2018 Grade 9 Math Challenge Elimination Level Questions - Part 2

2018 Grade 9 Math Challenge Elimination Level Questions – Part 2

This is the 2018 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.) Find all possible values of n in the proportion (n – 5) : (n – 3) = (n + 3) : 20.

27.) An angle in a quadrilateral has measures 45°, while the others have degree measures in the ratio 5 : 7 : 9. Find the measure of the largest angle.

28.) In rhombus QRTS, $\angle RQS = 5 \angle QRT.$ Find angle RTS.

29.) The diagonals of the rhombus PRAY intersect at G. If AG = 3n, PG = 6, RG = 3m – 2n, and YG = m + 2n, find the length (in units) of the shorter diagonal.

30.) Find the perimeter (in units) of the rhombus PRAY in the previous problem.

31.) In parallelogram ABCD, AB = 8, BC = 5, CD = 7x – 2y, and AD = z + y. Find x.

32.) In parallelogram LMNO, $\angle M = (2x + 10)^\circ, \angle N = (5x - 5)^\circ.$ Find x.

33.) In an isosceles trapezoid, the lengths of the diagonals are 2x + 3 and 6x – 5. Find x.

34.) The diagonals of quadrilateral ABCD are perpendicular and they intersect at E. If BE = DE = 4, AC is twice as long as EC, and the area of the quadrilateral is 24 sq. units. Find the length (in units) of AE.

35.) The sides of $\triangle MNO$ are 5 cm, 7 cm and 10 cm. If $\triangle MNO ~ \triangle PQR,$ find the length of the shortest side of $\triangle PQR$ if its longest side is 15 cm.

36.) The ratio of the lengths of corresponding sides of two similar triangles is 3 : 4. Find the ratio of their areas.

37.) Given the points P(0, 0), Q(12, 0), R(24, 0) and S(6, 6) on the plane, the point T is chosen so that PS || QT and QS || RT. Find the coordinates of T.

38.) Two sides of a rectangular are 10 cm and 24 cm. Find the length of a diagonal.

39.) The two legs of a right triangle are in the ratio $\dfrac{\sqrt{3}}{2}.$ If the hypotenuse is 10 units long, find the area (in square units) of the triangle.

40.) In $\triangle ABC, \angle C = 90^\circ$ and sin A = $\dfrac{5}{13}.$ Find sin B.

(For problems 41 – 43. )In $\triangle ABC, \angle C = 90^\circ.$ Let D be a point on AB so that $CD \perp AB.$

41.) Suppose AD = 9 and BD = 4. Find CD in units.

42.) Suppose AD = 20 and BD = 5. Find BC in units.

43.) Suppose AC = 24 and $\dfrac{AB}{BD} = 4.$ Find BC in units.

44.) A ladder is leaning against a vertical wall which is 5m high. The top of the ladder slides all the way down the wall so that the bottom of the ladder slides 1m away from its original position. How long is the ladder?

Answer key:

26.) n = 7, 13
27.) 135°
28.) 15°
29.) 12
30.) 40
31.) x = 2
32.) x = 25°
33.) x = 2
34.) 3/2 units
35.) x = 7.5 cm
36.) 9 : 16
37.) (18, 6)
38.) 26
39.) $\dfrac{100 \sqrt{3}}{7}$
40.) 12/13
41.) 6
42.) $5\sqrt{5}$
43.) 13m

View Part 1 here:2018 Grade 9 Math Challenge Elimination Level Questions – Part 1