# MMC National Finals Team Category-4th Year

These questions were taken from the official FB page of MMC. This year, they were posting the questions simultaneously on their FB page while the MMC finals are being held.

15-second question

1. Quadrilateral ABCD is inscribed in a circle. If $\angle A=78^\circ$ and $\angle B=95^\circ$, what is $\angle D$? [85 degrees]

2. The value of a certain ancient artifact appreciates 10% every year. Two years ago, its values was set at 500,000 pesos. How much is the artifact now? [P 605,000]

3. Find the real roots of the equation $(2x+1)^2=(2x+1)$? [-1/2,0]

4. In $\triangle ABC$ with $AB=AC$, if $\angle B=(3x+10)^\circ$ and $\angle C=(5x-30)^\circ$, what is $\angle A$? [40 degress]

5. If x is 10% o fy, and y is 40% of z, then z is how many percent of x? [2500%]

6. In a class of 40 students, 20 have brothers, 15 have sisters, and 5 have both brothers and sisters. How many students in the class are single child in the family? [10]

7. In the graph of $y=x(x+2)^2$, for what values of x is the graph situated above the x-axis? [ x>0]

8. A demograher predicts that the population of a country t years from now can be modeled by the function $P(t)=10t^4+8,000,000$. Using this model, after how many years will the current population double? [30]

9. if $\log_45=a$, what is $\log_85$ in terms of a? [2a/3]

10. What is the remainder when $32x^4-x^2$ is divided by $2x-1$? [7/4]

30-second questions

1. In a circle centerred at (1,-1), one endpoint of a diameter lies at (4,2). Find the coordinates of the other endpoint of this diameter? [(-2,4)]

2. Factor completely the expression $4x^4+2x^3+2x^2+x$ over the set of real numbers. [x(2x+1)(2x^2+1)]

3. The first three terms of an arithmetic sequence are $2y-4$, $y+6$, and $5y+1$. What is the fifth term of the sequence? [30]

4. If $2^{sinx}=16^{cosx}$, what is $sec^2x$? [17]

5. 5 points are on the coordinate of plane, no three of which are collinear. How many polygons can be drawn with these points as vertices? [16]

1-minute question

1. Let f be a quadratic function such that f(-1)=0, and f(0)=f(1)=-8. What is f(3)? [16]

2. Find the number of permutations of letters of the word CHALLENGE. Evaluate factorials in your answer. [90,720]

3. Find all x between 0 degrees and 90 degrees such that $2sin^2x+cosx=sinx+sin2x$ [30 degrees, 45 degrees]

4. Three vertices of a parallelogram are (0,0), (4,0), and (1,3). Find the coordinates of the fourth vertex so that the resulting parallelogram has the largest possible perimeter. [(-3,3)]

5. If $x+y=4$ and $xy+6z=z^2+13$, find the values of $x,y$ and $z$. [(2,2,3)]