2016 Grade 10 Math Challenge Elimination Level Questions with Answers – Part 2

This is the 2016 Grade 10 Math Challenge Elimination Level Questions with Answers – Part 1 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.) Suppose an object is dropped from the roof of a very tall building. After t seconds, its height from the ground is given by h = -16t^2 + 625, where h is measured in feet. How long does it take to reach ground level?

27.) In \triangle ABC, AB || DE, AC= 10cm, CD = 7 cm, and CE = 9 cm. Find BC.

28.) Find a polynomial P(x) of degree 3 that has zeroes -2, 0, and 7, and the coefficient of x² is 10.

29.) Find the equation (in the form ax + by = c) of the perpendicular bisector of the line segment joining the points (1, 4) and (7, 2).

30.) The sides of a polygon are 3, 4, 5, 6, and 7 cm. Find the perimeter of a similar polygon, if the side corresponding to 5 cm is 9 cm long.

31.) If tan \theta = \dfrac{2}{3} and \theta is in Quadrant III, find cos \theta.

32.) The first term of a geometric sequence is 1536, and the common ratio is \dfrac{1}{2}. Which term of the sequence is 6?

33.) In \triangle ABC, \angle B = 2 \angle A. The bisectors of theses angles meet at D, while BD extended meet AC at E. If \angle CEB = 70^\circ, find \angle BAC.

34.) Find the sum of the series: \dfrac{1}{3} + \dfrac{2^1}{3^2} + \dfrac{2^2}{3^3} + \dfrac{2^3}{3^4}... .

35.) What is the remainder when x^3 - x + 1 is divided by 2x - 1?

36.) Triangle ABC has right angle at B. If \angle C = 30^\circ and BC = 12, find AB.

37.) What is the largest root of the equation 2x^3 + x^2 - 13x + 6 = 0?

38.) Find the equation (in the form x^2 + y^2 + cx + dy = c) of the circle that has the points (1, 8) and (5, 6) as the endpoints of the diameter.

39.) The distance from the midpoint of a chord 10 cm long to the midpoint of its minor arc is 3 cm. What is the radius of the circle?

40.) Find the equation (in the form ax + by = c) of the line tangent to the circle x^2 + y^2 = 25 at the point (3, 4).

41.) How many triangles can be formed by 8 points, no three of which are collinear?

42.) Two tangents to a circle form an angle of 80°. How many degrees is the larger intercepted arc?

43.) Find all real solutions of the equation x^{\frac{1}{2}} + x^{\frac{1}{6}} - 2 = 0.

44.) The sides of a triangle are 6, 8, and 10, cm, respectively. What is the length of its shortest altitude?

45.) In a circle of radius 10 cm, arc AB measures 120°. Find the distance from B to the diameter through A.

46.) Find the remainder when x^100 is divided by x^2 - x.

47.) Find the area (in terms of ) of the circle inscribed in the triangle enclosed by the line 3x + 4y = 24 and the coordinate axes.

48.) In how many different ways can 5 persons be seated in an automobile having places for 2 in the front seat and 3 in the back if only 2 of them can drive and one of the others insists on riding in the back?

49.) Factor completely the expression x^4 + 3x^2 + 4.

50.) A bag is filled with red and blue balls. Before drawing a ball, there is a \dfrac{1}{4} chance of drawing a blue ball. After drawing out a ball, there is now a \dfrac{1}{5} chance of drawing a blue ball. How many red balls are originally in the bag?

Answer key:

26.) 6.25 s
27.) \dfrac{90}{7} cm
28.) P(x) = 10x^3 - 50x^2 - 490x
29.) x - y = 2
30.) 45 cm
31.) -\dfrac {3\sqrt{13}}{13}
32.) 7
33.) 35°
34.) 1
35.) \dfrac{5}{8}
36.) 4 \sqrt{3} cm
37.) 2
38.) x^2 + y^2 - 6x - 2y = 48
39.) \dfrac{17}{3} cm
40.) 3x - 4y = 25
41.) 56
42.) 260°
43.) 1
44.) \dfrac{24}{5} cm
45.) 5\sqrt{3} cm
46.) x
47.) \pi units^2
48.) 12
49.) (x^2 + x + 2)(x^2 - x + 2)
50.) 12

View Part 1 here: 2016 Grade 10 Math Challenge Elimination Level Questions with Answers – Part 1

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