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 and are consecutive terms of a geometric sequence.

27.) What is the smallest positive angle which is co-terminal to

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 when* x* = 14 and *y* = 6, find *z* when *x* = 37 and *y* = 9.

31.) Express in terms of sines or cosines of and simplify:

32.) Right 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 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

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 is 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 are 3 and 4.

41.) Find all *k* so that the graph of is tangent to the x-axis.

42.) The diagonals of parallelogram *JKLM* intersect at *P*. If *PM* = 3*x* – 2, *PK* = *x* + 3 and *PJ* = 4*x* – 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 is equal to the maximum value of

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

46.) In 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 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, and 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 find r when s = 18 and

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

Answer key:

26.) -6

27.) 315°

28.)

29.) 27

30.) 3

31.)

32.)

33.) 46

34.)

35.) 16 ft

36.) 5

37.) 4

38.) positive

39.) 60 cm

40.) a = 7, b = -29

41.)

42.) 7

43.) 194%

44.)

45.) -11, 11

46.) 28

47.) 15

48.)

49.) 1

50.) 130

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