2018 Grade 10 Math Challenge Elimination Level Questions – Part 2

This is the 2018 Grade 10 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.) If \theta is an angle in a triangle and cos \theta = \dfrac{5}{13}, find csc \theta.

27.) In \triangle ABC, BC = 6, CA = 7, and AB = 8. Find \dfrac{sin C}{sin A}.

28.) In \triangle ABC, AB= 3, AC = 7, and \angle A = 60^{\circ}. Find BC.

29.) In a circle, chord PQ is bisected by chord RS and T. If RT = 3 and ST = 6, find PQ.

30.) A line through a point A outside a circle is tangent to the circle at D. Another line through A intersects the circle at points B (closer to A) and C. If BC/AB = 2 and AD = 6, AC.

31.) Triangle ABC is inscribed in a circle. If arc AC = 146° and arc BC = 104°, find angle BCA.

32.) Square ABCD is inscribed in a circle, and a point P is chosen on arc AB. Find angle APB.

33.) A triangle having sides \sqrt{31}, \sqrt{33}, and 8 units, is inscribed in a circle. Find the circumference of the circle.

34.) In a circle, chords AB and CD intersect at E. If arc AC = 120° and arc BD = 20°, find angle AEC.

35.) Two concentric circles have radii 5 and 13 units. Find the length of a chord of the larger circle which is tangent to the smaller circle.

36.) Find n if \dfrac{(n!)^2}{(n + 1)!(n - 1)!} = \dfrac{4}{5}.

37.) In an experiment having 20 samples points, even A has 13 sample points. At least how many sample points should event B have to guarantee that A and B are not mutually exclusive?

38.) In how many ways can 4 different books be arranged in shelf?

39.) How many four-digit positive integers can be formed using the digits 2, 3, 4, 5 and 6 if no digit can be repeated?

(For Problems 40 and 41) A photographer needs to arrange 7 students for a club picture. A requirement is that the 3 officers of the club must always be together.

40.) How many arrangements are possible?

41.) How many arrangements are possible if Job and Tim (neither is an officer) should be placed at the opposite ends of the row?

42.) How many committees can be formed?

43.) How many committees can be formed if there should be 3 members chosen from each barangay?

44.) Two fair dice are rolled. What is the probability that a die above 2 shows while the other shows an odd prime number?

(For Problems 45 and 46) The numbers 1, 2, …, 24 are each written on a slip of paper which are then placed in a box.

45.) If two slips are picked at the same time from the box, find the probability that one number is even and the other is odd.

46.) If a slip of paper is picked from the box, find the probability that it is even or a multiple of 3.

47.) In a class of Grade 10 students, the probability that a randomly chosen student likes dogs is 0.72, that a student likes cats is 0.54, and that a student likes dogs or cats is 0.89. Find the probability that a student likes both dogs and cats.

(For Problems 48 and 49) Among the 50 employees of a company, 30 are women. Half of the men wear glasses while only a third of women wear glasses.

48.) What is the probability that a randomly selected employee is a man or wears glasses?

49.) What is the probability that an employee is a woman, if its known that this employee does not wear glasses?

50.) A rectangle has sides 4 and 6 units. On each of its four sides, squares are drawn externally. Their centers form another quadrilateral. What is the area (in sq. units) of this quadrilateral?

Answer key:

26.) \dfrac{13}{12}
27.) \dfrac{4}{3}
28.) \sqrt{13}
29.) 6\sqrt{2}
30.) 6\sqrt{3}
31.) 55°
32.) 135°
33.) 8π
34.) 70°
35.) 24
36.) 4
37.) 8
38.) 24
39.) 120
40.) 720
41.) 72
42.) 8008
43.) 2940
44.) \dfrac{1}{9}
45.) \dfrac{12}{23}
46.) \dfrac{2}{3}
47.) 0.37
48.) \dfrac{3}{5}
49.) \dfrac{2}{3}
50.) 50

View Part 1 here: 2018 Grade 10 Math Challenge Elimination Level Questions – Part 1

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