2016 Grade 9 Math Challenge – Elimination Round with answer key – Part II

Below are the 2016 Grade 9 Math Challenge – Elimination Round questions and answers – Part II. More reviewers can be found on the Past Tests and All Posts pages.

26.) Find x so that x - 2, x + 2, and x + 4 are consecutive terms of a geometric sequence.

27.) What is the smallest positive angle which is co-terminal to -1125^\circ?

28.) What is the height of an equilateral triangle whose perimeter is 6 meters?

29.) By what factor is the volume of a cube increased if each of its sides is tripled?

30.) z varies directly as x and varies inversely as the square of y. If z =\frac{7}{2} when x = 14 and y = 6, find z when x = 37 and y = 9.

31.) Express in terms of sines or cosines of \theta and simplify:
\dfrac{cot^2 \theta + 1}{tan^2 \theta + 1}

32.) Right \bigtriangleup ABC, with right angle at C, has sides b = 5 and c = 7. Find csc B.

33.) In the following figure, the double arrows indicate parallel lines. Find x.

34.) What is the perimeter of an equilateral triangle whose area is 75 \sqrt{3} square centimeters?

35.) A person is standing 40 ft away from a street light that is 25 ft tall. How tall is he if his shadow is 10 ft long?

36.) What is the maximum value of f(x) = -2x^2 - 4x + 3?

37.) The figure shows a segment joining the midpoints of two sides of a triangle. What is the sum of x and y?

38.) If x > 1, is
\dfrac{3}{2}x^{\frac{1}{2}} - \dfrac{3}{2}x^{-\frac{1}{2}} positive or negative?

39.) The diagonals of a rhombus are in the ratio of 1 : 3. If each side of the rhombus is 10 centimeters long, find the length of the longer diagonal.

40.) Find a and b so that the zeros of ax^2 + bx + 24 are 3 and 4.

41.) Find all k so thatthe graph of y = -\dfrac{1}{4}x^2 + kx - 9 is tangent to the x-axis.

42.) The diagonals of parallelogram JKLM intersect at P. If PM = 3x – 2, PK = x + 3 and PJ = 4x – 3, find the length of PL?

43.) Suppose that w varies directly as x and the square of y and inversely as the square root of z. If x is increased by 80%, y is increased by 40%, and z is increased by 44%, by how many percent will w increase?

44.) Find k so that the minimum value of f(x) = x^2 + kx + 8 is equal to the maximum value of g(x) = 1 + 4x - 2x^2.

45.) The difference of two numbers is 22. Find the numbers so that their product is to be minimum.

46.) In \bigtriangleup ABC shown below, A’C” is parallel to AC. Find the length of BC”.

47.) Find the length of hZAZAZAPNq, the height drawn to the hypotenuse, of the right \bigtriangleup ABC with right angle at C.

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Answer key:

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View Part II here: 2016 Grade 9 Math Challenge – Elimination Round with answer key – Part I

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