Mahajana Mathematics Competition Sample Grade 8 ________________________________________________________________
Transcription
Mahajana Mathematics Competition Sample Grade 8 ________________________________________________________________
Mahajana Mathematics Competition Sample Grade 8 ________________________________________________________________ Part A (10 Questions, each question is worth 2.5 marks) 1. The second largest number in the set {0.3, 0.9, 0.18, 0.27, 0.081} is (A) 0.8 0.3 2. 0.9 (B) 0.9 (C) 0.3 (D) 0.27 3 (A) 3 Equals (B) 0.3 (C) 0.03 (D) 0.003 3. A student using an electronic calculator mistakenly multiplies by 10 instead of dividing by 10. The incorrect answer on display is 600. The correct answer is (A) 0.6 (B) 6 (C) 60 (D) 6000 4. The Canadian dollar was equivalent in value to $0.98 in American currency. The value of one American dollar in Canadian currency at that time was (A) $1.0204 (B) $1.025 (C) $1.180 5. The arc lengths of three semicircles are as shown on the right side figure. The area of the shaded region is (A) 18 (B) 9 (C) 36 (D) 72 (D) $1.144 Mahajana Mathematics Competition Sample Grade 8 ________________________________________________________________ 6. Ram was walking home from shop when he realized he had forgotten buy milk for his mother. He walked back to the shop, bought milk and then walked home. The graph shows his distance from home at different times. The total distance Ram walked is A) 1000 meters B) 1100 meters C) 1200 meters D) 1400 meters 7. The circle graph shows the favorite ice cream flavors of those surveyed in Sir John McDonald Collegiate. In the above survey, the fraction of students who selected either chocolate or Vanilla as their favorite flavour of ice-cream is A) 2/3 B) 3/4 C) 1/2 D) 5/8 8. A room having dimension of 12m long, 8m wide and 10m high, is to have the wall and ceiling painted. Each paint container covers 250 square meters of surface area. The number of containers needed to paint one coat is (A) 2 (B) 3 (C) 4 (D) 6 9. Triangular numbers follow this pattern: As shown, the first four triangular numbers are 1, 3, 6, and 10. The seventh triangular number is (A) 36 (B) 28 (C) 25 (D) 21 Mahajana Mathematics Competition Sample Grade 8 ________________________________________________________________ 10. A perfect number is an integer that is equal to the sum of all of its positive divisors, except itself. For example, 6 is a perfect number because 6 = 1 + 2 + 3. Which of the following is a perfect number? (A) 10 (B) 13 (C) 24 (D) 28 Part B (10 Questions, each question is worth 4.5 marks) 11. The “Rectangle 1”, “Rectangle 2”, and “Rectangle 3” are arranged to form the following sequence of rectangles as shown below: The above rectangles are formed by 1cm by 1cm squares. Many more rectangles are drawn, with each rectangle having one more row and two more columns than the previous rectangle. How many 1cm by 1cm squares would there be in Rectangle 4? A) 28 B) 45 C) 40 D) 35 12. The coordinates of the vertices of rectangle PQRS are given in the diagram on the right side. The perimeter of rectangle PQRS is 44. The value of p is A) 12 B) 10 C) 15 D) 14 Mahajana Mathematics Competition Sample Grade 8 ________________________________________________________________ 13. In the diagram on right side, AB=6cm, AC=4cm, the value of CD is (A) 7.8 (B) 7.2 (C) 6.8 (D)5.8 14. The figure shown can be folded along the lines to form a rectangular prism. The surface area of the rectangular prism is 280 cm2. The length is (A) 3cm (B) 5cm (C) 8cm (D) 10cm 15. Mark has a bag that contains 3 black marbles, 6 gold marbles, 2 purple marbles, and 6 red marbles. Mark adds a number of white marbles to the bag and tells Susan if she now draws a marble at random from the bag, the probability of it 1 3 being black or gold is . The number of white marbles that Mark adds to the bag is (A) 5 (B) 2 (C) 6 (D) 10 16. In 2010 Mahajanans Contest Grade 8, the marks of 32 mathematics students on Test are all multiples of 10 and are shown on the bar graph below. What was the average (mean) mark of the 32 students in the class? A) 70 B) 74 C) 68 D) 76 Mahajana Mathematics Competition Sample Grade 8 ________________________________________________________________ 17. Steve completes a job in 8 days. Arun completes the same job in 12 days. Steve and Arun together complete the same job in (A) Less than 5 days (B) Less than 6 days (C) More than 6 days (D) More than 8 days 18. The volume of a cylinder is equal to the area of the bases times the height of the cylinder (π r2 h). The volume, in cm3, of the largest cylinder which will fit inside a cube 10 cm by 10 cm by 10 cm (A) 25π (B) 100π (C) 250π (D) 500π 19. In the figure on the right side formed by one unit square blocks, the Point B is the midpoint of AC and the Point D is the midpoint of CE. The line which passes through the point P and one of the point A, B, C, D, & E cuts the area of the shape into two pieces of equal area. (A)Point D (B) Point B (C) Point A (D) Point C 20. A single piece of string is laced through a hole in a piece of cardboard. The top side of the card is shown. One of the diagrams below, that could not be the underside of the card is Mahajana Mathematics Competition Sample Grade 8 ________________________________________________________________ Part C (5 Questions, each question is worth 6 marks) 21. A cube having an edge length of 10 cm is sliced in to two sections by a cut in the plane ABC, as shown in the diagram. Find the volume of the smaller section (A) 225.6 (B) 166.6 (C) 500 (D) 750 22. The shape “S “shown on the right side is Constructed from four semicircles. B & D are the centers of the semi circles on the left side of AE and the radius is 2r. On the right side of AE, the larger circle radius is 3r and smaller circle radius is r. When the length is increased by 8 times, the new area of the shape “S “is increased by: A) 8 B) 16 C) 32 D) 64 23. In Bourbon College, Saimala receives the following marks out of 100 in seven of her eight courses. When Samantha actually finds out her French mark, it turns out that her average in all eight courses is 85. What is her actual French mark? A) 86 B) 92 C) 100 D) 96 Mahajana Mathematics Competition Sample Grade 8 ________________________________________________________________ 24. In the tile pattern, there are three tiles in horizontal row and one tile below this row. Another row of three tiles is added to the top of each consecutive figure. The correct set of figures for the above data is (A) (B) (C) (D) 25. In the triangular pattern of numbers shown on the right side, every row begins with a 1 and ends with a 2. Each of the numbers, not on the end of a row, is the sum of the two numbers located immediately above and to the right, and immediately above and to the left. For example, in the fourth row the 9 is the sum of the 4 and the 5 in the third row. If this pattern continues, the sum of all of the numbers in the 7th row is A) 1228 B) 192 C) 245 D) 189 Mahajana Mathematics Competition Sample Grade 8 ________________________________________________________________ Bonus Questions (10 marks) The addition shown below, representing 2 + 22 + 222 + 2222 + _ _ _, has 101 rows and the last term consists of 101 two's: (a) Determine the value of the ones digit A. (b) Determine the value of the tens digit B and the value of the hundreds digit C. (Write down all steps). Good Luck!