2017 Metrobank-MTAP-DepEd Math Challenge Division Finals – Team Oral Competition – Grade 10 15-Second Questions [2 points each]
1. What is the sum of the 10 consecutive integers starting from 4 ? 2. Find the least least value value of x of x that satisfies the inequality 5
[ 85 ]
− 4x ≤ 2.
[ 3/4 ]
3. The sides of a triangle are 8, 12, and 14 cm long. A new triangle is constructed constructed by by joining the midpoints midpoints of the the sides sides of the first first tria triangl nglee with segmen segments. ts. What is the the perime perimeter ter of of this this new tria triangl ngle? e? [ 17 cm ] 4. What is the remainder remainder when when 1
2
3
2 x − 3x is divided by x + 1 ? − x + 2x 5. Find the values values of x x that satisfy the equation |x| + x = 0.
[7] [x
6. A map map has has a scal scalee of 2 cm is to to 5 km. km. If a high highwa way y is 28 k km, m, how how long long is it in in the the map? map?
≤ 0 ]
[ 11.2 cm ]
7. Two Two chords chords of a circle circle inters intersect ect inside inside it. If the segment segmentss of one chord chord are 12 and 16 cm long, and one segme segment nt of the the sec secon ond d cho chord rd is is 24 cm, cm, how how long long is the the oth other er seg segme men nt of the the sec secon ond d cho chord rd?? [ 8 cm ] 8. What is the sum of the first 100 even positive integers?
[ 10 10 100 ]
√
9. What is the perimeter of a square that is inscribed inscribed in a circle with circumfe circumference rence 10π 10π cm?
[ 4 5 cm ]
10. Two Two men are repain repaintin tingg a wall. wall. Working orking alone, alone, the first first man can finish finish it in 10 hours, hours, and the second second man ma n in 12 hour hours. s. Wor Worki king ng toget togethe her, r, what what part part of the the wall can can they they repa repain intt in 2 hour hours? s? [ 11/ 11/30 ] 11. What is the center center of the circle with equation equation x2 + y 2
− 4y = 10 ?
[ (0, 2) ]
30-Second Questions [3 points each]
1. The The firs firstt term term of a geo geome metr tric ic sequ sequen ence ce is 10, 10, and and its its thi third rd term term is 20. 20. What What is its its fift fifth h ter term? m?
[ 40 ] √ 2. The legs legs of a right right triang triangle le are 2 and 2 2 cm long. What is the radius of the circle that circumscribes the √ triangle? [ 3 cm ] 3. What What is the range range of the functi function on f f ((x) = 2x + 4 − 2x ? [ (−∞, 9/2] ] 4. What What is the sum sum of 1 − 2 + 3 − 4 + 5 − 6 + · · · + 2017 ? [ 1009 ] 5. Find the solution solution set of the inequality inequality x( x (x − 4)(x 4)(x + 2) ≤ 0. [ {−2} ∪ [0, [0, 4] ] 6. Two factors factors of a third-degree third-degree polynomial polynomial P ( P (x) are x + 2 and x − 4. If P If P (0) (0) = 8 and P (1) P (1) = −9, find the remaining factor of P ( P (x). [ 2x − 1 ] 2
2
1-Minute Questions [5 points each]
1. The larger larger of two two concen concentri tricc circle circless has radius radius 8 cm. If a chord chord of the larger larger circle circle that is tangen tangentt to the smaller circle has length 4 14 cm, what is the radius of the smaller circle? [ 2 2 cm ]
√ 2. If 0 ≤ θ ≤ 180 and cos θ = − , what is sin θ + tan θ ? √ x + 1 + √ x − 1 √ = 3. 3. Solve Solve for for x x in the equation √ x + 1 − x − 1 ◦
√ √ [ −4 2/3 ]
1 3
◦
4. Find all ordered ordered pairs pairs (x, (x, y) that satisfy both equations x equations x + + y y = = 4 and y and y = 2x2
[ 5/3 ]
− x + 2.
[ ( 1, 5), (1, (1, 3) ]
−
5. An equilateral equilateral triangle triangle and a square square have have equal perimeters. perimeters. If the area of the square is 45 cm2 , what is the area of the triangle? [ 20 3 cm2 ]
√
6. From a given convex convex quadrilateral, a second quadrilateral is formed by joining the midpoints of its adjacent sides with a segment. segment. If the sum of the lengths of the diagonals of the given quadrilatera quadrilaterall is 24 cm, what is the perimeter of the second quadrilateral? [ 24 cm ] Clincher Questions
C.1. A line has slope 2 and passes passes through the the point (4, (4, 1). What is its y its y--intercept? C.2. If a a 1 = 2 and a and a = 3a n
n−1
+ 2 for n
is a ≥ 2, what is a
4
?
[
−7 or (0, (0, −7) ]
[ 80 ]
C.3. A number number is reduced reduced by p by p percent. percent. How many percent should it be raised then to go back to the original number? [ 100 p/(100 p/(100 p) p) ]
−
Do-or-Die Question
DoD. Find three positive positive integers integers that form a geometric geometric sequence, sequence, given that their sum is 21 and the sum of 7 their reciprocals is 12 . [ 3, 6, 6 , 12 ]
This is a property of the Metrobank Foundation and the Mathematics Teachers Association of the Philippines. c 2017 This material is not for sale, reproduction, and/or distribution.
10.1. The
larger of two concentric circles has radius 8 cm. If a chord of the larger circle that is tangent to the smaller circle has length 4 14 cm, what is the radius of the smaller circle?
10.2.
√
If 0◦
≤ θ ≤ 180◦ and cos θ = − , what is sin θ + tan θ ? 1 3
√ x + 1 + √ x − 1 √ 10.3. Solve for x in the equation √ = 3. x + 1 − x − 1 10.4. Find
all ordered pairs ( x, y ) that satisfy both equations x + y = 4 and y = 2x2 x + 2.
−
10.5. An
equilateral triangle and a square have equal perimeters. If the area of the square is 45 cm2, what is the area of the triangle?
10.6. From
a given convex quadrilateral, a second quadrilateral is formed by joining the midpoints of its adjacent sides with a segment. If the sum of the lengths of the diagonals of the given quadrilateral is 24 cm, what is the perimeter of the second quadrilateral?
10.C.3. A
number is reduced by p percent. How many percent should it be raised then to go back to the original number?
10.DoD. Find
three positive integers that form a geometric sequence, given that 7 their sum is 21 and the sum of their reciprocals is 12 .
