# 2013 Metrobank- MTAP – Dep-Ed Math Challenge 4th Year

- One of the two complementary angles added to one-half the other yields
*62*°. Find the measures of the two angles. - Find the amplitude and the period of the function
*y=-3sin(**θ**/5)* - Find the equation of the line passing through
*(3,-10)*and whose slope is half the slope of the line*4x-2y+1=0* - A closed rectangular box is of uniform thickness x inches. The box has outer dimension 6 inches,
*4*inches, and*3*inches and it has an inside volume of 30 cubic inches. Find x. - Find the center and radius of the circle
*x*^{2}-4x+y^{2}+14y+47=0. - Find the exact value of
*cos75°.* - Simplify
- How many
*5*-digit even numbers can be formed out of the digits*2,4,5,8*, and*9*without repetition? - Find the inverse of the function
- In parallelogram RSTU, , , and . Find .
- Supposed that represents the bacteria present in a culture t minutes from the start of an experiment. Give an expression for the number of minutes needed for the bacteria to double.
- One side of a rectangle is 6 centimeters, and its adjacent side measure one-third of the rectangle’s perimeter. Find the dimensions of the rectangle.
- If the area of a rectangle is
*6x-2x*and its width is^{3}+4*2-x*, find its length. - The diameter of a basketball is 9 inches. If it is completely submerged in water, how much water will be displaced? Give your answer in terms of π.
- Find all
*x**ϵ**[**π**/2,**π**]*such that - Solve the inequality
- Find two points that divide the segment joining
*(-2,5)*and*(4,-7)*into three equal parts. - If , find
*f(x).* - Workers
*A*and*B*, working together, can finish a job in*8*hours. If they work together for hours after which worker*A*leaves, then worker*B*needs*9*more hours to finish the job. How long does it take worker A to do the job alone? - Find the coefficient of term involving
*x*in the expansion^{2}*(x+3x*^{-2})^{8 } - In the figure, arc
*RS=115*°, arc*RT=80°*, and °, find arc*TU*.

22. In the figure, *Δ**ABC* is similar to *Δ**ADB*. If *AD* = *3* and *AB*= *8*, find *AC*.

23.In the figure, concentric circles with radii *4* and *5* have center at *P*. find , given that it is tangent to the inner circle and is a chord of the outer circle.

24. If a fair coin is tossed five times, find the probability that exactly three tosses show heads.

25. Find the value of x so that the points (-1,-2), (6,a) and (-10,2) lie on a straight line.

26. Find the product of the roots of quadratic equation 3x-5x^{2}+1=0

27. Miranda trained consistently, so that she can finish a race in one hour. During the race, she ran at the rate of *8* kph. However, upon reaching the halfway point of the race, she realized she needed to run faster so she increased her speed to *10* kph. If she reached her goal just in time, how long was the race?

28. Solve for r in terms of s, where .

29. The expression *x ^{3} + ax^{2} +bx + 6* has the same remainder when divided by

*x+1*or by

*2-x*. If the remainder when the expression is divided by

*x+3*is

*-60*, find

*a*and

*b*.

30. A square is inscribed inside a circle of radius *10* *cm*. Find the perimeter of the square.

31. Write as a single logarithm.

32. A bookshelf has *8* history books and *10* cooking books. You will select *10* books ( *2* history books and *8* cooking books) to bring on a trip. How many choices are possible?

33. Factor completely *2x ^{6} + 3x^{5} – 8x^{4} – 12x^{3}*.

34. In parallelogram *ABCD*, *AC* meets *BD* at *O*. Supposed that *OA = 3x-2*, *OC = 13-6x*, and *OB = 3x+2*. Find *OD*.

35. Solve for *x: log(x-4) + log(x-7)=1.*

36. If , find the possible value of *x* and *y*.

37. If and , find the domain of *(f**◦**g)(x).*

38. The angles of a quadrilateral are in the ratio *4:2:6:3*. Find the measure of the largest angle.

39. Supposed that *P(x)* is a polynomial such that the remainder of *P(x)÷(x-2)* is *-5* and the remainder of *P(x) ÷(x-30* *)*is *7*. Is it possible for *P(x)* to have;

(a) exactly one root between *2* and *3*?

(b) two roots between *2* and *3*?

( c) no root between *2* and *3*

40. Simplify to a single fraction:

41. The dial on a combination lock contains three wheels, each of which is labeled with a digit from 0 to 9. How many possible combinations does the lock have if digits may not be repeated?

42. Find and identify the asymptotes of the graph of

43. Solve for x:

44. Let *C* be a circle of radius *8* inches, having a chord of length *3* inches. Find the central angle opposite this chord.

45. If *p = log2*, *q= log5*, *r= log7*, express log50 + 2log70 – in terms of *p,q*, and *r*.

46. If four-number codes are formed randomly from the digits *0* to *9*, what is the probability that the two middle digits are the same?

47. For what value/s of *k* does the graph of *y= 3x ^{2} – kx + k* have a minimum value of

*3*?

48. Find the domain of the function

49. The x- and y-intercepts of a line are *-9* and *6*, respectively. Find the point on the line whose ordinate is *5*.

50. Supposed that an airplane climbs at an angle of *30*°. If its speed is maintained at *550* kilometers per hour, how long will it take to reach a height of *15* kilometers?

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