4th YEAR QUESTIONS (TEAM ORAL NATIONAL LEVEL)

EASY QUESTIONS (To be answered within 15 seconds MENTALLY)

1. If  a * b = a^2 + ab , what is x in the equation 2 * x = 0 ?

2. A line passes through the point  (-2,0), and is perpendicular to the line  y = 2x. What is the equation of the line in slope-intercept form ?

3. In a class of 30 students, the average weight is 40 Kg. If 20 of the students weigh 780 Kg. altogether, what is the average weight of the other 10 students ?

4. At what points do the graphs of  y = -x^2 and y = -x  intersect ?

5. The lengths of the diagonals a  rhombus are 8 cm and 5cm respectively. What is the area of the rhombus ?

6. Teacher Ramon jogs to school from his house every morning, and walks back to his house in the afternoon using the same route. If he reaches school after 1 hour of jogging at a rate of 300 m/min, how long does it take for him to go back to his house if he walks at 100 m/min ?

7. The sum of two numbers is 9 and their difference is 16. What is the smaller number ?

8. If  f(x) = 2^x + x^2 - 2, what is f (0) ?

9. A rectangle has dimensions 30 by 35 units. What is the least number of squares into which rectangle can be cut ?

10. Let A and B be the sets composed of the letters in the word "metrobank" and "mathematics" respectively. What is A   ∩ B ?

AVERAGE QUESTIONS (To be answered within 30 seconds IN ANY WAYS)

1. Find the area of the quadrilateral with vertices at (0,0), (7,4), (4,6), and (0,5) ?

2. If  f(x) = 3- 2x and (f • g)(x) = 1 - 8x, what is g(-1) ?

3. Solve for x in the equation : 4^x + 2^x = 12 ?

4. Give all pairs of prime numbers whose sum is 50.

5. If x^2 + y^2 = 4, what is the maximum value of  x + y ?

DIFFICULT QUESTIONS (To be answered within 60 seconds IN ANY WAYS)

1. What is the remainder when x^2013 is divided by x^2 - 1 ?

2. The vertex of the parabola is at (2,3), and the parabola passes through the origin. Find the equation of the parabola in the form y = ax^2 + bx + c.

3. Find the number for  four boys and three girls to sit around a table if the girls sit next to each other.

4. Triangle ABC is right angled at B. If AB = 15 cm and BC = 20 cm, what is the area of circle centered at B and tangent to the hypotenuse AC.

5. Solve for x in the equation  : 2^{(sin^2)(x)} = 1 + 2^{(cos^2)(x)}.

CLINCHER QUESTIONS

EASY 1. A square is inscribed in a circle of radius 12 cm. What is the perimeter of the square ?

AVERAGE 2. Factor completely the polynomial 2x^3 - x^2 - 5x - k if x +1 is given as one of it's factors.

DIFFICULT 3. If 100! is expressed into it's prime factorization, what is the power of 7 ?