Below are the 2013 Grade 9 Math Challenge – Elimination Round questions and answers – Part II. More reviewers can be found on the **Past Tests** and **All Posts** pages.

26.) A right trangle has legs and . How long is the hypotenus?

27.) Quadrilateral *PQRS* has right angles at *P* and *R*. If *PQ* = 9, *PS* = 12 and *QR* = 10, find *RS*.

28.) What is the area of quadrilateral *PQRS* from the previous problem?

29.) 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.

30.) Suppose *FG* = 12, *IJ* = 18 and *JK* = 21. Find *GH*.

31.) (Figure 3) Suppose *FG* = *x – 3*, *FH* = *x* + 5, *IJ* = *x + 3* and *IK* = *2x*. Find *x*.

32.) (Figure 3) Suppose the perimeters of and are 20 and 48, respectively. If *GH* = 12, find *JK*.

33.) *ATOM* is an isosceles trapezoid having bases *AT* and *MO*, with *AT* < *MO*. If *AT* = 12, *TO* = 6 and , find the perimeter of *ATOM*.

34.) Find the area of *ATOM* from the previous problem.

35.) The diagonals of a rhombus differ by 4. If the perimeter is 40, find its area.

36.) The diameter of a sphere is the same as the side of a cube. If the cube’s volume is , find the sphere’s exact volume.

37.) (Figure 4) If and , find *RT*.

38.) (Figure 4) If and , find *TQ*.

39.) (Figure 5) Find the perimeter of *STUV*.

40.) (Figure 6) Find

41.) (Figure 6) Find

42.) (Figure 7) Find *PA*.

43.) (Figure 7) Find *DC*.

44.) Circles *A* and *B* have radii 5 and 7 respectively, and the distance between their centers *A* and *B* is 6. If the two circles intersect at points *M* and *N*, find the length of the common chord *MN*.

45.) What is the 16th term of the arithmetic sequence 13, 16, 25, …

46.) What is the sum of the first 21 terms of the arithmetic sequence from the previous problem?

47.) If and are three consecutive terms of an arithmetic sequence, find their common difference.

48.) A geometric has first term 5 and fourth term . What is the second term?

49.) A geometric sequence of positive terms has fifth term 24 and ninth term 384. Find the sum of its first 6 terms.

50.) Suppose a ball rebounds the distance it falls. If it is dropped from a height of 20 m, how far does it travel before coming to rest?

Answer key:

26.) 10

27.)

28.)

29.) 22

30.) 14

31.) 15

32.)

33.)

34.)

35.) 96

36.)

37.)

38.) 9

39.)

40.)

41.)

42.) 6

43.) 9

44.)

45.) 103

46.) 1533

47.) 14

48.)

49.)

50.) 100 m

View Part I here: 2013 Grade 9 Math Challenge – Elimination Round with answer key – Part I