This is my recorded video, with a few polishes, explaining how you can solve this question most efficiently.

Question 9: Let ABCD be a quadrilateral with coordinates (2,2), (14,2), (16,0), and (0,0).
This quadrilateral is inscribed in a circle. What is the area of this circle?

(A) 61π (B) 64π (C ) 79π (D) 81π (E) 100π

Question 10: Consider the sequence t_1,t_2,t_3,...,t_{15},t_{16},t_{17}. This sequence has the following three properties.

(i) Each of the 17 integers from 1 to 17 appears exactly once in the sequence.

(ii) The sum of each pair of consecutive terms is a perfect square. (For example, t_1 +t_2 is a perfect square, t_2 +t_3 is a perfect square, and so on.)

(iii) t_1 = 17.

What is the value of t_5?

(A) 3 (B) 6 (C ) 10 (D) 13 (E) 15

Question 11: Alphonse drives to Beryl’s house, intending to arrive at a certain time. There is no traffic on the road between the two houses, and so Alphonse can drive at a constant speed.

If Alphonse drives at x kilometres per hour, then he will arrive 7 minutes early.
If Alphonse drives at y kilometres per hour, then he will arrive 7 minutes late.
If Alphonse drives at 72 kilometres per hour, then he will arrive exactly on time.

If x and y are positive integers, what is the smallest possible value of x+ y?

(A) 144 (B) 147 © 150 (D) 156 (E) 162 (F) 180

Question 12: Suppose we remove two diagonally-opposite corner squares from an 8 by 8 board, as shown in the diagram below.

How many squares and rectangles, of all sizes, appear on this modified board?

(A) 1127 (B) 1158 (C ) 1159 (D) 1169 (E) 1200 (F) 1296

Question 13: You are given a biased coin, where Heads comes up with probability \frac{2}{3} and Tails comes up with probability \frac{1}{3}.

You play a game where you start with 0 points. Each time you flip Heads, you add 2 points to your score. Each time you flip Tails, you add 1 point to your score.

If you reach a total of exactly n points, then you win. However, if you go over n points, then you lose.

Let P_n be the probability that you win the game with a target score of n points. For example, P_2 =\frac{7}{9} because you win the game by flipping H (probability \frac{2}{3} ) or TT (probability \frac{1}{9} ) but lose by flipping TH (probability \frac{2}{9} ).

Determine the value of P_8, rounded to three decimal places.

(A) 0.576 (B) 0.584 (C ) 0.592 (D) 0.600 (E) 0.608 (F) 0.616

Question 14: Let A,B,C,D,E,F be six points equally spread out around a circle. Draw all 15 edges connecting two of these six points. Aponi picks 8 of these 15 edges and colours them red; the remaining 7 edges are then coloured blue.

Consider all triangles that can be formed from three of these six points. For each triangle that has only red edges, Aponi scores 1 point. For each triangle that has only blue edges, Aponi scores 2 points. For all other triangles (e.g. a triangle with two red edges and one blue edge), Aponi scores 0 points.

Let X be the maximum score that Aponi can obtain, and let Y be the minimum score that Aponi can obtain.

What is the value of X−Y?

(A) 5 (B) 6 (C ) 7 (D) 8 (E) 9 (F) 10