Math Kangaroo Competition 2020 Grade 12 Sample Paper : mathkangaroo.in

Organisation : International Olympiad Academy
Exam : Math Kangaroo Competition
Document Type : Sample Paper
Class : Grade 12
Year : 2020
Website : https://www.mathkangaroo.in/sample-papers/2020

Math Kangaroo Competition Sample Paper

International Olympiad Academy Math Kangaroo Competition 2020 Grade 12 Sample Paper

Related / Similar Question Paper : Math Kangaroo Competition 2020 Grade 10 Sample Paper

Math Kangaroo Grade 12 Sample Paper

Section – A (3 Point Problems):
1. What is the sum of the last two digits of the product 1 . 2 . 3 . 4 .5 . 4 . 3 . 2 . 1.
(A) 2
(B) 4
(C) 6
(D) 8
(E) 16

2. Let a, b and c be integers satisfying 1 <= a <= b <= c and abc = 1 000 000. What is the largest possible value of b?
(A) 100
(B) 250
(C) 500
(D) 1000
(E) 2000

3. If D dogs weigh K kilograms and E elephants weigh the same as M dogs, how many kilograms does one elephant weigh?
(A) DKEM
(B) DK/EM
(C) KE/DM
(D) KM/DE
(E) DM/KE

4. There are two dice. Each one has two red faces, two blue faces and two white faces. If we roll both dice together, what is the probability that both show the same color?
(A) 1/12
(B) 1/9
(C) 1/6
(D) 2/9
(E) 1/3

Section – B (4 Point Problems):
1. A blue rectangle and a red rectangle are overlapping. The figure shows 4 different such cases. We denote by B the area of the part of the blue rectangle that is not common to the two rectangles, and we denote by R the area of the red rectangle that is not common to the two. Which of the following statements is true about the quantity B – R?

(A) In case 1 the quantity B-R is larger than in the other cases
(B) In case 2 the quantity B-R is larger than in the other cases
(C) In case 3 the quantity B-R is larger than in the other cases
(D) In case 4 the quantity B-R is larger than in the other cases
(E) The quantity B-R is the same in all cases

2. Five coins are lying on a table with the “heads” side up. At each step you must turn over exactly three of the coins. What is the least number of steps required to have all the coins lying with the “tails” side up?
(A) 2
(B) 3
(C) 4
(D) 5
(E) It’s not possible to have all the coins with their “tails” side up.

3. Four identical boxes are glued together to make the shape shown in the picture. One litre of paint is needed to paint the outside of one such box. How many litres of paint are needed to paint the outside of the glued construction?
(A) 2.5
(B) 3
(C) 3.25
(D) 3.5
(E) 4

4. Three cuboids are arranged to make a larger cuboid as in the figure. The width of one of them is 6 and the areas of some of their faces are 14, 21, 16, 30, as shown. What is the area of the face with the question mark?
(A) 18
(B) 24
(C) 28
(D) 30
(E) cannot be determined

Section – C (5 Point Problems):
1. The figure shows a section of the parabola with equation y = ax2 + bx + c. Which of the following numbers is positive?
(A) c
(B) b + c
(C) ac
(D) bc
(E) ab

2. On a square grid paper, a little kangaroo draws a line passing through the lower left corner P of the grid and colours in three triangles as shown Which of the following could be the ratio of the areas of the triangles?
(A) 1 : 2 : 3
(B) 1 : 2 : 4
(C) 1 : 3 : 9
(D) 1 : 4 : 8
(E) None of the previous is correct

3. A large integer N is divisible by all except two of the integers from 2 to 11. Which of the following pairs of integers could be these exceptions?
(A) 2 and 3
(B) 4 and 5
(C) 6 and 7
(D) 7 and 8
(E) 10 and 11

4. In the morning, the ice-cream shop offers 16 flavours. Anna wants to choose a 2-flavour ice cream. In the evening several flavours are sold out and Bella wants to choose a 3-flavour ice cream from those flavours left. Both Anna and Bella can choose from the same number of possible combinations. How many flavours were sold out?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6

5. Tony has 71 marbles at his disposal in a box. He is allowed to take out exactly 30 marbles from the box or to return exactly 18 marbles to it. Tony is allowed to apply each operation as many times as he wishes. What is the smallest number of marbles than can be in the box?
(A) 1
(B) 3
(C) 5
(D) 7
(E) 11

6. An iceberg has the shape of a cube. Exactly 90% of its volume is hidden below the surface of the water. Three edges of the cube are partially visible over the water. The visible parts of these edges are 24m, 25m and 27m. How long is an edge of the cube?
(A) 30 m
(B) 33 m
(C) 34 m
(D) 35 m
(E) 39 m

Instructions

1. Please Do Not Open the contest booklet until the proctor has given permission to start.
2. There are 30 questions in this paper. Easy: 3 points for each correct answer. Medium: 4 points for each correct answer. Hard: 5 points for each correct answer. 1 point will be deducted for each incorrect answer, and no penalty for skipping a question.
3. All questions are compulsory. There is only ONE correct answer to each question.
4. No electronic devices capable of storing and displaying visual information are allowed during the exam.
5. Use of calculator is strictly prohibited in the exam.
6. Fill your Name, Roll No., Grade and School Name in the answer sheet.
7. To mark your choice of answers by darkening the circles in the Answer Sheet, use an HB Pencil or a Blue/Black Ball Point Pen only.

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