Free Printable Mock Test_5-11_Plane and Solid Geometry

Worksheets

Mock Test_5-11_Plane and Solid Geometry

Total questions: 140

Worksheet time: 7hrs 0mins

Name

Class

Date

What condition exists if an axiomatic system is independent?

It can be proven from the other axioms.

It cannot be proven from the other axioms.

It is true based on the other axioms.

It is false based on the other axioms.

What is the illustration to define the undefined terms so that the axioms are true?

Model

Replica

Isometry

Diagram

What is any statement that can be proven using logical deduction from the axioms?

Undefined Terms

Definition

Theorem

Axiom

What is a list of undefined terms together with a list of axioms (presupposed to be “true”), a definition in proving theorems and other components of mathematical system?

Mathematical Structure

Mathematical Set

Axiomatic Structure

Axiomatic Set

What condition exists if an axiomatic system is complete?

If every true statement can be proven from the axioms.

If every true statement exists.

If every true statement can stand on its own.

If every true statement is independent and consistent.

What condition exists if an axiomatic system is consistent?

It can be proven from the other axioms.

It cannot be proven from the other axioms.

There is a model for an axiomatic system where the axioms are all true .

There is a model for an axiomatic system where one axiom is independent.

How many models can be used to illustrate axiomatic systems?

Only one

Two models

Three models

Cannot be determined

What is an axiom?

presupposed to be “true”

always true

presupposed to be “false”

always false

Which of the following axioms cannot be proven from other presupposed axioms?

Consistent

Redundant

Independent

Inconsistent

10.

Which axiom satisfies the model below?

Each pot is a set of two flowers.

Each flower is on exactly one pot.

Two flowers may be together on more than one pot.

There is at least one flower.

11.

∠A ≅∠?

∠B

∠E

∠D

∠F

12.

∆ABC≅∆XYZ
which is true?

AB≅XY

AB≅YX

AB≅XZ

BC≅CB

13.

∆EHG≅∆KFC
Which is a true statement?

EH≅FK

HG≅KF

EG≅KC

∠E≅∠C

14.

Solve for x

15.

Solve for y

16.

Complete the congruence statement.

CRP

PCR

RPC

PRC

17.

What does CPCTC stand for?

Congruent parts of congruent triangles are congruent

Corresponding parts of congruent triangles are congruent

Corresponding parts of corresponding triangles are corresponding

Corresponding parts of congruent triangles are Canadian.

18.

Complete the congruence statement.

OEG

OGE

EGO

GOE

19.

Which is a correct congruence statement.

20.

Use the congruency statement to answer the following:
∠F = ___

∠H

∠I

∠G

not congruent to another angle

21.

Which theorem can be used to prove the quadrilateral is a parallelogram?

Parallelogram Opposite Sides Converse Theorem

Parallelogram Opposite Angles Converse Theorem

Opposite Sides Parallel and Congruent Theorem

Parallelogram Diagonals Converse Theorem

22.

Which theorem can be used to prove the quadrilateral is a parallelogram?

Parallelogram Opposite Sides Converse Theorem

Parallelogram Opposite Angles Converse Theorem

Opposite Sides Parallel and Congruent Theorem

Parallelogram Diagonals Converse Theorem

23.

Which theorem can be used to prove the quadrilateral is a parallelogram?

Parallelogram Opposite Sides Converse Theorem

Parallelogram Opposite Angles Converse Theorem

Opposite Sides Parallel and Congruent Theorem

Parallelogram Diagonals Converse Theorem

24.

Which theorem can be used to prove the quadrilateral is a parallelogram?

Parallelogram Opposite Sides Converse Theorem

Parallelogram Opposite Angles Converse Theorem

Opposite Sides Parallel and Congruent Theorem

Parallelogram Diagonals Converse Theorem

25.

Find the value of x that makes the quadrilateral a parallelogram.

This quadrilateral cannot be a parallelogram.

26.

Find the value of x that makes the quadrilateral a parallelogram.

27.

Find the value of x that makes the quadrilateral a parallelogram.

28.

Find the value of x that makes the quadrilateral a parallelogram.

29.

Which method will NOT prove the quadrilateral is a parallelogram.

Show that a pair of sides are congruent and parallel.

Show that both pairs of opposite sides are congruent

Show that both pairs of opposite sides are parallel

Show that a pair of sides are parallel

30.

Is this enough information to prove this quadrilateral is a parallelogram?

Yes, if two pairs of consecutive sides are congruent, then it is a parallelogram.

No, there is not enough information.

31.

The formula

P = 2L + 2W

Is the formula for what type of polygon?

Quadrilateral

Square

Rectangle

Tetragon

32.

The formula for the area

\pi r^2

is the area of what kind of shape?

Ellipse

Circle

Hemisphere

Sphere

33.

What is the formula for the perimeter of any triangle, given their side measurements as Latin alphabet letters?

P = a + b

P = a + b + c

P = a + b + c + d

P = a + b + c + d + e

34.

The formula for the area

lw

can be associated to what type/s of quadrilateral/s?

Rectangle

Rectangle and parallelogram

Rectangle and rhombus

Rectangle and kite

35.

The sum of the area of two isosceles triangles will give you the area of a ______________?

Rhombus

Square

Rectangle

Circle

36.

Given that you want to find the surface area of a frustum of a regular pyramid. How do you solve for its lateral surface area?

Four times the area of the regular isosceles trapezoids

Four times the area of the regular trapezoids

Four times the area of the regular rhombuses

Four times the area of the regular parallelograms

37.

Given that you do not know the exact formula for finding the area of a regular hexagon, how will you solve for the area?

Get the area of the 6 equilateral triangles inside of the figure

Get the area of the 6 isosceles triangles inside of the figure

Get the area of the 6 scalene triangles inside of the figure

Get the area of the 6 acute triangles inside of the figure

38.

What is the best strategy to solve for the area of an irregular polygon?

Deconstruction of the polygon

Reconstruction of the polygon

Re-assembly of the polygon

Creating a new polygon

39.

The formula

\pi ab

,where a is the major axis and b is the minor axis, is the formula for the area of what figure?

Circle

Ellipse

Ellipsoid

Sphere

40.

The surface area of a cylinder is equal to?

Two times the circular base plus the circumference of the base multiplied by the height of cylinder

Two times the elliptical base plus the circumference of the base ellipse by the height of cylinder

Two times the rectangular base plus the perimeter of the base multiplied by the height of cylinder

Two times the apeirogon-base plus the perimeter of the apeirogon-base multiplied by the height of cylinder

41.

The word "frustum" is a Latin word meaning:

Piece cut off

Piece add

Piece divided

Piece un-removed

42.

How do you solve for the surface area of a hemisphere?

Divide the surface area of a sphere by 2

Divide the surface area of a sphere by 2 then add the area of the circular base

Divide the surface area of a sphere by 2 then add half the area of the circular base

Divide the surface area of a sphere by 2 then add half the volume of the sphere

43.

A cone is ______ of a cylinder

1/2

1/3

1/4

1/5

44.

All the Platonic solids have _________ polygonal faces.

Regular

Irregular

Incongruent

Congruent

45.

An icosahedron has 20

Equilateral-triangle-shaped faces

Acute-triangle-shaped faces

Obtuse-triangle-shaped faces

Isosceles-triangle-shaped faces

46.

The formula

V=\frac{1}{3}πh(R^2+Rr+r^2)

is the formula for the volume of a _________.

Cylinder

Frustum of a cylinder

Cone

Frustum of a cone

47.

The formula

2πh(R-r)+2π(R-r)

is the formula for the ____________.

Surface area of the frustum of a cone

Volume of the frustum of a cone

Surface area of a hollow cylinder

Volume of a hollow cylinder

48.

What is the main difference of a tetrahedron from a pyramid?

Number of vertices

Number of sides

Number of angles

Number of faces

49.

The volume of a pyramid is ___________?

1/3 the volume of a rectangular prism

1/3 the volume of a cube

1/3 the volume of a parallelepiped

1/3 the volume of a tetrahedron

50.

The general formula for solving the surface area of any solid figure is:

SA = LSA + BA

SA = LSA + 2(BA)

SA = 2(LSA) + BA

SA = (LSA + BA)/2

51.

Which statement BEST describes why the shape below is a rhombus?

It is a square with no right angles.

It is a parallelogram with equal sides.

It is a polygon with equal sides and equal angles.

It is a quadrilateral with one pair of acute angles and one pair of obtuse angles.

52.

A rectangle must be a __________ and a __________.

parallelogram, rhombus

square, quadrilateral

trapezoid, square

quadrilateral, parallelogram

53.

Select ALL the properties that both rectangles and parallelograms share.

4 sides

4 right angles

2 pairs of parallel sides

2 pairs of sides with equal length

2 acute angles and 2 obtuse angles

54.

The definition of a trapezoid is a quadrilateral with __________.

all four sides the same length and opposite sides parallel

at least one pair of parallel sides

both pairs of opposite sides parallel

four right angles and opposite sides parallel

55.

Which statement is true?

A quadrilateral is always a parallelogram.

A square is always a parallelogram

A parallelogram is never a rhombus.

A trapezoid never has two congruent sides.

56.

Select ALL the properties that all trapezoids and squares share.

4 sides

4 sides of equal length

at least 1 pair of parallel sides

2 pairs of sides of equal length

2 pairs of angles of equal measure

57.

Which statement correctly compares these two isosceles triangles?

Both figures are polygons whose interior angles total 360 degrees.

Both figures are polygons with one right interior angle.

Both figures are polygons with one pair of sides of equal length.

Both figures are polygons with 3 acute interior angles.

58.

Which of the following statements supports the fact that an equilateral triangle is also an isosceles triangle?

They both have at least two congruent sides.

They are both triangles.

The sum of all the measures of the angles is 180 degrees.

All the angles are congruent.

59.

Using this hierarchy of two dimensional figures, determine which of the following labels can be given to the shape below. Select three that apply.

paralellogram

polygon

quadrilateral

rectangle

60.

Which of these correctly arranges the figures in a hierarchy based on their classification?

polygon→isosceles→triangle→equilateral

polygon→triangle→equilateral→isosceles

polygon→triangle→isosceles→equilateral

polygon→isosceles→equilateral→triangle

61.

Look at the hierarchy. Which figure can be placed below the rectangle in this hierarchy?

rhombus

trapezoid

square

triangle

62.

Which of the following characteristics of rectangles help to distinguish them from parallelograms?

Rectangles have opposite angles that are congruent.

Rectangles have opposite sides that are congruent.

Rectangles have four right angles.

Rectangles have at least two parallel sides.

63.

Which of the following characteristics of rhombi help to distinguish them from parallelograms?

Rhombi have four congruent sides.

Rhombi have opposite angles that are congruent.

Rhombi have opposite sides that are parallel.

Rhombi have four right angles.

64.

How would you differentiate between a line segment and a ray?

A. By their angles

B. By their lengths

C. By their endpoints

D. By their positions in space

65.

Discuss the importance of angles in real-life application, providing examples of situations where understanding angles is crucial.

A. Angles have no practical significance in real life.

B. Angles are used solely for artistic purposes and have no practical value.

C. Understanding angles is essential in architecture for designing buildings.

D. Angles are only relevant in academic settings and have no real-life applications.

66.

In a city map, which geometric concept is most relevant for representing a one-way street?

A. Angle

B. Line

C. Line Segment

D. Ray

67.

Compare and contrast the concepts of a point and a line segment in terms of their geometric properties and applications.

A. Point and line segment are identical geometrically.

B. A line segment has length and two endpoints, while a point has no size.

C. A point has length but no width, while a line segment has both length and width.

D. A point has no size, while a line segment extends infinitely in both directions.

68.

If you were given three points, how would you determine if they lie on the same line?

A. By arranging them in a triangular shape.

B. By calculating the angles between each point.

C. By measuring the distance between each point.

D. By connecting them and checking if it forms a straight path.

69.

How does the concept of a point contribute to the definition of other geometric figures?

A. It determines the orientation of circles.

B. It defines the size and shape of polygons.

C. It serves as the basis for defining lines and angles.

D. It is not relevant to the definition of other geometric figures.

70.

Solene was tasked to create a model to represent a 90° angle, which of the following would be most appropriate?

A. Drawing a curved line.

B. Drawing two intersecting lines.

C. Drawing a line with a single arrowhead.

D. Drawing a straight line with two arrowheads.

71.

Why is it important to understand the concept of a plane geometry, particularly in three-dimensional space?

A. It defines the shape of two-dimensional figures.

B. It helps in calculating the perimeter of polygons.

C. It determines the intersection of lines and points.

D. It provides a framework for understanding the spatial relationship between shapes.

72.

How does the concept of an angle relate to the concept of a line?

A. An angle is a subset of a line.

B. An angle is always perpendicular to a line.

B. An angle is formed by the intersection of two lines.

D. An angle extends infinitely in both directions, similar to a line.

73.

In a construction project, which geometric concept would be most useful for ensuring that two walls meet at a precise angle?

A. Angle

B. Line

C. Ray

D. Plane

74.

What is surface area?

Inside of the object

The sum of all the areas of all the shapes that cover the surface of the object.

Something Mrs. MacGregor made up?

Surface area is what you get when you boil unicorn tears.

75.

What is the surface area formula for a cylinder?

SA = πrl + πr²

SA = 2πrh + 2πr²

SA = 4πr²

SA = πr²h

76.

Find the total surface area of the cylinder.

100.53 square inches

351.86 square inches

251.33 square inches

50.27 square inches

77.

Find the surface area

60.4 m²

188.4 m²

94.2 m²

881.9 m²

78.

Find the surface area

140.25 cm^2

439.82 cm^2

219.91 cm^2

192.25 cm^2

79.

What shape is this?

Cylinder

Rectangular Prism

Cube

Cone

80.

Find the surface area of the rectangular prism.

94 cm. squared

60 cm. squared

12 cm. squared

19 cm. squared

81.

Find the Surface Area

556 cm²

278 cm²

680 cm²

340 cm²

82.

Find the surface area of the rectangular prism with the following dimensions:
length = 9 m
height = 10 m
width = 12 m

630 m squared

636 m squared

710 m squared

1080 m squared

83.

Find the surface area of this figure.

148 cm²

120 cm²

84.

_{Find the Surface Area}

500 ft²

515 ft²

525 ft²

510 ft²

85.

Find the surface area of the figure.

Round your answer to the nearest hundredth.

576.40 $in^2$

1,031.8 $in^2$

2,504.70 $in^2$

517.3 $in^2$

86.

Find the surface area of the figure.

Round your answer to the nearest hundredth.

89.4 $yd^2$

163.20 $yd^2$

44.7 $yd^2$

64.8 $yd^2$

87.

Find the surface area of the figure.

Round your answer to the nearest hundredth.

542.87 $mm^2$

271. 44 $mm^2$

221.06 $mm^2$

442.12 $mm^2$

88.

Find the surface area of the figure.

Round your answer to the nearest hundredth.

73.6 $m^2$

362.2 $m^2$

36.8 $m^2$

181.1 $m^2$

89.

Find the surface area of the figure.

Round your answer to the nearest hundredth.

311.4 $ft^2$

155.7 $ft^2$

196.2 $ft^2$

248.4 $ft^2$

90.

Find the surface area of the figure.

Round your answer to the nearest hundredth.

857.18 $km^2$

428.59 $km^2$

1,537.34 $km^2$

771.64 $km^2$

91.

Find the surface area of the figure.

Round your answer to the nearest hundredth. (Hint: you'll have to use Pythagorean Theorem to find the slant height)

2,400 $ft^2$

1,200 $ft^2$

1,560 $ft^2$

18,000 $ft^2$

92.

Find the surface area of the figure.

Round your answer to the nearest hundredth.

353.43 $mm^2$

833.67 $mm^2$

176.7 $mm^2$

566.76 $mm^2$

93.

Find the surface area of the figure.

Round your answer to the nearest hundredth.(Hint: use the Pythagorean theorem to find half of the side length of the square)

696.96 $cm^2$

541.44 $cm^2$

348.48 $cm^2$

329.76 $cm^2$

94.

13.5 m

29.06 m

10 m

14.46 m

95.

11.4 cm

8.5 cm

10 cm

21.45 cm

96.

Find the surface area of the figure.

Round your answer to the nearest hundredth.

696.80 $mm^2$

348.40 $mm^2$

436.80 $mm^2$

1,034.80 $mm^2$

97.

Determine the area of a regular 6-star polygon if the inner regular hexagon has 10 cm sides.

441.66 cm2

467.64 cm2

519.60 cm2

493.62 cm2

98.

A regular pentagon has sides of 20 cm. An inner pentagon with sides of 10 cm is inside and concentric to the large pentagon. Determine the area inside and concentric to the larger pentagon but outside of the smaller pentagon.

430.70 cm3

573.26 cm3

473.77 cm3

516.14 cm3

99.

The area of a circle is 89.42 sq. inches. What is the length of the side of a regular hexagon inscribed in a circle?

5.533 in.

5.335 in.

6.335 in.

7.335 in.

100.

A regular hexagon is inscribed in a circle whose diameter is 20 m. Find the area of the 6 segments of the circle formed by the sides of the hexagon.

36. 45 sq. m

63. 54 sq. m

45. 63 sq. m

54. 36 sq. m

101.

In triangle ABC, angle C = 70o, A= 45o, AB = 40 m. What is the length of the median drawn from vertex A to side BC?

36.3 m

36.6 m

36.9 m

37.2 m

102.

The angle of a sector is 30 degrees and the radius is 15 cm. What is the area of the sector?

89.5 cm2

58.9 cm2

59.8 cm2

85.9 cm2

103.

What is the radius of the circle circumscribing an isosceles right triangle having an area of 162 sq. cm?

13.52

14.18

12.73

1564

104.

Two complementary angles are in the ratio 2:1. Find the larger angle.

30°

60°

75°

15°

105.

One side of a parallelogram is 10 m and its diagonals are 16 m and 24 m, respectively. Its area is:

156.8 sq. m.

185.6 sq. m.

158.7 sq. m.

142.3 sq. m.

106.

The area of a rhombus is 132 square cm. if its shorter diagonal is 12 cm, the length of the longer diagonal is:

20 centimeter

21 centimeter

22 centimeter

23 centimeter

107.

A regular octahedron has an edge 2m. Find its volume (in m3).

3.77

1.88

3.22

2.44

108.

The central angle of a spherical wedge is 1 radian. Find its volume if its radius is 1 unit.

2/3

1/2

3/4

2/5

109.

The bases of a right prism is a hexagon with one of each side equal to 6 cm. The bases are 12 cm apart. What is the volume of the right prism?

1211.6 cm3

2211.7 cm3

1212.5 cm3

1122.4 cm3

110.

A circular cylinder with a volume of 6.54 cu. m is circumscribed about a right prism whose base is an equilateral triangle of side 1.25 m. What is the altitude of the cylinder in meters?

3.50

3.75

4.00

4.25

111.

The height of a right circular base down is h. If it contains water to depth of 2h/3 the ratio of the volume of water to that of the cone is:

1:27

2:3

8:27

26:27

112.

A conical vessel has a height of 24 cm. and a base diameter of 12 cm. It holds water to a depth of 18 cm. above its vertex. Find the volume of its content in cc.

387.4

381.7

383.5

385.2

113.

The slant height of a right circular cone is 5m long. The base diameter is 6m. What is the lateral area in sq. m?

37.7

40.8

114.

The base areas of a frustum of a cone are 25 sq. cm. and 16 sq. cm, respectively. If its altitude is 6 cm, find its volume.

120 cm3

122 cm3

129 cm3

133 cm3

115.

The surface area of the sphere is 4πr2. Find the percentage increase in its diameter when the surface area increases by 21%.

10%

15%

20%

116.

If a solid steel ball is immersed in an eight cm. diameter cylinder, it displaces water to a depth of 2.25 cm. the radius of the ball is:

3 cm

6 cm

9 cm

12 cm

117.

A ___________is any closed, two-dimensional shape.

quadrilateral

figure

plane figure

solid figure

118.

A ______________ is three-dimensional, having length, width and height.

plane figure

solid figure

triangle

quadrilateral

119.

Any flat surface of a solid figure is called a ____.

edge

face

vertice

shape

120.

The line segment where two faces of a solid figure intersect is called ______.

face

vertex

edge

121.

The point at which two or more lines, line segments, or rays meet to form an angle. In solid figures, a _______ is the point at which three or more faces meet.

face

edge

vertex

122.

What shape am I?

I have one circle and one curved side. My curved side surface meets at a sharp point. I have no edges.

cube

sphere

cone

triangular prism

123.

What shape am I?

I have two congruent circles that are joined by a curved surface. I have no edges or vertices, but I can roll.

Cylinder

Sphere

Cone

Cube

124.

What shape am I?

I am round with no edges, vertices, or edges.

Cyclinder

Sphere

Cone

Circle

125.

What shape am I?

I have 6 faces , 12 edges, and 8 vertices. I have all the same shaped faces. All my edges are the same length.

Square Pyramid

Rectangular Prism

Cube

Cone

126.

What shape am I?

I have 12 edges, 8 vertices, and 6 faces. I have both square and rectangular faces.

Rectangle

Cube

Square Pyramid

Rectangular Prism

127.

What shape am I?

I have 5 faces, 8 edges, and 5 vertices. I have two different shaped faces.

Square Pyramid

Rectangular Prism

Cube

Cyclinder

128.

What geometric figure will be created?

Cube

Rectangular Prism

Square Pyramid

Cone

129.

What geometric shape will be created?

Cube

Rectangular Prism

Squares

Cyclinder

130.

What combinations of shapes would you need to create a cube?

6 square faces

6 rectangle faces

4 squares and 2 rectangles faces

4 rectangles and 2 square faces

131.

What combinations of shapes would you need to create a rectangular prism?

6 square faces

6 rectangle faces

4 squares and 2 rectangles faces

4 rectangles and 2 square faces

132.

It is a segment drawn from a vertex that bisects that vertex angle.

Median

Angle Bisector

Altitude

hypotenuse

133.

Find x.

134.

Determine x

135.

What type of triangle is this?

right

scalene

equilateral

isosceles

136.

Find the area of this triangle.

15.59

13.5

137.

Name the postulate, if possible, that makes the triangles congruent.

SAS

ASA

AAS

Not Possible

138.

It is the longest side of a right triangle

Hypotenuse

Median

Base

Altitude

139.

The sum of the lengths of any two sides of a triangle is _____ than the third side

less

greater

equal

140.

The Pythagorean Theorem ONLY works on which triangle?

obtuse

scalene

isosceles

right

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Mock Test_5-11_Plane and Solid Geometry

Total questions: 140

Worksheet time: 7hrs 0mins

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