Embed Size (px)
Citation preview
Click when ready...
Click when ready...
IndividualCompetition
Part IIQuestions 26 - 50
• There are 25 multiple choice questions
• You have 2 minutes to finish each question
• There will be no break in this round
• A trial question will now follow
Click when ready...
You now have 30 seconds left 10987654321STOP
Trial Question (2 minutes)
(a)– log25 (b) log52
(c) log105 (d) log25 (e)
If 3 = k . 2r and 15 = k . 4r , then r =
25
You now have 30 seconds left 10987654321STOP
Suppose that * is an operation on the integers defined by a*b = a2+b.What is the value of 3 * (2 * 1)?
(a) 12 (b) 14 (c) 54 (d) 170 (e) 172
26
You now have 30 seconds left 10987654321STOP
27. An office building has 50 storeys, 25 of which are painted black and the other 25 of which are painted gold. If the number of gold storeys in the top half of the building is added to the number of black storeys in the bottom half of the building, the sum is 28. How many gold storeys are there in the top half of the building?
A. 3
B. 14
C. 22
D. 24
E. None of these
You now have 30 seconds left 10987654321STOP
28. What is the number of distinct real numbers r which have the property that the median of the five numbers r,6,4,1,9 is equal to their mean?
A. 0
B. 1
C. 2D. 3E. 5
You now have 30 seconds left 10987654321STOP
Two perpendicular line segments divide a large rectangleinto 4 small rectangles. The areas of 3 of these 4 smallrectangles are shown. What is the area of the other smallrectangle?
6 9 8
(a) 12 (b) 13 (c) 14 (d) 15 (e) 16
29
You now have 30 seconds left 10987654321STOP
30. A can build a building in 3 hours, B can build the building in 4 hours. Together, A and B, and C can build the building in 1 hour. D can build the building in half the time it takes C to build the building. How long does it take C and D to build the building together?
A. 36 minutesB. 48 minutesC. 60 minutesD. 72 minutesE. 84 minutes
You now have 30 seconds left 10987654321STOP
31. Triangle ABC has sides AB = 12, BC = 10, and AC = 20. A circle is drawn with radius 10 centered at C. Segment AB is extended, intersecting the circle at point D. Determine the length of BD.
A. 2√21
B. 10
C. 2√39
D. 13
E. None of these
You now have 30 seconds left 10987654321STOP
32. A block of wood in the form of a cuboid 6" x 9" x 14" has all its six faces painted pink. If the wooden block is cut into 756 cubes of 1" x 1" x 1", how many of these would have pink paint on them?
A. 420
B. 560
C. 585
D. 624
E. 758
You now have 30 seconds left 10987654321STOP
33.
If x + y = 0 and x ≠ 0, then what is the value of x2007
y2007 ?
(a) -2007 (b) -1 (c) 0 (d) 1 (e) 2007
You now have 30 seconds left 10987654321STOP
34. The perimeter of a rectangle is P, and the area of the rectangle is A. What is the product of the diagonals?
Ap
24
2A. B. C. P2 – 2A
Ap
24
2
D. P2 + 2A E. None of these
You now have 30 seconds left 10987654321STOP
35.
You now have 30 seconds left 10987654321STOP
36.
You now have 30 seconds left 10987654321STOP
37.Evaluate the sum
1- 2 + 3 – 4 + 5 – 6 +…+ 997 – 998 + 999 - 1000
A . -500 B. -1000
C. -999 D. -1001 E. 500500
You now have 30 seconds left 10987654321STOP
38. Let N be the largest integer for which both N and 7N have exactly 100 digits each. What is the 50th digit (from the left) of N?
A. 5 D. 4
B. 1 E. 2
C. 8
You now have 30 seconds left 10987654321STOP
39.
You now have 30 seconds left 10987654321STOP
40. The number 6 is divisible by 1, 2, 3 and 6, so 6 has 4 divisors. How many divisors has 6718464 = (2^10) x (3^8)?
A. 99 B. 109 C. 98 D. 100 E.93
(Remark. “a^b” means “a to the power of b”.)
You now have 30 seconds left 10987654321STOP
41.
You now have 30 seconds left 10987654321STOP
42. A cylindrical beaker 8 cm high and 12cm in circumference was standing on a table. On the inside of the beaker, 2 cm from the top, is a drop of honey. Diametrically opposite the honey and lower is a spider which is on the outside of the beaker, 2 cm from the bottom. What is the shortest distance the spider has to walk to reach the honey?
A. 10 cm B. 12 cmC. 13 cmD. 100 cmE. None of the above
You now have 30 seconds left 10987654321STOP
43.
You now have 30 seconds left 10987654321STOP
44. In year N, the 300th day of the year is a Tuesday. In year N + 1, the 200th day is also a Tuesday. On what day of the week did the 100th day of the year N-1 occur?
A. Thursday
B. Friday
C. Saturday
D. Sunday
E. Monday
You now have 30 seconds left 10987654321STOP
45. A square with sides of length 1 is divided into two congruent trapezoids and a pentagon, which have equal areas, by joining the centre of the square with points on three of the sided, as shown. Find r, the length of the longer parallel side of each trapezoid.
A. B. C. D. E.3
26
5
4
38
7
5
3
r
You now have 30 seconds left 10987654321STOP
46.
You now have 30 seconds left 10987654321STOP
47. In square ABCD, with sides of length 2, segments AE, BF, CG, and DH are drawn (figure below), bisecting the sides. These segments form quadrilateral JKLM. Determine the area of quadrilateral JKLM.
A. 2/5
B. 4/5
C. 1
D. 2
E. None of these
A 1 H 1 B
D F C
E G
LK
JM
You now have 30 seconds left 10987654321STOP
48. Define a sequence of real numbers
by and for all
Then equals
...,,321 aaa
11a aa nn
33
199
.1n
a100
A. 3333
B. 3399
C. 9933
D. 9999
E. None of these
You now have 30 seconds left 10987654321STOP
49.The equiangular convex hexagon ABCDEF has AB = 1 , BC = 4, CD = 2 and DE = 4. The area of the hexagon is
32
15 39A. B. C. 16
34
39 34
43D. E.
You now have 30 seconds left 10987654321STOP
50.
