# 4th Year MMC National Finals Questions-Individual Category

Here are the questions in 4th Year 2015 MMC National Finals individual category. These questions are answers are taken from the official Facebook page of MMC.

15-second quesition

1. What is the sum of all multiples of 4 between 10 and 30? [100]

2. Let ABC be an acute triangle inscribed in a circle with center O. If , what is angle ABC? [57 degrees]

3. In rolling a pair of dice, what is the probability of getting a sum of 5? [1/9]

4. If 5 arithmetic means are inserted between -15 and 9, what is the largest of such means? [5]

5. Factor completely the expression . [x(x+1)(2x+3)]

6. If 9^x=10, what is 27^{2x}? [1000]

7. Solve for x in the inequality (2x+5)^2\sqrt{5x}-1\le 0 [-5/2, 1/5]

8. The first term of a geometric sequence is 32, and its common ratio is 2. What is the 5th term? [3]

9. If (x-2) is a factor of , what is k? [-3]

10. A snail crawls 16 meters on the first hour, 12 meters on the second hour, and every succeeding hour, it crawls only 3/4 the distance it crawled the previous hour. Can it reach a total distance of 60 meters from where it started after a finite number of hours? [YES]

30-second question

1. In an investment that promises a rate of 10% compounded annually, how much are you going to invest now in order to receive Php 544,00 in 2 years? [ PhP450,000]

2. If and 0<x<5, what is the corresponding of values of y? [ y is less than 6 but greater than or equal to -3]

3. If g(x)=4x-2 and f(g(x))=4-6x, what is f(4)? [-5]

4. In a circle, the chords PQ and RS intersects at X. If PX=4, QX=5, and RX=SX+2, what is RS? [2√21]

5. A committee of 4 is to be formed from a group of 5 men and 3 women. In how many ways can this be done if the committee must have at least 1 woman? [ 65]

60-second questions

1. What is the constant term in the expansion of (x+x^-3/2)^10? [210]

2. The first and the last terms of a geometric sequence are 6 and 486, respectively. If the sum of all terms is 726, find the common ration. [3]

3. A building has a flagpole on top of it. On the ground, 90 meters from the base of the building, the angle of eleveation of the top of the building is 30 degrees and that of the top of the flagpole is 45 degrees. How high is the flagpole? [90-30√3 m]

4. When 3x^3+9x^2-28x+10 is divided by a polynomial D(x), the quotient and the remainder are both (x+5). What is D(x)? [3x^2-6x+1]

5. Solve for x in the equation . [√2, cube root of 2]

### Dan

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