Transcript Slide 1

SEAMC 2007
Multiple Choice Section
SEAMC 2007
Multiple Choice Section
SEAMC 2007
Multiple Choice Section
You will have exactly 1½ minutes
to read each question and select the
best answer.
Following this slide will be a practice
question to try.
Here is the practice question:
SEAMC 2007
Multiple Choice Section
Question 0 (practice)
In the diagram, the value of x is equal
to:
A. 34
B. 33
C. 46
D. 23
20o
60o
xo
54o
xo
SEAMC 2007
Multiple Choice Section
And the answer of course is …
A. 34
B. 33
C. 46
D. 23
SEAMC 2007
Multiple Choice Section
You will have exactly 1½ minutes
to read each question and select the
best answer.
Shade the square of the letter of
your preferred choice of answer.
For example, the answer to the previous question was D:
A
B
C
D
SEAMC 2007
Multiple Choice Section
SEAMC 2007
Multiple Choice Section
Question 1
The average of four numbers is 48. If 8 is
subtracted from each number, the average of
the four new numbers is:
A. 16
B. 40
C. 46
D. 44
SEAMC 2007
Multiple Choice Section
Question 2
PQRS is a rectangle enclosing 2 circles each of radius
2cm. The area of rectangle PQRS, in square
centimeters, is:
A. 8
P
Q
S
R
B. 16
C. 24
D. 32
SEAMC 2007
Multiple Choice Section
Question 3
The number of nails weighing 5 grams each that can
be made from 11.5 kilograms of wire is:
A. 230
B. 2 300
C. 23 000
D. 230 000
SEAMC 2007
Multiple Choice Section
Question 4
One of the elephants in the zoo is on a special diet, and eats
every day a portion of carrots which is equal to what one of
the rabbits eats in 1 year (365 days). Together, in one day,
the elephant and rabbit eat 111 kilograms of carrots. How
many kilograms of carrots does the rabbit eat in one day?
A.
1
2
B.
37
122
111
C.
165
D.
19
61
SEAMC 2007
Multiple Choice Section
Question 5
The digits 1, 2, 3 and 5 can be arranged to form 24
different four-digit numbers. The number of even
numbers in this set is:
A. 18
B. 12
C. 6
D. 2
SEAMC 2007
Multiple Choice Section
Question 6
Between the last 5 questions, a diagram of a
famous fractal has been momentarily
displayed. The name of this fractal is:
A. Pascal’s Triangle
B. Koch Snowflake
C. Sierpinski’s Triangle
D. Mandelbrot Set
SEAMC 2007
Multiple Choice Section
Question 7
The value of the product
where the
2n  1
th
n factor is 1 
, is:
2
3
5
7
9
41
(1  )( 1  )( 1  )( 1  )...(1 
)
1
4
9
16
400
A. 441
B. 4041
C. 4410
D. 4001
n
SEAMC 2007
Multiple Choice Section
Question 8
If the figure shown is folded to form a cube, then three faces
meet at every vertex. The numbers on the three faces meeting
at any vertex can be multiplied together. What is the largest
such product for the vertices of this cube?
A. 120
B. 90
C. 72
D. 60
1
4
2
3
5
6
SEAMC 2007
Multiple Choice Section
Question 9
How many positive integers less than 1000
have the sum of their digits equal to 6?
A. 28
B. 27
C. 19
D. 18
SEAMC 2007
Multiple Choice Section
Question 10
A formula in physics states
1 1
1
 
R R1 R2
If R1 = 3 and R2 = 6, then R is equal to
A. ½
B. 2
C. 1/9
D. 9
SEAMC 2007
Multiple Choice Section
Question 11
A 3x8 rectangle is cut into 2 pieces as indicated. The
2 pieces are rearranged to form a right-angled
triangle. One side of the resulting triangle has length
4
A. 9
B. 7
C. 6
D. 4
3
4
5
8
SEAMC 2007
Multiple Choice Section
Question 12
A cube with each edge of length 1 unit is turned into
a solid star by adding a square pyramid with each
edge of length 1 unit to every face. The number of
edges this new solid has is:
A. 28
B. 24
C. 48
D. 36
SEAMC 2007
Multiple Choice Section
Question 13
The regular octagon shown has side length 4cm. What
is the area, in square centimeters, of the shaded
region?
A. 16
B. 8(1  2 )
C. 24
D. 16(1  2 )
SEAMC 2007
Multiple Choice Section
Question 14
What is the highest power of 2 which divides
exactly into 1 000 000?
A. 23
B. 25
C. 26
D. 28
SEAMC 2007
Multiple Choice Section
Question 15
What is the radius of the largest circle that can be
drawn inside a quarter circle of radius 1 unit?
A.
2 1
2
B.
3
C. ½
D.
1
2 2
?
SEAMC 2007
Multiple Choice Section
Question 16
If n is an integer, which of the following must
be an odd integer?
A. 5n
B. n2 + 5
C. 2n2 + 5
D. n3
SEAMC 2007
Multiple Choice Section
Question 17
In the diagram, all triangles are right
isosceles triangles, and PQR is a straight line.
Given that PQ is 12 units, what is the length
of QR?
1
A. 3
5
3
C. 3
4
B. 4
2
D. 3 
2
Q
P
R
SEAMC 2007
Multiple Choice Section
Question 18
If the following were arranged in order from
biggest to smallest, the biggest being the
first, which would be the third number?
A. 2(2)7
B. 2(2)6 – 2
C. 2 + 2(2)6
D. 27
SEAMC 2007
Multiple Choice Section
Question 19
If xy = 3, then x3y + 2 equals
A. 11
B. 8
C. 29
D. 35
SEAMC 2007
Multiple Choice Section
Question 20
If four different positive integers m, n, p and q
satisfy the equation (7 – m)(7 – n)(7 – p)(7 – q) = 4
then the sum m+n+p+q is equal to
A. 28
B. 26
C. 24
D. 21
SEAMC 2007
Multiple Choice Section
Question 21
1 1
  m where p and q are
p q
If p +q = n and
both positive,
then (p – q)2 equals
A.
n m
n
B.
n  4m n
2
2
m
n

4
n
C.
m
2
D.
n m
2
SEAMC 2007
Multiple Choice Section
Question 22
For m and n integers, how many solutions (m, n) of
2
2
the inequality
4  m  n  17 are there?
A. 36
B. 48
C. 15
D. 52
SEAMC 2007
Multiple Choice Section
Question 23
Two parallel planes are 10cm apart. A point P lies on
one of the planes. The set of points which are all
equally distant from the two planes and 6cm from P
is:
A. a point
B. a straight line
C. a circle
D. a hollow sphere
SEAMC 2007
Multiple Choice Section
Question 24
7  13 
A.
B.
13
3
2
7  13
C.
D.
3
2
4
2 13
equals
SEAMC 2007
Multiple Choice Section
Question 25
A cube measuring 3 units on each edge is painted. It
is then cut into 27 one-unit cubes. How many faces
of the one-unit cubes are not painted?
A. 108
B. 81
C. 72
D. 36
SEAMC 2007
Multiple Choice Section
SEAMC 2007
Multiple Choice Section
SEAMC 2007
Multiple Choice Section
You will have exactly 1½ minutes
to read each question and select the
best answer.
Shade the square of the letter of
your preferred choice of answer.
For example, if the answer is C:
A
B
C
D
SEAMC 2007
Multiple Choice Section
Question 26
If n is a positive integer and n(n+1) is divided
by 3, the remainder can be
A. 0 only
B. 2 only
C. 0 or 1 only
D. 0 or 2 only
SEAMC 2007
Multiple Choice Section
Question 27
A cart track is made up of one large semicircle, and
three small semicircles each of radius 100m. What is
the total length of the track?
A. 150π
B. 300π
C. 450π
D. 600π
SEAMC 2007
Multiple Choice Section
Question 28
If
A. 2
1
2

2x  3 5
B.
3
2
then
C.
2
3
1
2x 1
1
D.
2
equals
SEAMC 2007
Multiple Choice Section
Question 29
If a, a+d, a+9d, (d>0), are the sides of a
right-angled triangle, then the ratio a:d is
A. 4:1
B. 8:1
C. 20:21
D. 20:1
SEAMC 2007
Multiple Choice Section
Question 30
A calendar watch loses one second per day. At this
rate, the approximate length of time, in years, for
the watch to lose exactly 24 hours is
1
A.
360
C. 240
1
B.
240
D. 2400
SEAMC 2007
Multiple Choice Section
Question 31
If
1 1 1 1
1  2  2  2  2  ...  x then
2 3 4 5
1
1
1 1
1  2  2  2  2  ... is
2
4
6 8
x
A.
2
x
1
B.
2
x
1
C.
4
x
D.  1
4
the value of
SEAMC 2007
Multiple Choice Section
Question 32
The figure below which can be
obtained by rotating the figure
on the right is
A.
C.
B.
D.
SEAMC 2007
Multiple Choice Section
Question 33
A square of side 2x has four equilateral triangles
drawn on its sides (and exterior to the square). The
area of the figure formed is
A.
4(1  3) x
2
(
1

3
)
x
B.
4
2
2
(
4

3
)
x
C.
2
(
1

4
3
)
x
D.
SEAMC 2007
Multiple Choice Section
Question 34
Consider the set of 4-digit positive integers where
each integer is composed of four different digits.
When the smallest of these is subtracted from the
largest, the result is
A. 8876
B. 8642
C. 8853
D. 8646
SEAMC 2007
Multiple Choice Section
Question 35
PBCQ is a trapezoid in which PQ:BC = 2:3.
If the area of triangle ABC is 36, then the area of
the trapezoid PBCQ is
Q
P
A. 100
A
B. 90
C. 84
D. 72
B
C
SEAMC 2007
Multiple Choice Section
Question 36
If m pens are bought at n dollars each, and n pens
are bought at m dollars each, then the average cost
per pen, in dollars, is
A. mn
C. m  n
2
2mn
B.
mn
D. 1
SEAMC 2007
Multiple Choice Section
Question 37
Each side of a rhombus has length 10. The
sum of the squares of the diagonals equals
A. 50
B. 100
C. 200
D. 400
SEAMC 2007
Multiple Choice Section
Question 38
The slope of OA is
y
A. 4/3
A
B. 3/4
3
C. 5/3
D. 3/5
O
4
5
B
x
SEAMC 2007
Multiple Choice Section
Question 39
If the distance between consecutive fence posts is 5
meters, the number of fence posts needed to build a
fence around a triangular region with sides 20m,
20m, and 30m is
A. 11
B. 13
C. 14
D. 15
SEAMC 2007
Multiple Choice Section
Question 40
A bag contains 80 jelly beans – 20 are red, 20 are
green, 20 are yellow and 20 are blue. The least
number that a blindfolded person must eat to be
certain of having eaten at least one of each colour is
A. 5
B. 7
C. 23
D. 61
SEAMC 2007
Multiple Choice Section
Question 41
xy
xz
If x, y and z are positive and
a ,
b
x y
xz
yz
 c , then x equals
and
yz
abc
A.
ab  ac  bc
2abc
C.
ab  ac  bc
2abc
B.
bc  ac  ab
abc
D.
ac  bc  ab
SEAMC 2007
Multiple Choice Section
Question 42
As everyone knows, a normal cat has 18 claws, 5 on each front
leg and 4 on each back leg. At Harry’s Home for Distressed
Cats there are 4 three-legged cats, each one with a different
leg missing. How many claws do they have all together?
A. 52
B. 54
C. 64
D. 68
SEAMC 2007
Multiple Choice Section
Question 43
Three darts are thrown at the dartboard illustrated.
The three scores are added together, a miss counts
as zero. What is the smallest total score which is
impossible to obtain?
A. 14
B. 18
23
C. 19
12
D. 22
8
3
1
SEAMC 2007
Multiple Choice Section
Question 44
The last digit in the sum
A. 0
B. 1
C. 2
D. 4
317 + 713
is
SEAMC 2007
Multiple Choice Section
Question 45
Red rose plants are on sale for $3 each and yellow ones for $5
each. A young guy wants to buy a mixture of both types (at
least one of each) and decides to buy 13 in total, buying more
yellow ones than red ones. The number of dollars that the young
guy spends could be
A. 51
B. 57
C. 58
D. 65
SEAMC 2007
Multiple Choice Section
Question 46
If
4
GH
L
A.
(G  H ) 2
4
B.
4
G2  H 2
then L equals
C.
4
(G  H ) 2
D.
G2  H 2
4
SEAMC 2007
Multiple Choice Section
Question 47
2
n 1
2
A. 2n+2
B. 22n+2
C. 42n+2
D. 42n+1
n 1
equals
SEAMC 2007
Multiple Choice Section
Question 48
For all positive integers x and y such that
the greatest value that y can have is
A. 60
B. 84
C. 156
D. 288
1 1 1
 
x y 12
SEAMC 2007
Multiple Choice Section
Question 49
Each circle has an area of 1cm2.
The area of the overlap between any pair of intersecting circles
is 1/8 cm2.
The total area in cm2 of the region enclosed by the 5 circles is
A. 4
B. 4½
C. 43/8
D. 4¾
SEAMC 2007
Multiple Choice Section
Question 50
Some M&M’s had been eaten without the shop owner’s permission
by one or more of the 5 kids in the shop. When questioned,
they gave the following answers:
A. 1
B. 2
C. 3
D. 4
E. 5
Ace: One of us ate them
Bea: Two of us ate them
Cec: Three of us ate them
Dee: Four of us ate them
Eve: All of us ate them
The owner knew from past behaviour
that the guilty ones always lied while
the others told the truth. The number
of kids who ate the M&M’s was
SEAMC 2007
Multiple Choice Section