Short Answer Practice Problems
1.
First, fold a piece of
paper in half along the
diagonal to make a
triangle. Second, cut a
hole near each vertex
of the triangle you
have made. Third,
unfold the paper.
Which figure can you
have?
2.
In the diagram,
angles A and D are
right angles. AB=4
cm, AD=6 cm, and
CD=8 cm. Find the
area of ABCD in
square
centimeters.
3.
An ant sits at vertex V
of a cube with edge of
length 1 meter. The
ant moves along the
edges of the cube and
comes back to vertex
V without visiting any
other point twice.
Find the number of
meters in the length of
the longest such path.
4.
In this diagram, 17
toothpicks are
used to form a 2square by 3-square
rectangle. How
many toothpicks
would be needed
to form a 6-square
by 8-square
rectangle?
5.
As shown, the
length of each side
in the overlapping
rectangles is given,
in cm. Find the
sum of the areas of
the shaded
regions, in square
centimeters.
6.
The 14 digits of a
credit card
number are
written in the
boxes at the
side. If the sum
of any 3
consecutive
digits is 20, what
digit is in box A?
7.
How many
times does
x occur in
the diagram
at the right?
8.
A square piece of
paper is folded in half
as shown, and then
cut into two
rectangles along the
fold. The perimeter of
each of the 2
rectangles is 18
inches. What is the
perimeter of the
original square?
9.
In the figure at the
right, each number
represents the
length of the
segment that is
nearest to it. All
angles are right
angles. How many
square units are in
the area of the
figure?
10.
People were asked to choose
their favorite type of movie.
This graph shows the results
of the survey.
What was the total number of
people who were surveyed?
A. 60
B. 75
C. 90
D. 170
E. 270
11.
A palindromic number is
one which is the same
read backwards and
forwards. For example,
121 and 3443 are
palindromic numbers.
What is the next
palindromic number after
79311397?
12.
Insert
parentheses into
the expression
so the result is
as large as
possible. What
is the result?
13.
A wall with a
hole is shown
in the
picture. How
many bricks
are missing?
14.
In the picture, 6
dots appear in the
first figure, 10, 16,
and 24 dots are in
the successive
figures. If this
pattern continues,
how many dots are
in the 6th figure?
15.
This picture shows part of
a bee house that is made
with hexagons. The middle
hexagon is the 1st layer and
the six outside hexagons
are the second layer. If the
bee house has a total of 6
layers and each hexagon
has a bee inside, how
many bees live in the
house?
16.
A bat and a ball
together cost
$10. if the bat
costs $9 more
than the ball,
what is the cost
of the bat?
17.
If you roll two
dice, what is
the
probability
you will roll
two ones?
18.
A micron is a
thousandth of a
millimeter.
How many
microns are in
8 meters?
19.
Sara wouldn’t tell her
age, but she did agree
to give it as an algebra
problem:
“Nine times my age,
divided by 12 is equal
to 36.”
How old is Sara?
20.
What is the
probability of
getting a pair (like 2
aces or 2 tens), if
you are dealt two
cards from a
standard deck?
21.
What is
the next
1,
2,
6,
15,
31,
number
____
of this
sequence
?
22.
Four consecutive
(in a row)
numbers add up
to 110. What is
the smallest
number?
23.
What is the
product of this
multiplication?
24.
ABCD is a
square. AB=4.
BEFG is also a
square. BE=6.
O1 is the center
of ABCD and O2
is the center of
BEFG. Find the
shaded area O1
O2 B.
25.
As shown in the
figure, a square of side
length 5 cm has some
area overlapped with
another square of side
length 4 cm. Find the
difference of the nonoverlapping areas of
the 2 squares (A-B).
26.
In the picture,
AB is parallel to
CD and CE is
parallel to FG. If
angle BAC = 100
degrees, and
GFC = 110
degrees, find x.
27.
In this addition
different
letters
represent
different digits.
What digits do
A, B, C, and D
represent?
28.
A square has an area
of 144 square
centimeters. Suppose
the square is cut into
six congruent
rectangles as shown
here. How many
inches are there in the
perimeter of one of
the rectangles?
29.
3,6,9,12 are
some multiples
of 3. How many
multiples of 3 are
there between
13 and 113?
30.
What is
the
total of
one plus two plus three plus four plus five plus
one plus two plus three plus four plus five plus
one plus two plus three plus four plus five plus
one plus two plus three plus four plus five plus
one plus two plus three plus four?
31.
ABCD is a square
with area 16 sq.
meters. E and F
are midpoints of
sides AB and BC
respectively. What
is the area of
trapezoid AEFC, the
shaded region?
32.
A rectangle is 5 cm long
and 12 cm wide. A
triangle with a 2 cm
base and 3 cm height is
drawn inside the
rectangle. What is the
probability that a
random point inside
the rectangle is also in
the triangle?
33.
Bob’s age is 4 times
Michelle’s age, and
Sarah’s age is half
Bob’s age. If their
ages add up to 84,
what is Michelle’s
age?
34.
As shown in
the picture,
both ABCD and
BEFG are
squares. The
shaded area is
10. Find the
area of ABCD
35
Find
the
value
of y.
36.
Two identical squares
with sides of length 10
centimeters overlap to
form a shaded region
as shown. A corner of
one square lies in the
center of the other
square. Find the area
of the shaded region,
in square cm.
37.
At the right, boxes
represent digits
and different
letters represent
different non-zero
digits. What 3-digit
number is the least
possible product?
38.
As shown, ABCD and
AFED are squares with
a common side of AD
of length 10 cm. Arc
BD and arc DF are
quarter-circles. How
many square
centimeters are in the
area of the shaded
region?
39.
There are five
Mondays and
four Tuesdays in
August of a year.
What day is
th
August 8 of the
year?
40.
If you roll four
dice, what is
the probability
that you will
roll four ones?
41.
Bill and Steve
decided that they
would always have a
money ratio of 9:7
(Bill to Steve). If
Steve has $129.50,
how much money
should Bill have?
42.
How many cubic
millimeters
would fit inside
of a cubic box
that measures 2
meters per side?