# 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 that the 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 h, the height drawn to the hypotenuse, of the right $\triangle ABC$ with right angle at C if h divides the hypotenuse into two parts of length 25 (from A) and 9.

48.) In the figure below, $\angle BAC$ and $\angle DEC$ are both right angles, CD = 6, BC = 10, and the length of AD is one-fourth the length of AC. Find CE.

49.) The number r varies jointly as s and the square of t. IF r = 6 when s = 12 and $t = \dfrac{1}{2},$ find r when s = 18 and $t = \dfrac{3}{2}.$

50.) Given the figure below with AB parallel to DE. Find the length of AB.

26.) -6
27.) 315°
28.) $\sqrt{3} m$
29.) 27
30.) 3
31.) $\left( \dfrac{cos \Theta}{sin \Theta} \right)^2$
32.) $\dfrac{7}{5}$
33.) 46
34.) $30 \sqrt{3} cm$
35.) 16 ft
36.) 5
37.) 4
38.) positive
39.) 60 cm
40.) a = 7, b = -29
41.) $\pm 3$
42.) 7
43.) 194%
44.) $\pm 2\sqrt{5}$
45.) -11, 11
46.) 28
47.) 15
48.) $\dfrac{24}{5}$
49.) 1
50.) 130

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

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