[EASY 2] One number is three times another number, and their sum is 5/2. By how much does the larger number

exceed the smaller number?

(a)  

[EASY 3] What is the area of the circle with equation $$x^2 + y^2 - 2x = 4$$ (in square units)?

(a)  

[EASY 4] When a polynomial is divided by $$x + 2$$ , the quotient is $$x - 3$$ and the remainder is $$-2$$ . What is the remainder when the polynomial is divided by $$x+1$$ ?

(a)  

[EASY 5] What is the slope of the line tangent to the circle $$x^2 + y^2 = 10$$ at the point $$(-1, -3)$$ ?

(a)  

[EASY 6] If $$\sqrt{2x - 2} = 10$$ , what is $$\sqrt{x-2}$$ ?

(a)  

[EASY 7] If $$1 + 2 + 3 + \cdots + n = 78$$ , what is $$n$$ ?

(a)  

[EASY 8] From 12 noon to 3:40 PM, how many degrees does the tip of the hour hand travel?

(a)  

[EASY 9] What is the probability that three randomly chosen people were born on three different days of the week?

(a)  

[EASY 10] What is the radius of the circle inscribed in a $$15-20-25$$ triangle?

(a)  

[AVERAGE 1] If the equation of the perpendicular bisector of the segment joining the points (4, 3) and (1, -2) is general form (Ax + By + C = 0), find A + B + C.

(a)  

[AVERAGE 2] If $$x^2 + y^2 + 25 = 2(4y - 3x)$$ , what is $$x - y$$ ?

(a)  

[AVERAGE 3] The highest point of a parabola has coordinates (-1, 4). If it passes through the point (-5, -12), find the x -intercept of the parabola on the negative x-axis.

(a)  

[AVERAGE 4] Of ten fifty-peso bills, three are counterfeit. Six bills are chosen at random. What is the probability that all counterfeit bills are chosen?

(a)  

[AVERAGE 5] Find the number of integer solutions $$x$$ in the inequality $$\left|\sqrt[]{x}-20\right|<25$$ .

(a)  

[DIFFICULT 1] Two positive numbers differ by 6, and their reciprocals differ by $$\frac{1}{36}$$ . Find the sum of their squares.

(a)  

[DIFFICULT 2] The zeros of the polynomial P(x) = x³ + Bx² + Cx + D are thrice those of Q(x) = x³ - 4x² + 2x - 5. Find B + C + D.

(a)  

[DIFFICULT 3] In triangle ABC, AB = 4. BC = 6. and AC = 8. Point D is on AC such that BD = AB. Find AD.

(a)  

[DIFFICULT 4] In how many ways can the letters of the word DIVISIBLE be arranged without having 2 I's next to each other?

(a)  

[DIFFICULT 5] If 20x² + 25x +1 = A(x + 2)² + B(x + 5) + C for all x, find A + B + C.

(a)