Free Printable GEO EOC CONCEPTUAL UNDERSTANDING DAY 1

1.

Which formula is the correct one to use for midpoint?

a)

b)

c)

d)

2.

Which of the following is the formula to calculate the distance between 2 points on the xy plane?

a)

b)

c)

d)

3.

Determine the formula: $A=\frac{\pi r^2\theta}{360}\ ;\theta=central\ angle$

a)

Area of a Circle

b)

Circumference of a Circle

c)

Area of Sector

d)

Arc Length

e)

Segment of a Circle

4.

Determine the formula: $S=\frac{2\pi r\theta}{360}\ ;\theta=central\ angle$

a)

Area of a Circle

b)

Circumference of a Circle

c)

Area of Sector

d)

Arc Length

e)

Segment of a Circle

5.

Determine the formula: $A=\pi r^2.$

a)

Area of a Circle

b)

Circumference of a Circle

c)

Area of Sector

d)

Arc Length

e)

Segment of a Circle

6.

Determine the formula: $A=\frac{bh}{2};\ b=base\ and\ h=height.$

a)

Area of a Circle

b)

Area of a trapezoid

c)

Area of Sector

d)

Area of parallelogram

e)

Area of triangle

7.

Determine the formula: $V=Bh;\ B=area\ of\ base\ and\ h=height$

Select 2 answers.

a)

Volume of Prism

b)

Volume of Pyramid

c)

Volume of Cone

d)

Volume of Cylinder

e)

Volume of Sphere

8.

Determine the formula: $V=\frac{1}{3}Bh;\ B=area\ of\ base\ and\ h=height$

a)

Volume of Prism

b)

Volume of Pyramid

c)

Volume of Cone

d)

Volume of Cylinder

e)

Volume of Sphere

9.

Select all the statements that apply to an isosceles triangle.

a)

base angles are congruent

b)

at least two sides are congruent

c)

all sides are always congruent

d)

all interior angles sum to 180 degrees

e)

scalene triangle

10.

What is the formula for the Area of a Circle?

a)

b)

c)

d)

11.

What is the formula for the circumference of a circle?

a)

b)

c)

d)

12.

What is the formula for the Volume of a Rectangular Prism?

a)

b)

c)

d)

13.

What is the formula for the Volume of a Cylinder?

a)

b)

c)

d)

14.

This is the formula for what?

a)

Sphere

b)

Cylinder

c)

Cone

d)

Circle

15.

This is for formula for what?

a)

Area of rectangle

b)

Area of triangle

c)

Area of circle

d)

Volume of rectangular prism

16.

How do you find the volume of the figure?

a)

b)

c)

d)

17.

How do you find the area of the figure?

a)

b)

c)

d)

18.

What is the formula for volume of a sphere?

a)

b)

c)

d)

19.

How do you find the circumference of the figure?

a)

b)

c)

d)

20.

This is the formula for what?

a)

Volume of cone

b)

Circumference of circle

c)

Volume of cylinder

d)

Area of circle

21.

When do you use the partitioning formula?

a)

to find the distance of a line segment

b)

to find only the midpoint of a line segment

c)

to find a point that divides a line segment into a specific ratio

d)

to shorten a line

22.

In similar Polygons, corresponding sides are ___ and corresponding angles are ___. (Fill in the blanks)

a)

congruent, proportional

b)

proportional, congruent

c)

congruent, congruent

d)

proportional, proportional

23.

Use the converse of the side-splitter theorem to determine if $TU\parallel RS$ . Which statement is true?

a)

Line segment TU is parallel to line segment RS because $\frac{32}{36}=\frac{40}{45}$ .

b)

Line segment TU is not parallel to line segment RS because $\frac{32}{36}\ne\frac{40}{45}$

c)

Line segment TU is parallel to line segment RS because $\frac{32}{45}=\frac{40}{36}$ .

d)

Line segment TU is not parallel to line segment RS because $\frac{32}{45}\ne\frac{40}{36}$ .

24.

The Angle-Angle Similarity (AA ~) Theorem states if two angles of one triangle are _______________ to two angles of another triangle, then the triangles are ____________________.

a)

adjacent; equal

b)

complementary; scalene

c)

congruent; similar

d)

supplementary; isosceles

25.

Select ALL the true statements about an image after a dilation.

a)

The image is a different shape than the preimage.

b)

The image is a different size than the preimage.

c)

The image has the same angle measures as the preimage.

d)

The image is similar to the preimage.

e)

The image has the same side lengths as the preimage.

26.

What is the tangent ratio?

a)

b)

c)

27.

What is the sine ratio?

a)

\frac{opposite}{hypotenuse}

b)

$\frac{adjacent\ }{hypotenuse}$

c)

$\frac{opposite\ }{adjacent}$

d)

$\frac{hypotenuse}{opposite}$

28.

What is the cosine ratio?

a)

$\frac{opposite}{hypotenuse}$

b)

$\frac{adjacent\ }{hypotenuse}$

c)

$\frac{opposite\ }{adjacent}$

d)

$\frac{hypotenuse}{adjacent}$

29.

What would be the next step to solve for x?

a)

Multiply both sides by cos 75

b)

Divide both sides by cos 75

c)

Divide both sides by 75

d)

Multiply both sides by 11

30.

If sin x = cos y, what must be true about x and y?

a)

x + y = 90⁰

b)

x = y

c)

x = 2y

d)

x + y = 180⁰

31.

Select the correct equation to solve for x.

a)

3x + 6 = 2x + 5

b)

5x = 11

c)

6x = 30

d)

6x² = 30

32.

What is the definition of a tangent?

a)

A line that intersects the circle on two points.

b)

A line that passes through the center of the circle.

c)

A line segment that passes through the center of the circle.

d)

A line that intersects the circle on only one point.

33.

Which shows a tangent line?

a)

b)

c)

d)

34.

Which is the correct equation to find m<KLM?

a)

x = 1/2(140 - 66)

b)

x = 1/2(140+66)

c)

66 = 1/2(140 - x)

d)

66 = 1/2(140 + x)

35.

The circumference of a circle is.....

a)

The measurement from an edge of a circle to another edge.

b)

The measurement around the circle

c)

The measurement from an edge of a circle to another edge going through the center

d)

The measurement from the center of the circle to an edge of the circle

36.

is the formula for?

a)

arc length

b)

area of a sector

c)

area of a segment

d)

arc measure

37.

What is the ϴ called?

a)

sector

b)

segment

c)

arc

d)

central angle

38.

What is the green area called?

a)

sector

b)

segment

c)

arc

d)

section

39.

What is the equation of a circle in standard form?

a)

ax²+bx+c=0

b)

(x-h)²+(y-k)²=r²

c)

(x-h)+(y-k)=r²

d)

x²+y²+ax+by+c=0

40.

Quadrilateral ABCD is inscribed in the circle. Which sentence is true?

a)

A and B are supplementary

b)

A and C are supplementary

c)

m∠ A = m∠ B

d)

m∠ C = m∠ D

41.

In similar Polygons, corresponding sides are ___ and corresponding angles are ___. (Fill in the blanks)

a)

congruent, proportional

b)

proportional, congruent

c)

congruent, congruent

d)

proportional, proportional

42.

Which equation would you use to solve for the missing angle measure?

a)

x + 115 = 180

b)

x + 115 = 90

c)

x + 115 = 115

d)

x + 115 = 270

43.

WHAT TYPE OF ANGLES ARE THEY?

a)

ALTERNATE INTERIOR ANGLES

b)

SAME SIDE INTERIOR ANGLES

c)

CONSECUTIVE ANGLES

d)

CORRESPONDING ANGLES

44.

Two lines that are parallel will have ...

a)

Slopes that are negative reciprocals

b)

No slope

c)

equal slopes

d)

none of the above

45.

Two lines that are perpendicular lines have slopes that are ____________ .

a)

negative reciprocals

b)

No Slope

c)

Slopes that are the same

d)

none of the above

46.

What are vertical angles?

a)

Angles that are adjacent to each other

b)

Angles that add up to 180°

c)

Angles that are opposite of each other when lines intersect

d)

Angles that add up to 90°

47.

What are supplementary angles?

a)

Angles that add up to 180°

b)

Angles that add up to 90°

c)

Angles that are equal to each other

d)

Angles that are opposite of each other when lines intersect

48.

Are the two triangles congruent? If they are, select the correct congruence postulate. If there is not enough information. Select all that apply.

a)

ASA

b)

SSA

c)

SAS

d)

N/A

49.

Marsha is using a straightedge and compass to do the construction shown. Which best describes the construction Marsha is doing?

a)

a line through P parallel to line l

b)

a line through P intersecting line l

c)

a line through P congruent to line l

d)

a line through P perpendicular to line l

50.

What are the five ways to prove triangles congruent?

a)

SSS, ASA, AAS, SAS, HL

b)

SSS, SSA, HL, AAS, SAS

c)

SAS, SSA, HL, AAS, SSS

d)

HL, SAS, SSA, SSS, ASA

51.

Define: CIRCUMCENTER OF A TRIANGLE.

a)

the intersection point of the three perpendicular bisectors of a triangle

b)

when a circle passes through the three vertices of a triangle

c)

the point of intersection of three or more lines

d)

the intersection point of the three angle bisectors of a triangle

52.

Which is true about any midsegment in a triangle?

(Select all that apply.)

a)

The midsegment is parallel to its corresponding side.

b)

The midsegment is perpendicular to its corresponding side.

c)

The midsegment is half as long as its corresponding side.

d)

The midsegment connects the midpoints of two sides of a triangle.

e)

The midsegment is twice as long as its corresponding side.

53.

Which of the following will always have four right angles? Select all that apply.

a)

Square

b)

Rhombus

c)

Rectangle

d)

Parallelogram

54.

Which of these represents the point-slope form of a linear equation?

a)

y - y₁ = m(x - x₁)

b)

Ax + By = C

c)

y = mx + b

55.

The Triangle Sum Theorem states that the sum of all angles in a triangle is ______.

a)

45°

b)

90°

c)

180°

d)

360°

56.

Which one of these is the correct slope formula?

a)

b)

c)

d)

57.

Triangle ABC is transformed to create triangle MNL.

Which statement is true?

a)

The transformation is rigid because corresponding side lengths and angles are congruent.

b)

The transformation is rigid because corresponding side lengths are congruent and corresponding angles are not congruent.

c)

The transformation is nonrigid because the two triangles have different names.

d)

The transformation is nonrigid because the three sides and the three angles in each triangle have different measures.

58.

Match the picture to the definition of congruence.

a)

Two triangles are congruent if there exists a sequence of rigid motions that maps one figure to coincide with the other.

b)

Two triangles are congruent if their corresponding pairs of sides and corresponding pairs of angles are congruent.

59.

What are vertical angles?

a)

Angles that are adjacent to each other

b)

Angles that add up to 180°

c)

Angles that are opposite of each other when lines intersect

d)

Angles that add up to 90°

60.

What are supplementary angles?

a)

Angles that add up to 180°

b)

Angles that add up to 90°

c)

Angles that are equal to each other

d)

Angles that are opposite of each other when lines intersect

61.

Given: angle A

What is the first step in constructing the angle bisector of angle A?

a)

Draw ray AD

b)

Draw a line segment connecting points B and C.

c)

From points B and C, draw equal arcs that intersect at D.

d)

From point A, draw an arc that intersects the sides of the angle at points B and C.

62.

Which of the following describes a median of a triangle?

a)

A. A middle of the triangle.

b)

B. A segment with endpoints at the vertex and midpoint of the opposite side.

c)

C. A segment that connects two midpoints of two sides.

d)

D. A segment that connects the vertex and the opposite side at 90 degrees.

63.

Which of these represents the point-slope form of a linear equation?

a)

y - y₁ = m(x - x₁)

b)

Ax + By = C

c)

y = mx + b

64.

a)

b)

c)

d)

65.

The right triangle as shows is rotated $360\degree$ about the $y-axis$ in three dimensions. What is the 3-Dimensional solid resulting from the rotation?

a)

cone

b)

cylinder

c)

pyramid

d)

prism

66.

What is the formula for scale factor?

a)

$S.F=\frac{image}{pre-image}$

b)

$S.F.=\frac{pre-image}{image}$

67.

What formula do you use to measure the entire length of a diagonal?

a)

midpoint formula

b)

slope

c)

distance formula

d)

midpoint theory

68.

The Pythagorean Theorem ONLY works on which triangle?

a)

obtuse

b)

scalene

c)

isosceles

d)

right

69.

In the diagram, a circle centered at the origin, a right triangle, and the Pythagorean theorem are used to derive the equation of a circle, x² + y² = r².

If the center of the circle were moved from the origin to the point (h, k) and point P at (x, y) remains on the edge of the circle, which could represent the equation of the new circle?

a)

(h + x)² + (k + y)² = r²

b)

(x – h)² + (y – k)²= r²

c)

(k + x)² + (h + y)² = r²

d)

(x – k)² + (y – h)² = r²

70.

We can use SOH-CAH-TOA for...

a)

Any triangle ever

b)

Non-right triangles only

c)

Right Triangles only

d)

Never

71.

What is the cosine of angle P?

a)

p/q

b)

q/r

c)

p/r

d)

r/q

72.

Choose the answer which best describes how these formulas are related to each other.

a)

They both solve for circumference. In the first formula it uses diameter, in the second formula it uses two times the radius, which is the same thing as diameter.

b)

They both solve for circumference, in the first uses diameter and the second uses pi.

c)

They both solve for area. In the first formula it uses diameter, in the second formula it uses two times the radius, which is the same thing as diameter.

d)

They both use circumference to solve for pi. One uses radius, the other uses diameter.

73.

What is the equation for the Pythagorean Theorem?

a)

a^{2 +}b²= c²

b)

a + b = c

c)

y = mx + b

d)

y = mx

74.

The rule for reflection over the x-axis is

(x, y) --> _

a)

(-x, y)

b)

(x, -y)

c)

(y, x)

d)

(-y, -x)

75.

The rule for dilation is

(x, y) --> _

a)

(kx, ky)

b)

(x, -y)

c)

(-x, y)

d)

(x+a, y+b)

76.

Shapes that are the same shape and the same size are ________.

a)

similar

b)

unique

c)

congruent

d)

corresponding

77.

y = -2/3x + 2

y = 3/2x + 9

These lines are...

a)

Parallel

b)

Perpendicular

c)

Neither

78.

A transformation in which a graph or geometric figure is picked up and moved to another location without any change in size or orientation.

a)

Translation

b)

Rotation

c)

Reflection

d)

Dilation

79.

Which postulate can we use to prove the two triangles are congruent?

a)

SSS

b)

SAS

c)

ASA

d)

AAS

80.

If two figures are similar their angles are______.

a)

proportional

b)

congruent

c)

supplementary

d)

complementary

81.

The __________ is the ratio of the length of the new figure to the corresponding length on the original figure.

a)

reduction

b)

enlargement

c)

scale factor

d)

center of dilation

82.

Which transformation is NOT a rigid motion (the size changes)?

a)

reflection

b)

rotation

c)

dilation

d)

translation

83.

The rule for rotation of 180 degrees is

(x, y) --> _

a)

(-y, x)

b)

(-x, -y)

c)

(y, -x)

d)

(-y, -x)

84.

Translations, reflections and rotations are all known as ________________________.

a)

Geometry

b)

Transformations

c)

Congruent

85.

What is π ? (Best Choice)

a)

The ratio of the circumference of any circle to its diameter.

b)

Exactly 3.14

c)

Exactly 3.1415

d)

Exactly 3.141593

86.

Which is true about any midsegment in a triangle?

(Select all that apply.)

a)

The midsegment is parallel to its corresponding side.

b)

The midsegment is perpendicular to its corresponding side.

c)

The midsegment is half as long as its corresponding side.

d)

The midsegment connects the midpoints of two sides of a triangle.

e)

The midsegment is twice as long as its corresponding side.

87.

Which of the following angles are remote interior angles to angle d?

a)

Angle a and Angle b

b)

Angle b and Angle c

c)

Angle a and Angle c

d)

Angle a and Angle b and Angle c

88.

Define: CIRCUMCENTER OF A TRIANGLE.

a)

the intersection point of the three perpendicular bisectors of a triangle

b)

when a circle passes through the three vertices of a triangle

c)

the point of intersection of three or more lines

d)

the intersection point of the three angle bisectors of a triangle

89.

a)

centroid

b)

orthocenter

c)

circumcenter

d)

incenter

90.

Describe a transformation that moves point D on the grid to
D′ (7,-2)?

a)

reflect over x-axis

b)

reflect over y-axis

c)

translate up 4

d)

rotate 90 Degrees

91.

Which scenario describes the picture shown?

a)

A 5 foot ramp is 8 feet away from a building. What is the angle that the ramp makes with the ground?

b)

A 5 foot ramp leans against an 8 foot structure. What is the angle that the ramp makes with the ground?

c)

An 8 foot ramp leans
against a building 5 feet away. What angle does the ramp make with the ground?

d)

A 5 foot man is 8 feet away from a building. What is the angle of elevation?

92.

Volume of a sphere:

a)

V=(4/3)πr²

b)

V=πr²h

c)

V=¾πr³

d)

V=⅓πr²h

93.

The base of a cylinder is what?

a)

Rectangle

b)

Lateral Surface

c)

Circle

d)

Oval

94.

What formula do you use to measure the entire length of a diagonal?

a)

midpoint formula

b)

slope

c)

distance formula

d)

midpoint theory

95.

Polygon PQRS has the vertices P(-3 , 2), Q(-2, 6), R(2,7), (1, 3): What are the properties of this polygon. Select all that apply:

a)

Diagonals bisect to each other.

b)

Diagonal bisect the opposite angles

c)

Opposite angles are supplementary

d)

4 right angles

e)

Opposite sides are congruent and parallel

96.

What does "perpendicular" mean?

a)

Two lines that intersect

b)

Two coplanar lines that never intersect

c)

Two non-coplanar lines that never intersect

d)

Two lines that intersect at a 90-degree angle

97.

Which is the rule for a dilation by scale factor 2 around the origin?

a)

$x,y\rightarrow x+2,y+2$

b)

$x,y\rightarrow2x,2y$

c)

$x,y\rightarrow\frac{x}{2},\frac{y}{2}$

d)

$x,y\rightarrow2y,2x$

98.

Name the construction.

a)

Angle bisector

b)

Perpendicular line to a point not on a line

c)

Perpendicular line to a point on the line

d)

Perpendicular bisector of a line segment

GEO EOC CONCEPTUAL UNDERSTANDING DAY 1

Total questions: 98

Worksheet time: 3hrs 19mins

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