2013 Grade 9 Math Challenge – Elimination Round with answer key – Part II

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 4 \sqrt{5} and 2 \sqrt{5}. 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 \bigtriangleup FGH and \bigtriangleup IJK 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 \angle TOM = 45^\circ, 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 512 cm^3, find the sphere’s exact volume.

37.) (Figure 4) If TQ = 4\sqrt{5} and TS = 12\sqrt{5}, find RT.

38.) (Figure 4) If RS = 9 \sqrt{6} and TS = 18, find TQ.

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

40.) (Figure 6) Find \angle AOB.

41.) (Figure 6) Find \angle BEC.

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 10 - 4k, 2k - 42 and 27 - 3k are three consecutive terms of an arithmetic sequence, find their common difference.

48.) A geometric has first term 5 and fourth term 80\sqrt{2}. 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 \frac{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?

Answer key:

26.) 10
27.) 5 \sqrt{5}
28.) 54 + 25 \sqrt{5}
29.) 22
30.) 14
31.) 15
32.) \dfrac{144}{5} or 28.8
33.) 36 + 6\sqrt{2}
34.) 18 + 36\sqrt{2}
35.) 96
36.) \dfrac{256\pi}{3} cm^3
37.) 4\sqrt{15}
38.) 9
39.) 120 + 40 \sqrt{6}
40.) 140^\circ
41.) 50^\circ
42.) 6
43.) 9
44.) 4 \sqrt{6}
45.) 103
46.) 1533
47.) 14
48.) 10\sqrt{2}
49.) \frac{189}{2}
50.) 100 m

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

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