This reviewer was taken from 2013 Metrobank-MTAP-Dep-Ed Math Challenge for third year. This is also advisable for fourth year and second year.
Directions: Give all fractions in the lowest terms. Eliminate negative exponents and rationalize denominators. Give equation of the lines in slope-intercept form.
1. A right triangle has legs and . How long is the hypotenuse?
2. Quadrilateral PQRS has right angles at P and R. If PQ=9, PS=12, and QR=10, find RS.
3. What is the area of quadrilateral PQRS from the previous problem?
4. The shortest legs of two similar triangles are 5 and 7.5. if the bigger triangle has perimeter 33, find the perimeter of the smaller triangle.
6. (Figure 1) Suppose FG=x-3, FH=x+5, IJ=x+3 and JK=2x. Find x.
7. (Figure 1) Suppose the perimeter of ΔFGH and ΔIJK are 20 and 48, respectively. If GH=12, find JK.
8. ATOM is an isosceles trapezoid having bases AT and MO, with AT<MO. If AT=12, TO=6 and °, find the perimeter of ATOM.
9. Find the area of the ATOM from the previous problem.
10. The diagonals of a Rhombus differ by 4. If its perimeter is 40, find its area.
11. The diameter of a sphere is the same as the side of a cube. If the cube’s volume is 512 cm3, find the sphere’s exact volume.
13. (Figure 2) If and , find TQ.
14. (Figure 3) Find the perimeter of STUV.
15. Circles A and B have radii 5 and 7, respectively, and the distance between their centers A and B is 6. If two circles intersect at points M and N, find the length of the common chord MN.
16. What is the 16th term of the arithmetic sequence 13,19,25,. . .?
17. What is the sum of the first 21 terms of the arithmetic sequence from the previous problem?
18. A geometric sequence has first term 5, and fourth term . What is its second term?
19. A geometric sequence of positive terms has fifth term 24 and ninth term 384. Find the sum of its first 6 terms.
20. Suppose a ball rebounds 2/3 the distance it falls. If it is dropped from a height of 20 m, how far does it travel before coming to rest?