2004 Metrobank-MTAP-DepEd Math Challenge Sectoral Finals – Third Year Category A 15-second questions 1. If 203 = 2x x 5y , what are the values of x and y? [x=6, y=3] 2. An angle is 14º more than its complement. Find its supplement. [128º] 3. A point P lies on the terminal side of a 120º angle in standard position. If 0 is the origin and OP 4 , find the coordinates of P. [(-2), 2 3 ] 4. What is the greatest number of points at which 3 circles may intersect? [ 6 ] 5. Two sides of an equilateral triangle are 2x–3 and x+4. What is the perimeter of the triangle? [33] 6. What is the smaller angle between the hands of a clock at 5:15? [67.5] 7. A balloon can be seen from two observation posts. From A, the angle of elevation of the balloon is 30º
and from B, it is 45º. If the balloon is 1000m high, what is the maximum possible distance between A and B? [(1000+ 1000 2 )m] 8. For what values of x is x 2 3 x 10 0 ? [ -2
64125
2/3
?
[16/25 ]
30-second questions 1. ABCD is a trapezoid with AB//DC. If AD = AB and CDA 80 , find BDC . [40º] 2. In rt. ACB , CD is the altitude to the hypotenuse. If AD = 4 and CD = 8, find BD. [16] 3. ABCDE is a regular pentagon. AEP is an equilateral triangle with P outside ABCDE. Find PBE . [30º] ABC is similar to XYZ with 2/3 as the ratio of similitude. If the area of ABC is 72cm2 , what is the area of XYZ ? [162cm2] 5. If a = b + 2/3, what is the value of | a–b | + | b-a | ? [4/3] 6. Factor 8a 3 + 27/a 3. [(2a+3/a)(4a 2–6+9/a 2)]
4.
1-minute questions 1. ABCD is a trapezoid with base AB equal to twice CD. If the diagonals meet at E and AC=11, find AE. [AE=22/3]
2. The perimeter of isosceles triangle ABC is 36cm. If the altitude to the base BC is 12cm, find the area of ABC . [60 cm2] 3. ABCD is a square; E is a point on AC such that AE=AB; the line through E perpendicular to AC cuts BC, DC at F, G respectively. Find FAG . [45º] 4. Find an equation whose roots are the squares of the roots of x2-5x-3=0 [x2-31x+9= 0] 5. Two vertical poles, AB and CD, are 9ft and 15ft high respectively and the tops, A of AB and C of CD, are joined by a wire. P is a point on the wire AC such that AP = 2PC. How high is P from the ground? [13ft]
6. If 5 geometric are inserted between 3 and 192, what is the middle geometric mean? [24] Clincher round 1. The length of a rectangular field is 4times its length. If the length is decreased by 6meters and the width increased by 3 meters, the area will be increased by 54m. Find the length and width. [48m, 12m] 2. A group of 30 skilled carpenters can build a house in 12 days. 15 skilled and 5 unskilled carpenters can build it in 20 days. How long will 15 unskilled carpenters, assuming they can do it, build the same house? [40 days] 3. A total of P4,450 was collected for the tickets of 130 people. If minors paid P25 and adults paid P40, how many minors attended the show? [50]
