This is the 2015 Grade 9 Math Challenge Elimination Level Questions – Set 2. Answers and solutions will be posted later. Questions in the previous years can be accessed on the **Past Tests** page and all questions can be found in the** All Posts** page.

Instruction: Write your answer on the space provided before each item. Give all fractions in lowest terms, and all equations of lines in the form a*x + by = c* where *a*, *b* and *c* are relatively prime integers, with *a* > 0.

26.) If 4 men can paint a house in 5 days, in how many days can 10 men paint the same house?

27.) If *y* is proportional to the cube *x* and *x* is proportional to the fourth power *z*, then *y* is proportional to which power of *z*?

28.) Running at uniform speed in a race, Allan can beat Ben by 20 m, Ben can beat Carlo by 10 m and Allan can beat Carlo by 28 m. How long is the race?

29.) Find the measure of the vertex angle of an isosceles triangle whose base angles measure 65°.

30.) Find x if the angles of a quadrilateral measure and

31.) An equilateral triangle and a square have the same perimeter. What is the ratio of the length of a sides of the triangle to the length of a side of the square?

32.) John cuts an equilateral paper whose sides measures 2 cm. into pieces. He then rearranges the pieces to form a square without overlapping. How long is the side of the square formed?

33.) The sides of a triangle are of length 5, 12 and 13 cm. What is the length of the shortest altitude?

34.) Each side of triangle *ABC* measures 8 cm. If *D* is foot of the altitude drawn fro *A* to the side *BC* and *E* is the midpoint of *AD*, how long is the segment *BE*?

35.) A point *E* is chosen inside a square of side 8 cm. such that it is equidistant from to adjacent vertices of the square and the side opposite these vertices. Find the common distance.

36.) A point *E* is drawn inside rectangle *ABCD *and its distances from A, B and C are 2 cm., 3 cm. and 4 cm. How far is *E* from *D*?

37.) Find the area of a rectangle with diagonal of length 10 cm. is twice as long as it is wide.

38.) Triangle ABC has a right angle at C. If sin *A* = 1/3, what is cos A?

39.) A side of a triangle measures 3 cm. A line segment is drawn parallel to this side, forming a trapezoid whose area is 2/3 of the area triangle. How long is the line segment?

40.) A cone has a volume of If the cone is cut parallel to the base at a distance from the vertex equal to 1/4 of the height of the cone, what is the volume of the resulting cone?

41.) In figure 1 below, *ABCD *is a square with diagonal 2 cm. long and *AEC *is an equilateral triangle. Find the area of the quadrilateral *AECB*.

42.) Pegs are put on a bowl 1 cm apart both horizontally and vertically. What is the area of the quadrilateral formed by stretching a rubber band over four pegs as shown in the figure 2 above?

43.) In figure 3 above, *ABCD *is an isosceles trapezoid with *AB *as its longest side and *O *divides diagonals *AC *and *BD* in the ratio 1 : 2. What is the area of *ABCD *if the area of *BOC *is 2 m²?

44.) On triangle *ABC*, *D* and *E* are the midpoint of *BC *and *AB*, respectively. The median *AD *meets *CE *at *F*. If the area of the triangle *EFA *is 1 cm², what is the area of triangle *ABC*?

45.) Equilateral triangle *ABC *has side of length 2 cm, *M* is the midpoint of *AC *and *B* is the midpoint of *CD*. What is the area of triangle *MCD*?

46.) Points *D*, *E* and *F* are drawn one on each side of triangle *ABC* so that *ADEF* is a rhombus. If the lengths of *AC*, *AB* and *BC* are 6, 12 and 8 respectively, how long is a side of *ADEF*?

47.) A rectangular piece of paper 4 cm. in length and 3 cm. in width is folded so that a pair of diagonally opposite vertices coincide. How long is the crease (fold-mark) formed?

48.) In trapezoid *ABCD*, *AD || BC* and *AB = BC = AD/2.* Find angle *ACD*.

49.) Two angles of a triangle measures 30° and 105° and the side between these two angles measures 2 cm. What is the perimeter of the triangle?

50.) How many non-congruent triangles with perimeter 9 have sides of integer length?

View Set 1 here: 2015 Grade 9 Math Challenge Elimination Level Questions – Part 1