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 ax + 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