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.
The printed year 2018 controls catalogue identity; the supplied filename contains a different year.
In the figure, right triangle $ABC$ has $AB=3$, $AC=4$, $BC=5$ units. $D$ lies on $BC$ and $AD\perp BC$. What is the area of a square whose side is $AD$?
A mobile phone normally costs 26900 baht. A promotion reduces the price by 9000 baht. Credit-card payment receives another 5% discount, and the discounted price is paid in 10 equal monthly instalments without interest. How much is each monthly payment?
From one rectangle form rectangle 1 by increasing its length by 25% and decreasing its width by 20%; its area is $a$. Form rectangle 2 by decreasing the original length by 20% and increasing the original width by 25%; its area is $b$. Which statement is true?
At the 2018 FIFA World Cup, 32 teams were drawn into eight groups A–H of four teams. In the first round, every pair within a group played once. A win earned 3 points and a loss 0; a draw earned each team 1 point. The two highest-scoring teams in each group advanced to the second round.
Group C has Australia, Denmark, France and Peru. Results: France beat Australia 2–1; Peru lost to Denmark 0–1; Denmark drew with Australia 1–1; France beat Peru 1–0; Australia lost to Peru 0–2; Denmark drew with France 0–0. What is the total number of group C points after the first round?
At the 2018 FIFA World Cup, 32 teams were drawn into eight groups A–H of four teams. In the first round, every pair within a group played once. A win earned 3 points and a loss 0; a draw earned each team 1 point. The two highest-scoring teams in each group advanced to the second round.
Portugal led Spain 2–1 at half-time. In the second half the teams scored three more goals in total. Which final result is impossible?
At the 2018 FIFA World Cup, 32 teams were drawn into eight groups A–H of four teams. In the first round, every pair within a group played once. A win earned 3 points and a loss 0; a draw earned each team 1 point. The two highest-scoring teams in each group advanced to the second round.
After the first round, the total points of all 32 teams were 135. How many drawn matches were there across all groups?
Exponentiation $b^n$ has base $b$ and exponent $n$. For positive integer $n$, it means multiplying $n$ copies of $b$. For example, $3^2=9$, with base 3 and exponent 2. A tower is evaluated from the top: $3^{2^4}=3^{16}$ has base 3 and exponent $2^4=16$, not base $3^2$ and exponent 4. The latter requires parentheses: $(3^2)^4=3^8$.
Exponentiation $b^n$ has base $b$ and exponent $n$. For positive integer $n$, it means multiplying $n$ copies of $b$. For example, $3^2=9$, with base 3 and exponent 2. A tower is evaluated from the top: $3^{2^4}=3^{16}$ has base 3 and exponent $2^4=16$, not base $3^2$ and exponent 4. The latter requires parentheses: $(3^2)^4=3^8$.
In triangle $ABC$, $\angle BAC=20^\circ$ and $AB=AC=10$ units. Extend $BC$ beyond $C$ to $D$ with $BD=AB$. Through $D$ draw a line parallel to $AC$ meeting $E$ such that $\angle EBD=20^\circ$ and $BE=BD$. Find the perimeter of triangle $ABE$.
$ABC$ is equilateral and $WXVZ$ is a square as stated in the source (the drawing labels its upper-right vertex $Y$). Given $\angle CZY=40^\circ$, find $\angle XWB$.
