Metrobank-MTAP-DepEd Math Challenge 2013
NCR Sectoral Finals • Grade 7 • Category A 15-Second Questions [2 points each]
1. If x = x =
−1
and y and y = 2, what is 3y 3y − 2x?
[8]
2. What is the largest largest prime prime p that satisfies the inequality 1 + 2 p < 23?
[7] [ 1.8 × 107 ]
3. Express in scientific notation the product of 3000 and 6000. 4. Solve Solve for for x in the equation 4x 4x − 1 = 9 − x.
[2]
5. If 2 ≤ x ≤ 4 and y and y = 4 − 2x, what is the largest value of y of y?
[0]
6. If the complemen complementt of ∠A is 50 , what is the supplement of ∠A?
[ 140 ]
◦
◦
7. One leg leg of a right right triangl trianglee is 8 cm. If its area area is 48 cm2 , how long is the other leg?
[ 12 cm ]
8. The fifteenth prime number is 47. What is the eighteenth prime number?
[ 61 ]
9. Arnold Arnold and Ben are brothers. brothers. The sum of their their ages is 32. Four years years ago, Ben’s Ben’s age was Arnold Arnold’s ’s age now. How old is Arnold now? [ 14 years old ] 10. A cabinet drawer drawer contains contains white and black black socks. At least how many many socks should Carlo get to make sure that he has two pairs of socks of the same color? [7] 11. Simpli Simplify: fy: 1 + 21 + 31 .
[ 11/6 ]
30-Second Questions [3 points each]
1. Working orking together, together, a father and a son can finish a job in 6 hours. hours. If the father can finish finish the job alone in 10 hours, how long will it take the son to finish the job alone? [ 15 hours ] 2. Solve Solve the system system of equations: equations: 2x + 3y 3y = 10 and x and x + + 13 = 3y 3y .
[ x = x =
−1
and y and y = 4 ]
3. Two radii of a circle are perpendicular perpendicular to each other. other. If the chord joining joining the endpoints endpoints of these radii is 8 cm long, what is the area of the circle in terms of π? π ? [ 32π cm2 ] 4. Solve Solve for for x in the inequality 36 − 11 11x x ≤ 2 − 9(x 9(x − 2).
[x≥8]
5. The average average of five positive integers integers (not necessarily necessarily distinct) distinct) is 10. What is the largest largest possible integer among the six integers? [ 46 ] 6. What What is the area area of the triang triangle le formed formed by the line 2x 2x + 3y 3y + 8 = 0 with the two coordinate axes? [ 16 16//3 square units ] 1-Minute Questions [5 points each]
1. How How many many liters liters of water water must must be evapor evaporated ated from 50 liters liters of 3% salt salt solution solution so that that the remaini remaining ng solution will be 5% salt? [ 20 liters ] 2. One angle angle of a triang triangle le is twice twice as large large as anothe another, r, and 25 more more than than the third third angle. angle. Find Find the three three angles. [ 41 , 57 , 82 ] ◦
◦
1
3. Simplify: Simplify:
.
1
1− 1+
◦
◦
[ 2−x ]
1
1−x 4. Find the equation equation of the line passing through through the origin and is perpendicular perpendicular to the line joining the points (−2, 3) and (4, (4, 6). [ y = −2x ] 20133 − 2013 . 2012 · 2014 6. What is the largest largest integer integer n that satisfies the inequality 1 + 2 + 3 + · · · + n < 150? 5. Simplify: Simplify:
[ 2013 ] [ 16 ]
C.1. A line passes through through the point (0, (0, −2) and has a slope of −3. Find the equation of the line in the form ax + ax + by by + + c c = 0. [ 3x + y + y + + 2 = 0 ] C.2. The width of a rectangle rectangle is 9 cm. The length length is 1 cm shorter than the diagonal. diagonal. How long long is the diagonal? [ 41 cm ] C.3. C.3. If the the sum sum of two two n num umber berss is is 12 12 and and thei theirr produ product ct is 24, 24, wha whatt is is the the sum sum of thei theirr squa square res? s?
[ 96 96 ]
DoD. What is the smallest positive positive integer integer to be multiplied multiplied to 1260 so that the resulting product is a perfe p erfect ct cube? [ 7350 ]
1.A.1. How
many liters of water must be evaporated from 50 liters of 3% salt solution so that the remaining solution will be 5% salt?
angle of a triangle is twice as large as another, and 25◦ more than the third angle. Find the three angles.
1.A.2. One
1
1.A.3. Simplify:
.
1
1− 1+
1 1−x
1.A.4. Find
the equation of the line passing through the origin and is perpendicular to the line joining the points (−2, 3) and (4, 6).
20133 − 2013 1.A.5. Simplify: . 2012 · 2014
1.A.6. What
is the largest integer n that satisfies the inequality 1+2+3+· · · + n < 150?
1.A.C.3. If
the sum of two numbers is 12 and their product is 24, what is the sum of their squares?
1.A.DoD. What
is the smallest positive integer to be multiplied to 1260 so that the resulting product is a perfect cube?
