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 6*x* + 7*y* = 3.

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

30.) Find all values of the constant k so that the line (*k*² – 10)*z* + *ky* = 10 and (*k* – 4)*x* + 3*y* = 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 and Find *x*.

35.) In parallelogram and Find

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

40.) Quadrilateral *PQRS *has right angles at *P* and *R*. If and 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 2*x* – 1, *x* + 4 and 3 – 3*x* 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.) 7*x* – 6*y* = -120

29.) 12*x* + 5*y* = 30

30.) (3, -5)

31.) 2*x* – *y* = 3

32.) 720

33.) 4 cm

34.) 15

35.) 43°

36.) *x* = 2

37.) 120

38.) 108

39.) 101°

40.)

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