4th Year-2015 MMC Division Finals-Orals

Diligently typed by Isaiah James Maling, here are the questions with answer key in the recently concluded 2015 Metrobank-MTAP-Deped Mathematics Challenge, Division Finals- Oral category for 4th year.

Easy (15sec)

1. What is the y-intercept of 2x + 3y = 5.
Answer: 5/3

2. How many degrees are there in 1 1/5 revolutions?
Answer: 432 degrees

3. What is the vertex of the parabola y = x^2 + 2x + 3?
Answer: (-1,2)

4. Find the value of  log cbrt(2) to the base of sqrt(2)
Answer: 2/3

5. Evaluate sin 29pi/4.
Answer: -sqrt(2) / 2

6. Find the value of a if 8x^3 + 1 is divisible by x-a.
Answer: a = -1/2

7. What is the domain of ln (x-x^2)?
Answer. (0,1) or 0<x<1

8. What is the value of x in the harmonic sequence 1, 2/3, x?
Answer: 1/2

9. What is the x-intercept of f(x) = log (x-1)?
Answer: 2

10. For what value of a do 2x + 2y = 1 and 3x + 3y = a have infinitely many solutions?
Answer: a = 3/2

Average (30 sec)

1. What is the area bounded by the equation x/3 + y/4 = 1.
Answer: 6 square units.

2. What is the value of a if ax + 2y = 1 and 3x – 6y = 7 are perpendicular?
Answer: a = -4

3. What is the value of a if the equation f(x) = (ax+1) / (2x – 3) have range and domain which are both identical?
Answer: a = 3

4.If sec x = -13/5 and sin x is negative, what is the value of tan x?
Answer: 12/5

5. If p and q are the roots of the quadratic equation 3x^2 – 2x + 4 = 0, what is the value of p^2 + q^2?
Answer: -20/9

Difficult.

1. How many multiples of 3 are there between 5 and 200?
Answer: 65

2. If tanx = -2, what is sin 2x?
Answer: -4/5

3. Solve for x. 4^(x-x^2) = sqrt2
Answer: x = 1/2

4. What is the perimeter bounded by x+y = 1 and x^2 + y^2 = 1?
Answer: (2sqrt2+pi) / 2 units.

5. What is the remainder when 1+3x^3+5x^5+…+11x^11 + 13x^13 is divided by x – 1?
Answer: 49

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