2014 Grade 9 Math Challenge Elimination Level Questions – Part 2

This is the 2014 Grade 9 Math Challenge Elimination Level Questions – Part 2 with answers. Questions in the previous years can be accessed on the Past Tests page and all questions can be found in the All Posts page.

26.) (Figure 3) Find z.

27.) (Figure 4) The figure shoes a segment joining the midpoints of two sides of a triangle. Find x.

28.) Find the equation of the line passing through (-12, 6) and perpendicular to 6x + 7y = 3.

29.) Find the equation of the line having half the x-intercept and twice the y-intercept of 3x + 5y = 15.

30.) Find all values of the constant k so that the line (k² – 10)z + ky = 10 and (k – 4)x + 3y = 7 are parallel.

31.) Find the equation of the line perpendicular to and containing the midpoint of the segment joining (-2, 3) and (6, -1).

32.) What is the capacity, in cubic meters, of a swimming pool that is 15 m long, 8 m wide, and 5 m deep on the shallow end and 7 m on the deep end?

33.) A 40 cm × 30 cm × 21 cm rectangular block is completely submerged in a box containing water without spilling over. If the container’s base is 105 cm × 60 cm, by how much did the water level rise?

34.) In parallelogram PQRS, \angle P = (6x + 10)^\circ and \angle Q = (8x - 40)^\circ. Find x.

35.) In parallelogram ABCD, \angle DBC = 27^\circ and \angle ADC = 70^\circ. Find \angle BDC.

36.) The diagonals of parallelogram JKLM intersect at P. If PJ = 3x – 2, PK = x + 3, and PM = 5x – 5, find x.

37.) A rhombus has diagonals of lengths 10 and 24. What is its area?

38.) The lengths of the sides of three squares are s, s + 1 and s + 2. Find their total perimeter if their total area is 245.

39.) In quadrilateral REST, \angle R = 119^\circ, \angle E = 67^\circ and \angle S = 73^\circ. Find angle T.

40.) Quadrilateral PQRS has right angles at P and R. If PQ = 6, PS = 8 and QR = 4 \sqrt{5}, find RS.

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

42.) If y varies directly as x, and y – 14 when x = 6, f ind y when x = 15.

43.) If the radius of a circle is doubled, by what factor does the area increase?

44.) Suppose w varies jointly as x and the square of y, and inversely as x. If x is increased by 20%, y is increased by 50%, and z is doubled, by how much will w increase?

45.) Find the 11th term of an arithmetic sequence with 3rd term 47 and 9th term 29.

46.) Find the smallest integer n such that 1 + 2 + 3 … + n > 450.

47.) An arithmetic sequence has 2nd term -43 and 4th term -37. What is the first positive term of the sequence?

48.) Find x if 2x – 1, x + 4 and 3 – 3x are consecutive terms of an arithmetic sequence.

49.) Find the common ratio of a geometric sequence with 5th term -5 and 8th term 135.

50.) What number must be added to each 4, 7, and 12 so that the resulting numbers form a geometric sequence?

Answer key:

26.) 110
27.) x = 3
28.) 7x – 6y = -120
29.) 12x + 5y = 30
30.) (3, -5)
31.) 2xy = 3
32.) 720
33.) 4 cm
34.) 15
35.) 43°
36.) x = 2
37.) 120
38.) 108
39.) 101°
40.) 2\sqrt{5}
41.) 44
42.) 35
43.) 4
44.) 35%
45.) 23
46.) 30
47.) 2
48.) -2
49.) -3
50.) 1/2

View Part 1 here: 2014 Grade 9 Math Challenge Elimination Level Questions – Part 1

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