Transcript No Slide Title

M
S
E
C
A
Rules for Team Competition
Answer the question on the RED
ANSWER SHEET THEN…
 Hold up your TEAM NUMBER CARD so
that order recorders can see your team
number KEEP HELD UP until….
 Runners take your red sheet to markers
 With remaining time work on your 2nd
attempt (Blue Sheet)…
 Runners will collect these at the end of
question time.
st
nd
 Bonus marks: +4 for 1 , +3 for 2 , +2 for
3rd

Rules for Bonus Round
Fill in the BONUS ROUND QUIZ in any
spare time you have…it does not count
towards the team competition
 Place upside down on your table during
break
 Runners will collect in at the end
 1 mark per correct answer
st
 Prize for 1 winning team

Trial Question
There are 2 painters.
David can paint a wall in 6 minutes, and
Joanne can paint a wall in 3 minutes.
How long would it take
to paint the wall if they
worked together ?
You now have 30 seconds left
4
STOP
110
2
3
5
6
7
8
9
1. What is the last digit of 91997?
You now have 30 seconds left
4
STOP
110
2
3
5
6
7
8
9
2. A census-taker knocks on a door and asks
the woman inside how many children she
has and how old they are. “I have three
daughters, their ages are whole numbers,
and the product of their ages is 36,” says the
woman. “That’s not enough information”,
responds the census-taker. “I’d tell you the
sum of their ages, but you’d still be
stumped.” “I wish you’d tell me something
more.” “Okay’ my oldest daughter Jasmine
likes cats.”
What are the ages of the three daughters?
You now have 30 seconds left
4
STOP
110
2
3
5
6
7
8
9
3. A 4-digit number p is formed from the
digits 5,6,7,8 and 9. Without repetition.
If p is divisible by 3,5 and 7, find the
maximum value of p.
You now have 30 seconds left
4
STOP
110
2
3
5
6
7
8
9
4. Write
1
1
1
1


 ... 
1 2 2  3 3 4
99  100
as a fraction in lowest terms.
You now have 30 seconds left
4
STOP
110
2
3
5
6
7
8
9
5. The radius of the two smallest circles is one-sixth that of
the largest circle.
The radius of the middle-sized circle is double that of the
small circles. What fraction of the large circle is
shaded?
You now have 30 seconds left
4
STOP
110
2
3
5
6
7
8
9
6. Given that x represents the sum of
all the even integers from 1 to 200
and y represents the sum of all the
odd integers from 1 to 200,
evaluate x - y.
You now have 30 seconds left
4
STOP
110
2
3
5
6
7
8
9
7. As shown in the diagram, in a 5x4x4
cuboid, there are 3 holes of dimension
2x1x4, 2x1x5 and 3x1x4. What is the
remaining volume?
You now have 30 seconds left
4
STOP
110
2
3
5
6
7
8
9
8. A function f has the property
f ( n)  1
f (n  3) 
f ( n)  1
for all positive integers n.
Given that f ( 2002 ) is non- zero, what is
the value of f (2002)  f (2008) ?
You now have 30 seconds left
4
STOP
110
2
3
5
6
7
8
9
9. A tennis club has n left- handed players and
2n right-handed players, but in total ther are
fewer than 20 players. At last summer’s
tournament, in which every player in the club
played every other player exactly once, no
matches were drawn and the ratio of the
number of matches won by left-handed
players to the number of matches won by the
right-handed players was 3:4.
What is the value of n ?
You now have 30 seconds left
4
STOP
110
2
3
5
6
7
8
9
10.
1 p r
T  
x q s
where
0 pqrs x
Adding 1 to which variable would increase
T by the most?
You now have 30 seconds left
4
STOP
110
2
3
5
6
7
8
9
Click when ready...
11.
A
74 cents
B
80 cents
C
? cents
D
79 cents
You now have 30 seconds left
4
STOP
110
2
3
5
6
7
8
9
12.When the mean, median, and mode of
the list
10,2,5,2,4,2,x
are arranged in increasing order, they
form a non-constant arithmetic
progression. What is the sum of all
possible real values of x?
You now have 30 seconds left
4
STOP
110
2
3
5
6
7
8
9
13. Nine squares are arranged as shown.
If square A has area 1cm2 and square B
has area 81 cm2 then the area, in
square centimetres, of square I is
D
E
C
A F
B
G
I
H
You now have 30 seconds left
4
STOP
110
2
3
5
6
7
8
9
14. A circle of radius 6 has an isosceles
triangle PQR inscribed in it, where PQ=PR.
A second circle touches the first circle and
the mid-point of the base QR of the triangle
as shown. The side PQ has length 4√5.
The radius of the smaller circle is
P
Q
R
You now have 30 seconds left
4
STOP
110
2
3
5
6
7
8
9
15. What is the product of the real roots of the
equation
x 18x  30  2 x 18x  45
2
2
You now have 30 seconds left
4
STOP
110
2
3
5
6
7
8
9
16. Four different positive integers a,b,c,d
satisfy the following relations :
1
a

1
a

1
a
 1
,
1
a
1

b
1

c
 1
,
1
b

1
d

1
d
 1
Find d.
You now have 30 seconds left
4
STOP
110
2
3
5
6
7
8
9
17. A square XABD of side length 1 is
drawn inside a circle with diameter XY of
length 2. The point A lies on the
circumference of the circle. Another square
YCBE is drawn. What is the ratio of the
area of square XABD to area of square
YCBE? In the form 1 : n
You now have 30 seconds left
4
STOP
110
2
3
5
6
7
8
9
18. A square with sides of length 1 is
divided into two congruent trapezia and
a pentagon, which have equal areas, by
joining the centre of the square with
points on three of the sides, as shown.
Find x, the length of the longer parallel
side of each trapezium.
x
You now have 30 seconds left
4
STOP
110
2
3
5
6
7
8
9
19. In the xy-plane, what is the length of
the shortest path from (0,0) to (12,16)
that does not go inside the circle
(x – 6)2 + (y – 8)2 = 25?
You now have 30 seconds left
4
STOP
110
2
3
5
6
7
8
9
20.The figure on the right shows two
parallel lines L1 and L2. Line L1 is a
tangent to circles C1 and C3, line L2 is a
tangent to the circles C2
L1
L2
and C3 and the three circles
touch as shown.
C2
C1
Circles C1 and C2 have
radius s and t respectively.
What is the radius of
C3
circle C3 ?
You now have 30 seconds left
4
STOP
110
2
3
5
6
7
8
9