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.

5. (Figure 1) Suppose *FG=12*, *IJ=18* and *JK=21*. Find *GH*.

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 cm^{3}, find the sphere’s exact volume.

12. (Figure 2) If and , find *RT*.

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 16^{th} 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?