: (1) $2a$ is always greater than $a$; (2) $a^2$ is always greater than $a$; (3) $0.5a$ is always less than $a$; (4) $0a$ is always less than $a$. How many statements are true?
A box contains ten cards numbered 1 to 10, one number per card. Remove one card so that the remaining cards can be divided into two piles having equal products. What is that common product?
