Metrobank-MTAP-DepEd Math Challenge 2013 Individual Finals • Second Year • Category A Name:
School:
Score:
Part I. Write your answer on the space before each item. Each correct answer earns 2 points.
Give the equation equation of the line in 1. A line intersects the x-axis at (−2, 0) and the y -axis at (0, −3). Give a, b, c are pairwise relatively prime integers and a > 0. the form ax + by + c = 0, where a, 2. Find the smallest integer such that 8 less than thrice the integer is greater than 200. 3. Express the repeating decimal 0.035353535 . . . as a common fraction. 4. If x is a nonzero real number and y is its reciprocal, what is
7x x + 1
−
6 in terms of x? y + 1
4(k − 2) 3 reduce to ? 3k + 1 4 6. Find the average of the numbers 2 , 4, 6, 8, . . . , 98. 5. For what value of k does the fraction
7. Three numbers form an arithmetic sequence having a common difference of 5. If 2 is added to the
first number, 3 to the second, and 7 to the third, the resulting numbers form a geometric sequence. Find the largest of the original numbers. 8. A boat can travel 80 km downstream in 2 hours, but takes 4 hours to travel the same distance
upstream. Find the rate of the water current. 9. If ax + 15y = 25 and 8x + by = 20 represent the same line, find a + b. 10. For the first 4 hours, a car traveled at an average speed of 65 kph. How many hours more did the
car travel at an average speed of 70 kph if the average speed for the entire trip was 68 kph? 11. Divide:
y 2 − 2y − 15 12 − 4y ÷ . 2 2 y −9 y − 6y + 9
12. Subtract:
x + 5 x−1 . − x2 + 7x + 10 x2 + 5x + 6
left a town town at an averag averagee speed speed of 60 kph. Thirt Thirty y minutes minutes later, later, a bus left the town town in the 13. A car left same direction as the car, and overtook the car after 1.5 hours. How far from the town did the bus overtake the car? 14. In an arithmetic sequence, the first term is 8, the last term is 96, and the sum of all terms is 1196.
What is the common difference? 15. At most how many points of intersection do a parabola and a circle have? Part II. Write a complete and neat solution to each problem. Each correct solution earns 3 points.
many ordered pairs pairs (a, b) of positive integers satisfy the equation 3 a + 5 b ≤ 37? 1. How many number of positiv p ositivee integers integers less than 1000 that are divisible divisible by neither 6 nor 7. 2. Find the number finish a piece of work in 2 days less than Vincen Vincent. t. If both can finish the work in 225 days, how 3. Marvin can finish long will it take Marvin to finish the work alone? whose length is 4 cm more than twice twice the width and whose diagonal diagonal is 4. What is the area of the rectangle whose 2 cm longer than the length? q in terms of p if one root of the equation x 2 + px + q = expression on of q = 0 is 3 more than twice the 5. Find an expressi
other. Part III. Write a complete and neat solution to each problem. Each correct solution earns 5 points.
two pieces, and each each piece is bent to form a square. square. The total 1. A piece of wire is 44 cm long. It is cut into two area area of the two two squares squares is 65 cm2 . How long are the sides of each square? rectangle remains unchange unchanged d when it is made 2 cm longer and 1 cm narrower narrower,, or when it is 2. The area of a rectangle made 2 cm shorter and 4 cm wider. What is the area of the rectangle? 3. Company A and Company B submitted separate proposals for the construction of a bridge, with A offering the lower price for the winning bid. Had A and B reduced their bid prices by 5% and 10%, respectively, A still would have won the bid but the difference in their bids would have been reduced by Php 3 , 000. If the sum of their bids is Php 90, 000, what are the bids of A and B ?
