Chartered Accountants Syba
Inc. (Waterloo) IBM
Canada Ltd.
Canadian Institute of Actuaries
Do not open the contest booklet until you are told to do so.
You may u rulers, compass and paper for rough work.
Calculators are permitted, providing they are non-programmable and without graphic displays.
Part A: Each question is worth 5 credits.
1.The value of 0301
2..()+ is
(A ) 0.7(B ) 1(C ) 0.1(D ) 0.19(E ) 0.109
2.The pie chart shows a percentage breakdown of 1000 votes
in a student election. How many votes did Sue receive?
(A ) 550(B ) 350(C ) 330(D ) 450(E ) 9353.The expression a a a 9153× is equal to
(A ) a 45(B ) a 8(C ) a 18(D ) a 14(E ) a 21
4.The product of two positive integers p and q is 100. What is the largest possible value of p q +?
(A ) 52(B ) 101(C ) 20(D ) 29(E ) 25
5.In the diagram, ABCD is a rectangle with DC =12. If the area of triangle BDC is 30, what is the perimeter of
rectangle ABCD ?
(A ) 34(B ) 44(C ) 30
(D ) 29(E ) 606.If x =2 is a solution of the equation qx –311=, the value of q is (A ) 4(B ) 7(C ) 14(D ) –7(E ) –4
7.In the diagram, AB is parallel to CD . What is the value of
y ?(A ) 75(B ) 40(C ) 35
(D ) 55(E ) 50
8.The vertices of a triangle have coordinates 11,(), 71,() and 53,(). What is the area of this triangle?
(A ) 12(B ) 8(C ) 6(D ) 7(E ) 9
9.The number in an unshaded square is obtained by adding the
numbers connected to it from the row above. (The ‘11’ is one such number.) The value of x must be (A ) 4(B ) 6(C ) 9
企业邮箱怎么注册(D ) 15(E
) 10Scoring:There is no penalty for an incorrect answer.
Each unanswered question is worth 2 credits, to a maximum of 20 credits.考核指标
A B
C
D D
A
C B
10.The sum of the digits of a five-digit positive integer is 2. (A five-digit integer cannot start with zero.)
The number of such integers is
(A ) 1(B ) 2(C ) 3(D ) 4(E ) 5
Part B: Each question is worth 6 credits.
11.If x y z ++=25, x y +=19 and y z +=18, then y equals
(A ) 13(B ) 17(C ) 12(D ) 6(E ) –6
12. A regular pentagon with centre C is shown. The value of x
is
(A ) 144(B ) 150(C ) 120
(D ) 108(E ) 7213.If the surface area of a cube is 54, what is its volume?
(A ) 36(B ) 9(C ) 8138(D ) 27(E ) 1626
14.The number of solutions x y ,() of the equation 3100x y +=, where x and y are positive integers, is
(A ) 33(B ) 35(C ) 100(D ) 101(E ) 97
15.If y –55= and 28x =, then x y + equals英文自荐信
(A ) 13(B ) 28(C ) 33
16.Rectangle ABCD
has length 9 and width 5. Diagonal is divided into 5 equal parts at W , X , Y , and Z area of the shaded region.(A ) 36(B ) 365(C ) 18
(D ) 41065(E ) 2106
5
17.If N p q =()()()+75243 is a perfect cube, where p and q are positive integers, the smallest possible value
of p q + is
(A ) 5(B ) 2(C ) 8(D ) 6(E ) 12铁兰
18.Q is the point of interction of the diagonals of one face of
a cube who edges have length 2 units. The length of QR
is
(A ) 2(B ) 8(C ) 5(D ) 12(E ) 6
19.Mr. Anderson has more than 25 students in his class. He has more than 2 but fewer than 10 boys and
老是打嗝怎么治
more than 14 but fewer than 23 girls in his class. How many different class sizes would satisfy the conditions?
(A ) 5(B ) 6(C ) 7(D ) 3(E ) 4
20.Each side of square ABCD is 8. A circle is drawn through A and D so that it is tangent to BC . What is the radius of this
circle?
(A ) 4(B ) 5(C ) 6
(D ) 42(E ) 5.25
Part C: Each question is worth 8 credits.
21.When Betty substitutes x =1 into the expression ax x c 32–+ its value is –5. When she substitutes
x =4 the expression has value 52. One value of x that makes the expression equal to zero is
(A ) 2(B ) 5
2(C ) 3(D ) 72(E ) 4
22. A wheel of radius 8 rolls along the diameter of a micircle
of radius 25 until it bumps into this micircle. What is the
length of the portion of the diameter that cannot be touched
by the wheel?
(A ) 8(B ) 12(C ) 15治头疼的药
(D ) 17(E ) 2023.There are four unequal, positive integers a , b , c , and N such that N a b c =++535. It is also true that共工怒触不周山
N a b c =++454 and N is between 131 and 150. What is the value of a b c ++?
(A ) 13(B ) 17(C ) 22(D ) 33(E ) 36
24.Three rugs have a combined area of 2002m . By overlapping the rugs to cover a floor area of 1402m ,
呼伦贝尔大草原简谱
the area which is covered by exactly two layers of rug is 242m . What area of floor is covered by three layers of rug?
(A ) 122m (B ) 182m (C ) 242m (D
) 362m (E ) 422
m 25.One way to pack a 100 by 100 square with 10000 circles, each of diameter 1, is to put them in 100
rows with 100 circles in each row. If the circles are repacked so that the centres of any three tangent circles form an equilateral triangle, what is the maximum number of additional circles that can be packed?
(A ) 647(B ) 1442(C ) 1343(D
) 1443
(E ) 1344
