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Patterns Relationships and Algebraic Reasoning
1.
2.
Which of these shapes could never have perpendicular lines?
A.
Square
B.
Rectangle
C.
Triangle
D.
Circle
A rectangular prism is shown below.
What is the volume of this rectangular prism?
F.
240 cubic units
G.
110 cubic units
H.
83 cubic units
J.
54 cubic units
3.
Which of these rectangular prisms has a volume of 96 cubic units?
A.
C.
B.
4.
D.
A trapezoid is shown below.
Which statement about the trapezoid is true?
F.
The trapezoid has 3 acute angles.
G.
The trapezoid has 2 sides that are parallel lines.
H.
The trapezoid has 2 right angles.
J.
The trapezoid has 3 obtuse angles.
5.
A rectagular prism made of 1-centimeter cubes in shown below.
What is the volume of this rectangular prism?
A.
4 cm3
B.
9 cm3
C.
10 cm3
D.
20 cm3
6.
7.
Which statement about the figures shown below is true?
F.
Figures R and S are congruent.
G.
Figures Q and S each have parallel sides.
H.
Figures P and R each have at least 2 obtuse angles.
J.
Figures S and P each have all acute angles.
Examine the figure shown below.
Which of the statements below appears to be false?
A.
This figure is a square.
B.
All sides on this figure are congruent.
C.
All angles on this figure are right angles.
D.
This figure has only 1 pair of parallel line segments.
8.
Robbie found two bins of figures.
Bin 1 included the following shapes.
Bin 2 included the following shapes.
Which of the following shapes would MOST likely belong in Bin 2?
F.
H.
G.
J.
9.
A pentagon is shown below.
Which statement about the pentagon is true?
10.
A.
Line AF is parallel to line CD.
B.
All the angles are acute.
C.
There are no lines of symmetry.
D.
Line AB is congruent to line BC.
Which of these shapes could never have parallel lines?
F.
rhombus
G.
rectangle
H.
square
J.
triangle
11.
Which figure below is a dellies?
A.
B.
C.
D.
12.
A model made of 1-foot cubes is shown below.
What is the volume of this model?
13.
F.
120 cubic feet
G.
30 cubic feet
H.
24 cubic feet
J.
74 cubic feet
Which statement about the trapezoid STUV appears to be true?
A.
B.
C.
D.
and
forma a right angle.
and
are perpendicular.
and
form an acute angle.
and
are parallel.
14.
15.
16.
Which figure appears to include perpendicular lines?
F.
H.
G.
J.
Which figure appears to have 2 obtuse angles and 2 acute angles?
A.
C.
B.
D.
Brenda drew a figure that appeared to have 3 acute angles. Which could be the figure Brenda drew?
F.
H.
G.
J.
17.
18.
Which of the following does NOT describe a rectangle?
A.
4 faces
B.
2 pairs of parallel sides
C.
4 right angles
D.
2 pairs of congruent sides
Which statement about the figure appears to be true?
F.
G.
H.
J.
19.
is congruent to
.
is congruent to
.
is congruent to
.
is congruent to
.
Look at the figure below made up of 1-unit cubes.
What is the volume of the figure?
A.
16 cubic units
B.
40 cubic units
C.
80 cubic units
D.
160 cubic units
20.
All the sides of parallelogram PQRS are congruent.
Which of the following statements about parallelogram PQRS appears to be true?
F.
G.
H.
J.
21.
is parallel to
.
is parallel to
.
is perpendicular to
.
is perpendicular to
.
An equilateral triangle is shown below.
Which statement about the triangle is true?
A.
The triangle has 2 sides that form a right angle.
B.
All the triangle’s sides are the same length.
C.
None of the triangle’s sides are the same length.
D.
The triangle has only 2 sides that are congruent.
22.
The shapes in Set I are physors.
The shapes in Set II are not physors.
Which of the following shapes is a physor?
F.
H.
G.
J.
23.
24.
Which of the following shapes must have all four sides congruent?
A.
Quadrilateral
B.
Rectangle
C.
Trapezoid
D.
Square
Matt sees that the merry-go-round at the park is in the shape of a hexagon. There is one child sitting
on each side of the merry-go-round. If these are the only children on the merry-go-round, how many
children are on it?
Record your answer and fill in the bubbles on your answer document. Be sure to use the correct
place value.
25.
26.
Troy wants to show his younger sister what an acute angle looks like. Which of the following figures
should he use?
A.
Square
B.
Rectangle
C.
Sphere
D.
Trapezoid
Which statement is true about the figure below?
F.
G.
H.
J.
27.
28.
Which of the following does NOT describe a rhombus? Mark your answer.
A.
2 pairs of parallel sides
B.
4 angles
C.
4 equal sides
D.
4 edges
A rectangular prism made of 1-centimeter
cubes is shown below.
What is the volume of this rectangular prism?
29.
30.
F.
4 cm3
G.
9 cm3
H.
10 cm3
J.
20 cm3
Which shape could never have parallel sides?
A.
Rhombus
B.
Triangle
C.
Octagon
D.
Pentagon
Which figure appears to have only 1 pair of parallel sides?
F.
Figure S
G.
Figure T
H.
Figure U
31.
Look at the line segments in the figure below.
Which statement about the line segments in the figure appears to be true?
32.
33.
34.
A.
and
are congruent.
B.
and
are congruent.
C.
and
are perpendicular.
Judy wants to find the volume of a cube. What steps will she follow to find this?
F.
length x width x height
G.
length x width x height divided by 3
H.
length + height + width
J.
length + height + width multiplied by 2
Josiah wanted to help his brother find the volume of a rectangular prism that was 3 feet in length, 3
feet in height, and 2 feet in width. How could Josiah find the volume?
A.
Add the length, height, and the width.
B.
Multiply the length times the width, and then multiply that product times the height.
C.
Add the length and width, and then multiply the sum times the height.
D.
Multiply the width times the length and then subtract this product from the height.
Look at these shapes. Which shape does NOT have at least 2 sets of parallel lines?
F.
Figure A
G.
Figure B
H.
Figure C
J.
35.
Figure D
Sam drew this shape. Look at the shape he drew.
Which line segment is parallel to line segment DC?
36.
A.
AC
B.
BC
C.
AB
D.
AD
Look at this figure.
Which statement is true about this figure?
37.
F.
line CX is parallel to line SZ
G.
line YS is perpendicular to line SZ
H.
line XZ and line BT are parallel
J.
line AB and line YS are congruent
Kevin has an aquarium. The dimensions of the aquarium are 20 in. long, 12 in. tall, and 15 in.
deep. When he bought his new lizard, the pet shop told him the lizard needed 4,000 in.3. How
many more cubic inches does Kevin's aquarium need to be?
38.
Guess my name:
I am a 2-dimensional shape.
I have 4 vertices.
My sides are not all the same length.
Only 1 pair of my sides are parallel.
I sometimes have a line of symmetry, but not always.
What is my name?
F. Square
H. Trapezoid
G. Rectangle
J. Rhombus
39.
Who am I?
I am not a quadrilateral.
All my sides are congruent.
If you cut me in half from one vertex to the opposite vertex, you will have two trapezoids.
I have more than one line of symmetry.
What is my name?
A. Trapezoid
C. Pentagon
B. Hexagon
D. Octagon
40.
Can you guess who I am?
I am a special quadrilateral.
My opposite sides are parallel.
I have 2 acute angles that are equal and 2 obtuse angles that are equal.
I have exactly 2 lines of symmetry.
All of my sides are congruent.
If you cut me in half from one vertex to the opposite vertex, you would have 2 triangles.
What is my name?
F. Triangle
H. Square
G. Trapezoid
J. Rhombus
41.
The measurement of one Olympic swimming pool measures 50 meters long, 25 meters wide, and 2
meters deep. There are 10 lanes for swimming laps that measure about 2 meters each. What is the
volume of this Olympic size pool?
A.
250 cubic meters
B.
2,500 cubic meters
C.
25,000 cubic meters
D.
5,000 cubic meters
42.
Lakin drew the figure below.
Which line segments intersect each other but do not appear to be perpendicular?
F.
G.
H.
J.
43.
Two figures are shown below.
Which statement about these two figures appears to be true?
A.
There are a total of 5 acute angles.
B.
There are a total of 5 obtuse angles.
C.
There are a total of 2 acute angles.
D.
44.
45.
There are a total of 2 obtuse angles.
Which statement is always true about an equilateral triangle?
F.
It has 3 congruent angles.
G.
It has 1 right angle.
H.
It has exactly 2 congruent sides.
J.
The sum of any 2 angles is 180°.
Mr. Olivares installed a triangular piece of stained glass above his front door.
Which of the following best describes the triangle with the given measures?
A.
Acute equilateral triangle
B.
Obtuse isosceles triangle
C.
Right scalene triangle
D.
Right isosceles triangle
46.
Which of the following is a valid conclusion based on the diagram shown above?
47.
48.
F.
All rhombuses are squares.
G.
All rhombuses are rectangles.
H.
All quadrilaterals are parallelograms.
J.
All rectangles are parallelograms.
How many angles does a pentagon have?
A.
3
B.
4
C.
5
D.
6
A triangle with two congruent sides and an angle of 104° is —
F.
isosceles and right
G.
isosceles and obtuse
H.
isosceles and acute
J.
scalene and obtuse
49.
Paula wants to classify a triangle given the following clue.
Two angles of the triangle are complementary.
What type of triangle is the one Paula wants to classify?
50.
51.
A.
Right, because complementary angles add up to 90 o and the difference between 180o and 90o is
90o
B.
Obtuse, because complementary angles add up to 45o and the difference between 180o and 45o
is 135o
C.
Equiangular, because each of the two complementary angels is equal to 60o and the difference
between 180o and 120o is 60o
D.
Acute, because complimentary angles add up to 100 o and the difference between 180o and 100o
is 80o
Marshall is looking at a sign that is shaped like a regular polygon. It has 8 sides and 8 angles. What
figure is Marshall's sign? Mark your answer.
F.
pentagon
G.
hexagon
H.
octagon
J.
trapezoid
Which of the following is true of all squares and all rectangles?
I.
All squares and all rectangles are
II.
All squares and all rectangles are
equiangular.
equilateral
III.
A.
II only
B.
III only
C.
II and III only
D.
I, II, and III
All rectangles are squares.
52.
53.
The models below are made with 1-unit cubes. Which model has a volume of 108 cubic units?
F.
H.
G.
J.
Which of the following are obtuse isosceles triangles?
A.
P and R only
B.
Q and R only
C.
P, Q, and R only
D.
P, R, and S only
54.
55.
56.
Camille’s math teacher described a quadrilateral with 2 pairs of parallel sides and 4 lines of
symmetry. Which of these quadrilaterals must have the characteristics that Camille’s math teacher
described?
F.
Trapezoid
G.
Square
H.
Rhombus
J.
Parallelogram
Which type of triangle has 3 sides all with different lengths?
A.
Equilateral triangle
B.
Isosceles triangle
C.
Scalene triangle
Which statement about the triangles below is true?
F.
The triangles are equiangular triangles.
G.
The triangles are acute triangles.
H.
The triangles are right triangles.
57.
58.
Hank made this model to represent the size of his box. How many cubic units is his box?
A.
81 cubic units
B.
99 cubic units
C.
117 cubic units
D.
162 cubic units
Both of the models below are made of 1-inch cubes.
Which statement about these models is true?
59.
F.
The volume of Model S and Model T combined is 30 cubic inches.
G.
Model T has a greater volume than Model S.
H.
The volume of Model S and Model T combined is 53 cubic inches.
J.
Model S and Model T have the same volume.
A triangle has 2 angles that each measure 45°. Which of the following best describes this triangle?
A.
Right scalene
B.
Right isosceles
C.
Equilateral
D.
Obtuse isosceles
60.
61.
62.
63.
A triangle has 2 angles that each measure 45°. Which of these describes this triangle?
F.
Right scalene
G.
Right isosceles
H.
Equilateral
A box has a volume of 54cm3. The sum of the length, width, and height equals 14. What are the
dimensions of the box?
A.
Length=2
Width=9
Height=3
B.
Length=3
Width=6
Height=3
C.
Length=7
Width=5
Height=2
D.
Length=3
Width=6
Height=5
A box of nails is 10 cm wide, 15 cm long, and 20 cm high. Which is the best estimate of the volume
of the box.
F.
The volume is less than 50 cm3
G.
The volume is between 1,500 cm3 and 2,000 cm3
H.
The volume is less than 1,500 cm3
J.
The volume is between 2,500 cm3 and 3,500 cm3
Sam had a tissue box with a volume of 144 in3. What is a reasonable estimate for the dimensions of the box?
A.
Length=4
Width=8
Height=3
B.
Length=6
Width=2
Height=4
C.
Length=6
Width=8
Height=3
D.
Length=9
Width=3
Height=6
64.
65.
A.
B.
C.
If a cube has a volume of 216 m3 what measurement could the sides be?
F.
Height: 3
Length: 6
Width: 12
G.
Height: 6
Length: 6
Width: 6
H.
Height: 9
Length: 6
Width: 4
J.
Height: 9
Length: 2
Width: 12
Find a figure that has the same volume as the figure shown below.
D.
66.
Can you predict the new volume of the shape shown above if one row from the top
of the shape were removed? Justify your answer
67.
68.
F.
18, because the new length would be 3, width would be 3, and height would be 2.
G.
27, because the new length would be 3, width would be 3, and height would be 3.
H.
18, because the new length would be 2, width would be 3, and height would be 3.
J.
12, because the new length would be 2, width would be 2, and the height would be 3.
Jerrome built a toy box for his younger brother, Marcus. He must estimate the volume of the toy box
in order to know about how many toys his brother can store in it. When building the toy box, his
dimensions measured the length as 98 cm, the width is 31 cm, and the height is 39 cm. Which
method should Jerrome use to find the best estimated volume in cubic centimeters?
A.
First, round the measurements to the nearest hundred and then add the three rounded
numbers.
B.
First, add the measurements and then round the answer to the nearest hundred.
C.
First, multiply the measurements and then round the answer to the nearest ten.
D.
First, round the measurements to the nearest ten and then multiply the three rounded
numbers.
Samantha needs to estimate the number of cubes that will fit into her pencil box. If she can arrange
them into 4 rows with 5 on each row, and she can make 2 whole stacks, then what is the estimated
volume of cubic units that will fit?
F.
20 cubic units
G.
9 cubic units
H.
40 cubic units
J.
18 cubic units
69.
Look at this triangle.
Which of these classify the triangle?
A.
acute scalene triangle
B.
right isosceles triangle
C.
obtuse scalene triangle
D.
obtuse isosceles triangle