# 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?

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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