Indiana Academic
M A T H Bowl
M.A.T.H.
Invitational February 2010
Begin
Round
One
2010 MATH Invitational Round 1 Number 1
30 seconds
A(n)
( ) ________ off a circle is a
line segment whose two
endpoints lie on the circle.
A. arc
B. chord
C. circumference
D. radius
2010 MATH Invitational Round 1 Number 2
30 seconds
What is the area of the parallelogram?
10 in
A.
B.
C
C.
D.
70 in2
60 in2
30 iin2
35 in2
7 in
6 iin
2010 MATH Invitational Round 1 Number 3
30 seconds
Find the perimeter of the
rectangle
g that is 34 cm by
y 18
cm.
A. 52 cm
B. 104 cm
2
C. 612 cm
D. 1,224 cm
2010 MATH Invitational Round 1 Number 4
60 seconds
If Sue and Andy can finish 40
problems in 60 minutes
minutes, how
many can they finish in 2 hours?
A. 40 problems
p
B. 50 problems
C. 60 problems
D 80 problems
D.
2010 MATH Invitational Round 1 Number 5
45 seconds
Sam awakens at 6:30 A.M. He takes
45 minutes to get ready, then spends 6
minutes driving to the golf course
course. He
arrives 7 minutes before his tee time.
Wh t is
What
i Sam’s
S ’ ttee ti
time?
?
A. 7:21 A.M.
B 7:25 A
B.
A.M.
M
C. 7:28 A.M.
D. 7:30 A.M.
2010 MATH Invitational Round 1 Number 6
60 seconds
In the diagram
three
rectangles are pictured– two small
ones and one larger one. How many
are pictured in
?
A. 7
A
B. 9
C. 16
D. 18
2010 MATH Invitational Round 1 Number 7
60 seconds
The dimensions of a closed
rectangular box are 3,
3 4,
4 and
5 inches. What is the
surface area?
A 94 square iinches
A.
h
B. 60 square inches
C. 120 square inches
D. 194 square inches
Begin
Round
Two
2010 MATH Invitational Round 2 Number 1
30 seconds
Which transformation
f
occurs
when a shape is flipped over a
line?
A. dilation
B. reflection
C. rotation
D. translation
2010 MATH Invitational Round 2 Number 2
What type
yp of angle
g is shown?
A. Right
B. Left
C. Acute
D. Obtuse
30 seconds
2010 MATH Invitational Round 2 Number 3
Look at the shape to
the right. What is the
resulting image after a
rotation of 180º?
A.
C.
B
B.
D
D.
45 seconds
2010 MATH Invitational Round 2 Number 4
60 seconds
Clayton attempted 10 shots and made 4
field goals for 8 points in a basketball
game Sue attempted 5 shots
game.
shots. If Sue
had the same ratio of field goals to shot
attempts how
attempts,
ho many
man points did Sue
S e
make?
A. 2 points
B 4 points
B.
C. 6 points
D. 8 points
2010 MATH Invitational Round 2 Number 5
45 seconds
Which off the following
f
pairs off
angles make a pair of vertical
angles?
A. ∠a and ∠ b
B. ∠c and ∠ d
C. ∠a and ∠ c
D. ∠b and ∠ e
2010 MATH Invitational Round 2 Number 6
45 seconds
The area of each of the 9 small
squares is 9 cm2. What would be
th perimeter
the
i t off the
th largest
l
t
square?
q
A.
B.
C.
D
D.
12 cm
36 cm
81 cm
108 cm
2010 MATH Invitational Round 2 Number 7
30 seconds
The measure of one angle of an
isosceles triangle is 20°. Which of the
following could be the measure of
another angle of this triangle?
A.
B.
C
C.
D
D.
20°
40°
60°
180°
180
Begin
Round
Three
Th
2010 MATH Invitational Round 3 Number 1
30 seconds
C
Congruent
ffigures are:
A. the same shape, but not necessarily
the same size.
B the same size
B.
size, but not necessarily
the same shape.
C th
C.
the same shape
h
and
d size.
i
p nor size.
D. neither the same shape
2010 MATH Invitational Round 3 Number 2
What type of angle is shown?
A. Supplementary angle
B Complimentary angle
B.
C. Straight angle
D. Obtuse angle
30 seconds
2010 MATH Invitational Round 3 Number 3
How many faces
f
does
this solid have?
A. 6
B. 8
C. 12
D. 16
45 seconds
2010 MATH Invitational Round 3 Number 4
60 seconds
A trapezoid has bases of lengths
4 and 6,
6 respectively.
respectively If its height
is 5, what is its area?
A. 25
B. 50
C. 75
D 100
D.
2010 MATH Invitational Round 3 Number 5
60 seconds
What is the volume off a cylinder
that is 9 cm tall and has a base
that covers 12.56 cm2?
3
cm
A. 37.68
B. 113.04 cm3
3
C. 254.24 cm
3
D. 1,017.36 cm
2010 MATH Invitational Round 3 Number 6
Find the value for „
45 seconds
+ z if
„ x z = 24 and
d „ - z = 5.
A.
B.
C
C.
D.
11
4
6
8
2010 MATH Invitational Round 3 Number 7
60 seconds
There are four identical pieces of chain,
each three links long.
g It costs 4¢
¢ to
open a link and 5¢ to close one. Find
the least cost to join all twelve links into
a single circle.
A.
B
B.
C.
D.
22¢
27¢
33¢
44¢
Begin
Round
Four
2010 MATH Invitational Round 4 Number 1
30 seconds
Put these integers in order from
f
least to greatest:
3, 25, -3, 0, -41, 40
A. 0, -3, 3, 25, 40, -41
B. -41, 40, -3, 0, 3, 25
C. 40, 25, 3, 0, -3, -41
D. -41, -3, 0, 3, 25, 40
2010 MATH Invitational Round 4 Number 2
30 seconds
Maria s Pizza Parlor makes square
Maria’s
pizzas. After baking, the pizzas are cut
along
l
one di
diagonall iinto
t ttwo ttriangles.
i
l
What would the triangle look like?
A.
B.
C.
D.
right, equilateral
right, isosceles
acute, equilateral
acute, isosceles
2010 MATH Invitational Round 4 Number 3
45 seconds
∠BDE iis a right
i ht angle.
l ∠EDC
measures 63º.
63 . What is the
measure of ∠CDB?
A. 17
17º
B. 27º
C. 37º
D. 117º
2010 MATH Invitational Round 4 Number 4
30 seconds
Which segment is the hypotenuse of
the triangle?
A. segment XY
A
C. segment
g
XZ
B. segment YZ
B
D. The triangle
g
has no hypotenuse.
2010 MATH Invitational Round 4 Number 5
Find the area of
the complex
figure.
A. 40 km2
B. 64 km2
C. 144 km2
D 20
D.
20,736
736 km2
60 seconds
2010 MATH Invitational Round 4 Number 6
60 seconds
Sue, Nancy, Debbie, Brenda, and Jackie are
in line to buy lunch. Sue is between Nancy
and Debbie. Debbie is next to Jackie who is
first in line. If Sue leaves the line, which of
the following lists the remaining students in
order from first to last?
A.
B.
C.
D
D.
Jackie, Debbie, Nancy, Brenda
Jackie, Nancy,
y Debbie, Brenda
Jackie, Brenda, Nancy, Debbie
Jackie
Jackie, Nancy
Nancy, Brenda
Brenda, Debbie
2010 MATH Invitational Round 4 Number 7
45 seconds
Dog and cat food together cost $30.
If the dog food cost $10 more than
the cat food, how much did the dog
food cost?
A.$5
B.$10
C.$15
D.$20
Begin
Alternate
R
Round
d
2010 MATH Invitational Alternate Round Number 1
30 seconds
Which measuring tool would
yyou use to estimate the volume
of a shoebox?
A.
B.
C
C.
D.
compass
ruler
protractor
measuring cup
2010 MATH Invitational Alternate Round Number 2
30 seconds
What part of the circle is AC?
A.
A
B.
C.
D.
chord
arc
tangent
Not given
A
C
2010 MATH Invitational Alternate Round Number 3
30 seconds
I’m a 4-digit number. My first digit is
one-third of my
y second. My
y third digit
g
is the sum of the first and second. My
last digit is three times the second?
A 3,924
A.
3 924
B. 1,234
, 3
C. 1,349
D. 1,258
2010 MATH Invitational Alternate Round Number 4
60 seconds
What is the ratio off the area off
the orange square to the area of
the blue square?
A. 1 : 2
B. 1 : 2.5
C. 1 : 4
D. 1 : 5
2010 MATH Invitational Alternate Round Number 5
60 seconds
A rectangular lot that measures 30 ft by 40 ft
is surrounded by a concrete walk 5 ft wide
on all four sides
sides. What is the surface area of
the walk?
A.
B
B.
C
C.
D
D.
2
ft
800
2
700 ft
375 ft2
350 ft2
5
30
40
2010 MATH Invitational Alternate Round Number 6
45 seconds
What is the relationship
p between a
parallelogram and a triangle that have the
g
same base and height?
A. The area of the parallelogram is the
same as the area of the triangle squared
squared.
B. The area of the parallelogram is three
times the area off the triangle.
C. The area of the parallelogram is ½ the
area of the triangle.
parallelogram
g
is twice the
D. The area of the p
area of the triangle.
2010 MATH Invitational Alternate Round Number 7
45 seconds
Sue made 2 gallons of ice tea
tea.
How many people could she serve
if they received one cup each?
A.
B
B.
C.
D.
16 people
24 people
p p
32 people
36 people
Begin
g Extra
Practice Problems
2010 MATH Invitational EXTRA Number 1
60 seconds
Using the formula for area of a trapezoid:
A = ½ h (b1 + b2 ). Find the area of a
trapezoid that has bases of 15 meters and
18 meters and a height of 10 meters.
A.
B
B.
C.
D.
30 m2
60 m2
165 m2
330 m2
2010 MATH Invitational EXTRA Number 2
45 seconds
A case of canned goods weighs
8 2/3 pounds. How much do 4 ½
cases weigh?
A.
B.
C.
D.
19 lbs
27 2/3 lbs
32 ½ lbs
39 lbs
2010 MATH Invitational EXTRA Number 3
45 seconds
5 eggs
1 cup sugar
2 cans condensed milk
6 cups Chocolate Milk
1 1/2 tsp
tsp. vanilla
3 oz. semi-sweet melted chocolate
This ice cream recipe serves 6. How much
vanilla is needed for 32 people?
A. 1 ½ tsp. vanilla
B. 3 ¼ tsp. vanilla
C. 6 tsp. vanilla
D. 8 tsp. vanilla
2010 MATH Invitational EXTRA Number 4
60 seconds
Mark bought 6 cans of corn at 2 for
$1.20, 2 loaves of bread at 2 for
$1.95, and 1 gallon of milk at $2.19.
He had a co
coupon
pon for 25% off of the
total bill. How much did he save?
A. $1.00
B. $1.50
C $1.94
C.
$1 94
D. $2.00
2010 MATH Invitational EXTRA Number 5
60 seconds
There were 160 M&M’s in the box
yesterday but now there are 116
yesterday,
116,
what is the percentage difference?
A. 20% decrease
B. 25% decrease
C. 27.5% decrease
D. 30% decrease
2010 MATH Invitational EXTRA Number 6
30 seconds
Farmer Don has 2 4/5 acres of
farmland. He will create 7 equal
sized plots for different crops. What
fraction of an acre will be used for
each crop?
A 1/3 acre
A.
B. 2/3 acre
C. 1/5 acre
D. 2/5 acre
2010 MATH Invitational EXTRA Number 7
45 seconds
What are the next three numbers in the
sequence?
1, 8, 27, 64, 125, 216, …
A. 300, 398, 421
B. 324, 398, 445
C 343,
C.
343 512
512, 729
D. 347, 557, 739
2010 MATH Invitational EXTRA Number 8
60 seconds
Four cousins are buying gifts for their
grandmother. They buy her a new mug for $11.11,
and a p
pound of coffee for $9.19. The tax rate is
7%. If they split the cost equally, how much will
each cousin contribute, to the nearest cent?
A. $5.08
B. $5.43
C. $20.30
D. $21.72
$
ANSWER
SLIDES
2010 MATH Invitational Round 1 Number 1
A(n)
( ) ________ off a circle is a
line segment whose two
endpoints lie on the circle.
B. chord
2010 MATH Invitational Round 1 Number 2
What is the area of the parallelogram?
10 in
B.60 in2
A = bh
A = 10(6)
A = 60 in2
7 in
6 iin
2010 MATH Invitational Round 1 Number 3
Find the perimeter of the
rectangle
g that is 34 cm by
y 18
cm.
B. 104 cm
P = 2l +2
+2w
P = 2(34) + 2(18)
P = 68 + 36
P = 104
2010 MATH Invitational Round 1 Number 4
If Sue and Andy can finish 40
problems in 60 minutes
minutes, how
many can they finish in 2 hours?
D. 80 problems
p
40 problems in 1 hour
80 problems in 2 hours
2010 MATH Invitational Round 1 Number 5
Sam awakens at 6:30 A.M. He takes
45 minutes to get ready, then spends 6
minutes driving to the golf course
course. He
arrives 7 minutes before his tee time.
Wh t is
What
i Sam’s
S ’ ttee ti
time?
?
C 7:28 A
C.
A.M.
M
6:30 + 0:45 = 7:15
7:15 + 0:06 = 7:21
7:21 + 0:07 = 7:28
2010 MATH Invitational Round 1 Number 6
In the diagram
three
rectangles are pictured– two small
ones and one larger one. How many
are pictured in
?
Explanation on the next slide
D 18
D.
1
4
2
5
3
6
14
15
6 singles
7
8
2 triples
9
16
10
11
17
12
13
7 doubles
2 quads
18
1 sextuplet
2010 MATH Invitational Round 1 Number 7
The dimensions of a closed
rectangular box are 3,
3 4,
4 and
5 inches. What is the
surface area?
A 94 square iinches
A.
h
3 x 5 = 15
5 x 4 = 20
4 x 3 = 12
2(15 + 20 + 12) = 2(47)
2010 MATH Invitational Round 2 Number 1
Which transformation
f
occurs
when a shape is flipped over a
line?
B. reflection
2010 MATH Invitational Round 2 Number 2
What type
yp of angle
g is shown?
C. Acute
2010 MATH Invitational Round 2 Number 3
Look at the shape to
the right. What is the
resulting image after a
rotation of 180º?
C.
2010 MATH Invitational Round 2 Number 4
Clayton attempted 10 shots and
made 4 field goals for 8 points in a
b k tb ll game. Sue
basketball
S attempted
tt
t d5
shots. If Sue had the same ratio of
field goals to shot attempts, how
many points
i t did Sue
S make?
k ?
B 4 points
B.
Shots : FG : points
Clayton 10 : 4 : 8
Sue
5:2:4
2010 MATH Invitational Round 2 Number 5
Which off the following
f
pairs off
angles make a pair of vertical
angles?
D ∠b and
D.
d∠e
2010 MATH Invitational Round 2 Number 6
The area of each of the 9 small
squares is 9 cm2. What would be
th perimeter
the
i t off the
th largest
l
t
square?
q
B.36 cm
A=9 ⇒ s = 3 cm
So S = 9 cm for large square
P = 4S
P = 4(9)
2010 MATH Invitational Round 2 Number 7
30 seconds
The measure of one angle of an
isosceles triangle is 20°. Which of the
following could be the measure of
another angle of this triangle?
A. 20°
20 + 20 + 140 = 180
Or
20 + 80 + 80 = 180
Thus possibilities are 20 or 80
Thus,
80.
2010 MATH Invitational Round 3 Number 1
C
Congruent
ffigures are:
C th
C.
the same shape
h
and
d size.
i
2010 MATH Invitational Round 3 Number 2
What type of angle is shown?
C. Straight angle
30 seconds
2010 MATH Invitational Round 3 Number 3
How many faces
f
does
this solid have?
A.6
Top, bottom, front, back, left and right sides
2010 MATH Invitational Round 3 Number 4
A trapezoid has bases of lengths 4
and 6,
6 respectively.
respectively If its height is
5, what is its area?
A. 25
A = ½ h(b1 + b2)
A = ½ (5)(4 + 6)
A = ½ (5)(10)
A = 25
2010 MATH Invitational Round 3 Number 5
What is the volume off a cylinder
that is 9 cm tall and has a base
that covers 12.56 cm2?
B. 113.04 cm3
V = Bh
V = 12.56(9)
V = 113.04
2010 MATH Invitational Round 3 Number 6
Find the value for „
+ z if
„ x z = 24 and
d „ - z = 5.
A.11
8 X 3 = 24 and 8 – 3 = 5
So 8 + 3 = 11
2010 MATH Invitational Round 3 Number 7
There are four identical pieces of chain,
each three links long.
g It costs 4¢
¢ to
open a link and 5¢ to close one. Find
the least cost to join all twelve links into
a single circle.
B 27¢
B.
3( 5 + 4 ) ¢
2010 MATH Invitational Round 4 Number 1
Put these integers in order from
f
least to greatest:
3, 25, -3, 0, -41, 40
D. -41, -3, 0, 3, 25, 40
2010 MATH Invitational Round 4 Number 2
Maria s Pizza Parlor makes square
Maria’s
pizzas. After baking, the pizzas are cut
along
l
one di
diagonall iinto
t ttwo ttriangles.
i
l
What would the triangle look like?
B. right, isosceles
2010 MATH Invitational Round 4 Number 3
∠BDE is a right angle. ∠EDC
C
measures 63º
63 . What is the
measure of ∠CDB?
B. 27º
90 – 63 = 27
2010 MATH Invitational Round 4 Number 4
Which segment is the hypotenuse of
the triangle?
D The triangle has no hypotenuse.
D.
hypotenuse
The hypotenuse is the longest side of a RIGHT triangle. This is
an obtuse triangle.
2010 MATH Invitational Round 4 Number 5
Find the area off the complex
figure.
figure
A.40
2
km
8 X 8 – 2(6 x 2)
64 – 2(12)
64 – 24
40
2010 MATH Invitational Round 4 Number 6
Sue, Nancy, Debbie, Brenda, and Jackie are
in line to buy lunch. Sue is between Nancy
and Debbie. Debbie is next to Jackie who is
first in line. If Sue leaves the line, which of
the following lists the remaining students in
order from first to last?
A. Jackie, Debbie, Nancy, Brenda
Debbie
Jackie
Sue
Nancy
Brenda
2010 MATH Invitational Round 4 Number 7
Dog and cat food together cost
$30. If the dog food cost $10
more than the cat food, how much
did the dog food cost?
$30 - $10 extra
= $20 to split
D $20
D.
So cat food is
$10 and dog
food is $10 +
extra $10 or
$20.
2010 MATH Invitational Alternate Round Number 1
Which measuring tool would
yyou use to estimate the volume
of a shoebox?
A. A compass draws circles
B. ruler
C A protractor
C.
t t measures angles.
l
D. Shoe boxes don’t hold liquids!
2010 MATH Invitational Alternate Round Number 2
30 seconds
What part of the circle is AC?
A
B. arc
C
2010 MATH Invitational Alternate Round Number 3
I’m a 4-digit number. My first
digit is one-third
one third of my second.
second
My third digit is the sum of the
first and second. My last digit is
three times the second?
C. 1,349
,
2010 MATH Invitational Alternate Round Number 4
What is the ratio off the area off
the orange square to the area of
the blue square?
C. 1:4
2.5
2
52 : 52
6.25 : 25
1:4
2010 MATH Invitational Alternate Round Number 5
A rectangular lot that measures 30 ft by 40 ft
is surrounded by a concrete walk 5 ft wide
on all four sides
sides. What is the surface area of
the walk?
A. 800
2
ft
Outer length 5 + 40 + 5
Outer width 5 + 30 + 5
Area of walk – blue area
(50X40) –(30X40)
2,000 – 1,200
800
30
5
40
2010 MATH Invitational Alternate Round Number 6
What is the relationship
p between a
parallelogram and a triangle that have the
g
same base and height?
D. The area of the parallelogram is twice the
area of the triangle.
2010 MATH Invitational Alternate Round Number 7
Sue made 2 gallons of ice tea
tea.
How many people could she serve
if they received one cup each?
C.32 people
1 gallon is the same as
4 quarts or 8 pints or 16 cups
So 2 gallons equals 32 cups
2010 MATH Invitational EXTRA Number 1
Using
U
i th
the fformula
l ffor area off a ttrapezoid:
id
A = ½ h (b1 + b2 ). Find the area of a
t
trapezoid
id th
thatt h
has b
bases off 15 meters
t
and
d
18 meters and a height of 10 meters.
18
C 165 m2
C.165
A = ½ (10)(15 + 18)
A = ½(10)(33)
A = 5(33)
A = 165
10
15
2010 MATH Invitational EXTRA Number 2
A case of canned goods weighs
8 2/3 pounds. How much do 4 ½
cases weigh?
D.39 lbs
8 2/3 x 4 ½
26/3 x 9/2
234/6
2010 MATH Invitational EXTRA Number 3
5 eggs
1 cup sugar
2 cans condensed milk
6 cups Chocolate Milk
1 1/2 tsp
tsp. vanilla
3 oz. semi-sweet melted chocolate
This ice cream recipe serves 6. How much
vanilla is needed for 32 people?
1.5 : 6 = x : 32
6x = 1
1.5(32)
5(32)
x=8
D. 8 tsp. vanilla
2010 MATH Invitational EXTRA Number 4
Mark bought 6 cans of corn at 2 for
$1.20, 2 loaves of bread at 2 for
$1.95, and 1 gallon of milk at $2.19.
He had a co
coupon
pon for 25% off of the
total bill. How much did he save?
C. $1.94
((1.20x3)) + 1.95 + 2.19 = 7.74
7.74 x 0.25 = 1.935 in savings
2010 MATH Invitational EXTRA Number 5
There were 160 M&M’s in the box
yesterday but now there are 116
yesterday,
116,
what is the percentage difference?
C. 27.5% decrease
(160-116)/160 = 0.275
2010 MATH Invitational EXTRA Number 6
Farmer Don has 2 4/5 acres of
farmland. He will create 7 equal
sized plots for different crops. What
fraction of an acre will be used for
each crop?
2 4/5 ÷ 7 =
14/5 x 1/7 =
D 2/5 acre
D.
2010 MATH Invitational EXTRA Number 7
What are the next three numbers in the
sequence?
1, 8, 27, 64, 125, 216, …
C. 343, 512, 729
1x1x1=1
2x2x2=8...
7 x 7 x 7 = 343
83 = 512 and 93 = 729
2010 MATH Invitational EXTRA Number 8
Four cousins are buying gifts for their
grandmother. They buy her a new mug for $11.11,
and a p
pound of coffee for $9.19. The tax rate is
7%. If they split the cost equally, how much will
each cousin contribute, to the nearest cent?
B. $5.43
11.11
11
11 + 9
9.19
19 = 20
20.30
30
20.30 * 0.07 = 1.42
20 30 + 1
20.30
1.42
42 = 21
21.72
72
21.72 ÷ 4 = $5.43