2018 Metrobank-MTAP-DepED Math Challenge Elimination Round ________________________________________________________________________________ 1) Ten percent of 450 is 20% of what number? 2) Let r and s be the roots of x2 – 9x + 7 = 0. Find r + s + rs. 3) How many integers between 60 and 600 are divisible by 7? 4) Simplify: 8! . 6! 5) If A = {2,3,5,7}, B={2,4,6,8,10}, and C={3,6,9}. Find (A ∪ B) ∩ C 6) If the two terms of an arithmetic sequence are 3 and 7, find the 10 th term. 7) If the 1st and 5th terms of an arithmetic sequence are – 5 and 7 respectively, find the sum of the first 21 terms. 1 8) The 1st and the 6th terms of a geometric sequence are 4 and − , respectively. Find the 4th term. 8 9) Three numbers form an arithmetic sequence with common difference of 15. If the first is increased by 3 and the third by 21, a geometric sequence will be formed. Find the first number of the arithmetic sequence. 10) Find the sum of the infinite geometric series 9 – 6 + 4 – 8 3 …. 11) An infinite geometric series with sum 12 has first term 8. Find the first term of the series that is less than 1. 12) In a sequence {an}. an = 2n + 2n. Find a5 – a2. 13) If P(x3) = 4x9 – 7x6 + 2x3 + 27, find P(x). 14) Find the remainder when P(x) = 2x3 + 5x2 – 3x – 4 is divided by x + 2. 15) What is the coefficient of x in the quotient when p(x) = 4x3 – 17x2 + 8x + 11 is divided by x – 3. 16) Find the constant k if x – 2 is a factor of f(x) = 3x4 – kx3 + kx2 – 13x + 6. 17) Find the largest root x of 2x3 + 5x2 + x – 2 = 0 18) If p(x) is a 3rd degree polynomial and p(- 2) = p(2) = p(-1) = 0, and p(1) = - 18, find p(3). 19) Find the polynomial with smallest possible degree and all of whose coefficients are integers, with the leading coefficient positive and as small as possible, if it has √2 and 2 as zeroes. 20) Two lines with slopes 3 and – 4, intersect at a point P on the y-axis. If their x-intercepts are 14 units apart, find the distance of P from the origin. 21) The midpoint of P(7, -1) and R is Q(10.5, 2). Find the coordinates of R. 22) Find the radius of the circle with center (- 3, 5) and which passes through the origin. 23) Find the center of the circle with equation is x2 + y2 + 8x – 14y + 60 = 0. 24) Give the equation (in center-radius form) of the circle having as a diameter the segment with endpoints (-2, 10) and (4, 2). 25) Find the coordinates of the point on y axis having the same distance from (- 8, 7) as from (- 4, 1). 26) If