2013 Metrobank- MTAP – Dep-Ed Dep-Ed Math Challenge 4th Year 1. One of the two complementary angles added to one-half the other yields 62°. 62°. Find the measures of the two angles. 2. Find the amplitude and the period of the function y=function y=-3sin(θ/5) 3sin(θ/5) 3. Find the equation the equation of the line passing line passing through (3,-10) and (3,-10) and whose slope is half hal f the slope of the line 4x-2y+1=0 4. 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. 2
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5. Find the center and radius of the circle the circle x x -4x+y +14y+47=0. 6. Find the exact value of cos75°. 7. Simplify 8. How many 5-digit even numbers can be formed out of the digits 2,4,5,8, 2,4,5,8, and 9 without repetition? 9. Find the inverse of the function 10. In parallelogram RSTU, 11. Supposed that
,
, and
. Find
.
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. 12. 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. 3
13. If the area of a rectangle is 6x-2x +4 and +4 and its width is 2-x, 2-x, find its length. 14. 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. 15. Find all xϵ[π/2, all xϵ[π/2, π] such π] such that 16. Solve the inequality 17. Find two points that divide that divide the segment joining segment joining (-2,5) and (-2,5) and (4,-7) into (4,-7) into three equal parts. 18. If
, find f(x). find f(x).
19. Workers A Workers A and and B B,, working together, can finish a job in 8 hours. If they work together for hours after which worker A worker A leaves, leaves, then worker B worker B needs needs 9 more hours to finish the job. How long does it take worker A to do the job alone? 2
-2 8
20. Find the coefficient of term term involving x involving x in the expansion (x+3x ) 21. In the figure, arc RS=115 arc RS=115°, °, arc RT=80° arc RT=80°,, and
°, find arc TU .
22. In the figure, ΔABC figure, ΔABC is is similar to ΔADB. ΔADB. If AD If AD = = 3 and AB and AB= = 8, find AC find AC . 23.In the figure, concentric circles with radii 4 and 5 have center at P 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 o n a straight line. 2
26. Find the product of the roots of quadratic equation 3x-5x +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. 10 kph. If she reached her goal just in time, how long was the race? 28. Solve for r in terms of s, where 3
.
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29. The expression x expression x + ax +bx + 6 has has the same remainder when divided by x+1 by x+1 or or by 2-x. 2-x. If the remainder when the expression is divided by x+3 by x+3 is is -60, -60, find a and b. 30. A square is inscribed inside a circle of o f radius 10 cm. 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 ( 2history books and 8 cooking books) to bring on a trip. How many choices are possible? 6
5
4
3
33. Factor completely 2x + 3x – 8x 8x – 12x 12x . 34. In parallelogram ABCD parallelogram ABCD,, AC meets BD meets BD at at O. Supposed that OA = 3x-2, 3x-2, OC = 13-6x, 13-6x, andOB andOB = 3x+2. 3x+2. Find OD. OD. 35. Solve for x: for x: log(x-4) + log(x-7)=1. 36. If 37. If
, find the possible value of x of x and and y y.. and
, find the domain of (f◦g)(x).
38. The angles of a quadrilateral are in the ratio 4:2:6:3. 4:2:6:3. Find the measure of the largest angle. 39. Supposed that P(x) that P(x) is a polynomial such that the remainder of P(x)÷(x-2) of P(x)÷(x-2) is is -5 -5 and the remainder of P(x) of P(x) ÷(x-30 ) ÷(x-30 )is is 7 . Is it possible for P(x) for P(x) to 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 be a circle of radius 8 inches, having a chord of length 3 inches. Find the central angle opposite this chord. 45. If p If p = log2, log2, q= log5, log5, r= log7 , express log50 + 2log70 –
in terms of p,q 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? 2
47. For what value/s of k does does the graph of y= of y= 3x – kx kx + k have 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 -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°. 30°. If its speed is maintained at 550kilometers 550kilometers per hour, how long will it take to reach a height of 15 kilometers? 15 kilometers?
4th Year Math Challenge Practice Questions and Answers Part I 1. Which of the following is/are function/s; a.) x=y-4
2
2
b.)x=y -1
2
c.) y=x +2
2
d.)x +y =25
2. The sum of the supplement and complement of an angle is 228°. Find the measure ofthe angle. 3. ABCD is a quadrilateral inscribed in a circle. a circle. If If angle A is 25°. What is the measure of angle C? 4. Solve for x in the following equation: 2
5. Find the sum of the roots of m-3x-2x =0 where m is a real number. 6. What is the range of function f(x)=2x-1 in the domain [-2,2]? 2
7. What is the minimum value of y=2x -3x+2? 2
8. What the domain of y=log4(x -1)? 9. If f(x)=2x -1 and g(x)=x-1. What is f◦g? 2
10. What is the system of equations 2x-y=1 and x-2y=2? 11. Find the shortest distance between the point (2,3) and x-2y-4=0. 12. Find the equation of the line through (3,4) and parallel to 2x+y-4=0. 13. Find the equation of the line though (3,4) whose slope is twice the slope of 3x-2y-5=0 14. Triangle ABC is right angle at B and inscribed in circle O. If the legs of the triangle are 3 and 4. What is the area of the circle? 99
98
97
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15. What is the remainder when f(x)=99x +98x +97x + . . . + 2x +x is divided by x-1? 2
16. For what value/values of k does the equation y=3x -kx+3 has real and distinct roots? 2
17. Find the equation with integral coefficient coe fficient whose roots are the reciprocal of the roots of 2x +3x-1. 18. A pair of fair dice was tossed once. What is the probability that a sum of 6 is obtain? 19. The ratio of the sides of two regular hexagons is 4:5. What is the ratio of their areas respectively? 2
20. What is the positive root of x -4x-2=0? 21. The sum of the number and 3 less than twice the number is 15. What is the number? 22. What is the inverse function of f(x)=(x-2)/(2x+1)? 2
23. Find the solution set of x -5x+6<0 24. Find the solution set of │2x -3│<7 25. The perimeter of the rectangle is 24 cm. If the length is two more than the width, what is the area of the rectangle?
4th year Practice Math Challenge Questions and Answers Part II 1. What is the greatest integer function of 4.6? 2. The sum of the complement and twice the supplement of an angle is 111°. What is the angle? 3. What is the period of y=tan2x? 4. What is the range of y=log(x^2 – 4)? 4)? 5. Find the equation of the line though (2,-3) and perpendicular to 3x-4y-1=0. 6. A pair of fair dice is toss once, what is the probability of getting a prime sum? 7. PT is tangent to circle to circle O and a secant intersect the same circle at points A and B.PT = X , PB=9, PA=(x-2). PA=(x -2). How long is PT? 8. Find the equation of the th e line with slope of ½ and x-intercept of 3. 2
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9. The line x-2y+1=0 intersect the circle x +y =28 at two points. What the slope of the line joining these two points? 3n
n
n-4
10. Solve for n: (2 )(4 )=(1/2)
11. What is the inverse function of y=log4(x-2)? 12. In a math contest represented b y different schools, each school sent 3 participants; everyone has t o make a handshake with each other. If there were 105 handshakes happened. How many schools participated in the said contest? 13. What is the maximum number of diagonals can be drawn in a regular dodecagon? 2
14. The minimum value of y=2x +kx+3 is 1. What is/are the value(s) of K? 15. I have two sticks with lengths of 6 cm and 10 cm. I have a third stick measuring 20 cm. If I want to create the largest triangle out of three sticks. How long will I need to cut off from the third stick? 16. What is the median of the following data? {82,89,85,90,93,96,89,88}
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17. For what value(s) of y is the graph of y=16-x above x-axis? 18. Evaluate: 8+4+2+1+. . . . . 19. The area of the rectangle is 4 more than its perimeter. If the len gth is 2 more than the width. What Wh at is the dimension in meters? 2
20. What is the positive root of 2x -x-3=0? 4
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21. Three of the roots of the equation 2x +ax +bx+c=0 are -1, 2, and -3. What is b? 22. How many pairs of positive positive integral solution solution in x+y=10? 23. A regular hexagon is inscribed in a circle. Another regular hexagon circumscribes the same circle. What is the ratio of the area of the smaller hexagon to hexagon circle?
24. How long after 3 o’clock will the minute hand and hour hou r hand be together for the first time? 25. 5 fair dice is toss once, what is the probability that exactly three four’s will show up?
