Compiled by the Broward County Public Schools Office of Instruction and Intervention

Mathematics, Science, & Gifted Department

EOC FSA Warm-ups

Geometry

Name: ___________________

Page 3

Geometry EOC FSA Mathematics Reference Sheet

Customary Conversions

1 foot = 12 inches1 yard = 3 feet 1 mile = 5,280 feet1 mile = 1,760 yards

1 cup = 8 fluid ounces 1 pint = 2 cups 1 quart = 2 pints 1 gallon = 4 quarts

1 pound = 16 ounces 1 ton = 2,000 pounds

Metric Conversions

1 meter = 100 centimeters1 meter = 1000 millimeters1 kilometer = 1000 meters

1 liter = 1000 milliliters

1 gram = 1000 milligrams 1 kilogram = 1000 grams

Time Conversions

1 minute = 60 seconds 1 hour = 60 minutes1 day = 24 hours1 year = 365 days1 year = 52 weeks

FSA Mathematics Reference Sheets Packet

Florida Department of Education Updated January 8, 2015

Page 4

Geometry EOC FSA Mathematics Reference Sheet

Formulas

sin A° =

cos A° =

tan A° =

V = Bh

V = Bh

V = πr3

y = mx + b, where m = slope and b = y-intercept

y – y1 = m(x – x1), where m = slope and (x1, y1) is a point on the line

oppositehypotenuse

adjacenthypotenuse

oppositeadjacent

31

34

FSA Mathematics Reference Sheets Packet

Florida Department of Education Updated January 8, 2015

Name: ______________________ Class: _________________ Date: _________ ID: A

1

Geometry EOC FSA Warmups: 40 Day Countdown

Day 1

____ 1

A a reflection across line rB a reflection across line sC a rotation of 90° clockwise about point PD a rotation of 180° clockwise about point PE a rotation of 270° clockwise about point P

Name: ______________________ ID: A

2

____ 2

A CX ≅ CYB CZ ≅ XYC CXZ is isoscelesD CYZ is equilateralE XY is a diameter of circle C.

Name: ______________________ ID: A

3

Day 2___________________________________________________________

____ 3

A π

B 11π4

C 13π4

D 7π4

____ 4 Point B is the center of a circle, and AC is a diameter of the circle. Point D is a point on the circle different from A and C. If m∠BDA = 20°, what is m∠CBD?

A 20°B 40°C 70°D 140°

Name: ______________________ ID: A

4

Day 3___________________________________________________________

____ 5

A a cube C a rectangular prismB a cylinder D a sphere

6 The radius of the circle represented by the equation x 2 + y 2 − 4x + 2y = b is 7 units. What is the value of b in the equation? Enter your answer in the box.

Name: ______________________ ID: A

5

Day 4___________________________________________________________

____ 7

A r + s

B r - s

C s - r

D rs

____ 8 Which equations below represent lines that are perpendicular to the line that contains (1, -2) and (3, 4)? Select all that apply.

A y = − 13x − 5

B y = 3x − 3C y − 2 = 3(x + 1)D x + 3y = 9E 3x + y = −5

Name: ______________________ ID: A

6

Day 5___________________________________________________________

____ 9

A 6B 48C 8D 72

Name: ______________________ ID: A

7

10 The figure shows rectangle ABCD in the coordinate plane with point A at (0, 2.76), B at (3.87, 2.76), C at (3.87, 0) and D at the origin. Rectangle ABCD can be used to approximate the size of the state of Colorado with x and y scales representing hundreds of miles.

At the end of 2010, the population of Colorado was 5, 029, 196 people. Based on this information given, what was the population density at the end of 2010 in people per square mile? Enter your answer into the box.

Name: ______________________ ID: A

8

Day 6___________________________________________________________

____ 11

A Line A ʹ′C ʹ′will be parallel to line AC, and line P ʹ′Q ʹ′ will be parallel to line PQ.B Line A ʹ′C ʹ′will be parallel to line AC, and line P ʹ′Q ʹ′ will be the same line as line PQ.C Line A ʹ′C ʹ′will be perpendicular to line AC, and line P ʹ′Q ʹ′ will be parallel to line PQ.D Line A ʹ′C ʹ′will be perpendicular to line AC, and line P ʹ′Q ʹ′ will be the same line as

line PQ.

Name: ______________________ ID: A

9

____ 12 An unmanned aerial vehicle (UAV) is equipped with cameras used to monitor forest fires. The figure represents a moment in time at which a UAV, at point B, flying at an altitude of 1,000 meters (m) is directly above point D on the forest floor. Point A represents the location of a small fire on the forest floor.

A 170 metersB 353 metersC 364 metersD 728 meters

Name: ______________________ ID: A

10

Day 7___________________________________________________________

____ 13

A 1, 945, 000 cubic metersB 2, 562, 000 cubic metersC 5, 835, 000 cubic metersD 7, 686, 000 cubic meters

Name: ______________________ ID: A

11

____ 14 Quadrilaterals ABCD and EFGH are shown in the coordinate plane.

Quadrilateral EFGH is the image of ABCD after a transformation or sequence of transformations.

Which could be the transformation or sequence of transformations?

Select all that apply.

A a translation of 3 units to the right, followed by a reflection across the x-axisB a rotation of 180°C a translation of 12 units downward, followed by a reflection across the y-axisD a reflection across the y-axis, followed by a reflection across the x-axisE a reflection across the line with equation y = x

Name: ______________________ ID: A

12

Day 8___________________________________________________________

____ 15

A A ʹ′(1, -2), B ʹ′(4, -6), C ʹ′(4, -2)B A ʹ′(-1, -2), B ʹ′(-4, -6), C ʹ′(-4, -2)C A ʹ′(-1, 2), B ʹ′(-4, -6), C ʹ′(-4, 2)D A ʹ′(1, 2), B ʹ′(4, 6), C ʹ′(4, 2)

____ 16

A 0.6B 1.2C 1.8D 2.0

Name: ______________________ ID: A

13

Day 9___________________________________________________________

____ 17

A (-2, 9) E (3, 4)B (-1, 8) F (4, 3)C (0, 7) G (5, 2)D (1, 6) H (6, 1)

18 Quadrilateral MARK will be reflected across the x-axis and then rotated 90° clockwise about the origin to create quadrilateral M ʹ′A ʹ′R ʹ′K ʹ′. If M is located at (-3, 7), What will be the y-coordinate of M ʹ′? Enter your answer in the box.

Name: ______________________ ID: A

14

Day 10___________________________________________________________

____ 19

A The center of the dilation is at (-2, -1).

B The center of the dilation is at (-1, -2).

C The center of the dilation is at (0, 0).

D The scale factor is 12

E The scale factor is 2.

F The scale factor is 4.

Name: ______________________ ID: A

15

Day 11___________________________________________________________

____ 20

A m∠2 = 90°B m∠6 = 90°C m∠3 = m∠6D m∠1 +m∠6 = 90°E m∠3 +m∠4 = 90°F m∠4 +m∠5 = 90°

____ 21 Point B is the center of a circle, and AC is a diameter of the circle. Point D is a point on the circle different from A and C.

Indicate which statements must be true. Select all that apply.

A AD > CD

B m∠CBD = 12

(m∠CAD)

C m∠ADC = 90°D m∠ABD = 2(m∠ACD)E m∠ABD = m∠DBC

Name: ______________________ ID: A

16

Day 12___________________________________________________________

____ 22

A the coordinates of A ʹ′B the coordinates of B ʹ′C the perimeter of A ʹ′B ʹ′C ʹ′D the area of A ʹ′B ʹ′C ʹ′E the measure of ∠B ʹ′F the length of segment A ʹ′B ʹ′

Name: ______________________ ID: A

17

Day 13___________________________________________________________

____ 23

A The scale factor is 2, and the center of dilation is point B.

B The scale factor is 2, and the center of dilation is the origin.

C The scale factor is 12

, and the center of dilation is point B.

D The scale factor is 12

, and the center of dilation is point the origin.

Name: ______________________ ID: A

18

Day 14___________________________________________________________

____ 24

A If x = y, the volume of cylinder P is greater than the volume of cylinder S, because cylinder P is a right cylinder.

B If x = y, the volume of cylinder P is equal to the volume of cylinder S, because the cylinders are the same height.

C If x = y, the volume of cylinder P is greater than the volume of cylinder S, because cylinder S is slanted.

D If x < y, the area of a horizontal cross section of cylinder P is greater than the horizontal cross section of cylinder S.

E If x < y, the area of a horizontal cross section of cylinder P is equal to the horizontal cross section of cylinder S.

F If x < y, the area of a horizontal cross section of cylinder P is less than the horizontal cross section of cylinder S.

Name: ______________________ ID: A

19

Day 15___________________________________________________________

25

Name: ______________________ ID: A

20

____ 26

A Definition of congruent anglesB Congruence of angles is reflexiveC Congruence of angles is symmetricD Congruence of angles is transitiveE Vertical angles are congruent

Name: ______________________ ID: A

21

Day 16___________________________________________________________

27

Name: ______________________ ID: A

22

Day 17___________________________________________________________

28

Day 18___________________________________________________________

29 The equation x 2 + y 2 − 4x + 2y = b describes a circle. Determine the y-coordinate of the center of the circle. Enter your answer in the box.

Name: ______________________ ID: A

23

Day 19___________________________________________________________

30 Triangle ABC is graphed in the xy-coordinate plane with vertices A(1, 1), B(3, 4), and C(-1, 8) as shown in the figure.

Triangle ABC will be reflected across line y = 1 to form A ʹ′B ʹ′C ʹ′. Which quadrant will not contain any vertex of A ʹ′B ʹ′C ʹ′.

Name: ______________________ ID: A

24

Day 20___________________________________________________________

31 The figure shows rectangle ABCD in the coordinate plane with point A at (0, 2.76), B at (3.87, 2.76), C at (3.87, 0) and D at the origin. Rectangle ABCD can be used to approximate the size of the state of Colorado with x and y scales representing hundreds of miles.

Based on the information given, how many miles is the perimeter of Colorado? Enter your answer into the box.

Name: ______________________ ID: A

25

Day 21___________________________________________________________

32

What is the value of x? Enter you answer into the box.

Name: ______________________ ID: A

26

Day 22___________________________________________________________

33

Choose yes or no for each statement.

YES NOA. The length of CD is less than 10.B. The length of CD is equal to 10.C. The length of CD is greater than 10.D. CPD is equilateral.E. The measure of ∠CPD is less than 60°.F. The measure of ∠CPD is greater than 60°.

Name: ______________________ ID: A

27

Day 23___________________________________________________________

____ 34

The first step of the construction is to draw and arc centered at point A that passes through point B and point C. What is established by the first step?

A AB ≅ BCB AB ≅ ACC AD ≅ ACD BD ≅ CD

Name: ______________________ ID: A

28

Day 24___________________________________________________________

____ 35

The construction creates congruent triangles. ABD ≅ ACD (not shown). Which statement provides evidence that AD

→⎯⎯⎯

is the angle bisector of ∠BAC?

A ∠ACD ≅ ∠ABDB ∠BAC ≅ ∠BDCC ∠BAD ≅ ∠CADD ∠BAD ≅ ∠ABD

Name: ______________________ ID: A

29

Day 25___________________________________________________________

36 A steel pipe in the shape of a right circular cylinder is used for drainage under a road. The length of the pipe is 12 ft and its diameter is 36 inches. The pipe is open at both ends.

How many square feet of steel is the outer surface of the pipe?

Enter your answer into the box provided. Round to the nearest integer.

Name: ______________________ ID: A

30

Day 26___________________________________________________________

37 A steel pipe in the shape of a right circular cylinder is used for drainage under a road. The length of the pipe is 12 ft and its diameter is 36 inches. The pipe is open at both ends.

A wire screen in the shape of a square is attached at one end of the pipe to allow water to flow through, to keep animals from getting inside the pipe. The length of the diagonals of the screen are equal to the diameter of the pipe. The figure represents the placement of the screen at the end of the pipe.

What are the area and perimeter of the screen? Enter your answers into the given boxes. Round your answers to the nearest whole number.

Name: ______________________ ID: A

31

Day 27___________________________________________________________

38 An unmanned aerial vehicle (UAV) is equipped with cameras used to monitor forest fires. The figure represents a moment in time at which a UAV, at point B, flying at an altitude of 1,000 meters (m) is directly above point D on the forest floor. Point A represents the location of a small fire on the forest floor.

At the moment in time represented by the figure, the angle of depression from the UAV to the fire has a measure of 30°.

At the moment in time represented by the figure, what is the distance from the UAV to the fire? Enter your answer into the box.

Name: ______________________ ID: A

32

Day 28___________________________________________________________

39 An unmanned aerial vehicle (UAV) is equipped with cameras used to monitor forest fires. The figure represents a moment in time at which a UAV, at point B, flying at an altitude of 1,000 meters (m) is directly above point D on the forest floor. Point A represents the location of a small fire on the forest floor.

At the moment in time represented by the figure, the angle of depression from the UAV to the fire has a measure of 30°.

What is the distance, to the nearest meter, from the fire to point D?

Enter your answer in the box.

Name: ______________________ ID: A

33

Day 29___________________________________________________________

40

When θ = 28°, what is the distance from point A to point B to the nearest tenth of a foot. Enter a number into the box.

Name: ______________________ ID: A

34

Day 30___________________________________________________________

____ 41

When the spring is stretched and the distance from point A and point B is 5.2 feet, what is the value of θ to the nearest tenth of a degree.

A 35.2°B 45.1°C 54.8°D 60.0°

Name: ______________________ ID: A

35

Day 31___________________________________________________________

____ 42

A draw a line through P and SB draw a line through Q and SC draw a line through T and SD draw a line through W and S

Name: ______________________ ID: A

36

Day 32___________________________________________________________

____ 43

Which of the reasons listed contribute to proving the validity of the construction.

A When two lines are cut by a transversal and the corresponding angles are congruent, the lines are parallel.

B When two lines are cut by a transversal and the vertical angles are congruent, the lines are parallel.

C Definition of segment bisector.D Definition of angle bisector.

Name: ______________________ ID: A

37

Day 33___________________________________________________________

44

Enter your answers to each part in the boxes.

Part A

What is the perimeter of the plot of land rounded to the nearest tenth of a foot?

Part B

What is the area of the plot of land that does not include the warehouse and the parking area?

Part C

Luke is planning to put a fence along two interior sides of the parking area. The sides are represented in the plan by the legs of the trapezoid. What is the total length of fence needed to the nearest tenth of a foot?

Name: ______________________ ID: A

38

Day 34___________________________________________________________

____ 45

Select all correct answers.

A m∠U = m∠TB US = UTC US = STD m∠U = m∠SE STU is an isosceles triangle.F m∠T = m∠SG ST = UTH STU is an equilateral triangle

Name: ______________________ ID: A

39

Day 35___________________________________________________________

46

Enter your answer in the box.

Name: ______________________ ID: A

40

Day 36___________________________________________________________

47

Enter your answer into the box.

Name: ______________________ ID: A

41

Day 37___________________________________________________________

48

Part AFind the area of each of the five sectors in the circle. Use 3.14 for π and round your answer to the nearest hundredth. Enter your answers into the box.

Part BCheck your work by finding the sum of the five sector areas and comparing it to the area of the circle. Enter your response into the box.

Name: ______________________ ID: A

42

Day 38___________________________________________________________

49 Describe two methods to prove that ABC is a right triangle. Enter your answer into the box.

Name: ______________________ ID: A

43

Day 39___________________________________________________________

____ 50

A 577 kg /m 3

B 2308 kg /m 3

C 4615 kg /m 3

D 14,500 kg /m 3

____ 51 A water tank holds 15 L of water. Which of the following solids describe a container that could be completely filled from the water tank and leave less than .5 L of water in the tank? Recall that 1 L is 1000 cm 3

A A cone with radius 25 cm can height 27 cmB A cylinder with radius 15 cm and height 21 cmC A rectangular prism with length 22 cm, width 30 cm, and height 22 cmD A rectangular pyramid with base length 30 cm, width 50 cm, and height 10 cmE A square pyramid with base length 30 cm and height 50 cm

Name: ______________________ ID: A

44

Day 40___________________________________________________________

52

If triangle ABC is reflected across the line y=1 to for A ʹ′B ʹ′C ʹ′, what is the coordinate of B ʹ′?

Name: ______________________ ID: A

45

53

Given: Quadrilateral PQRS is a parallelogramProve: PT = RTST = QT

Statements Reasons1. Quadrilateral PQRS is a parallelogram 1. Given2. PQ Ä SR

PS Ä QR

2. Definition of parallelogram

3. ∠PQS ≅ ∠RSQ

∠QPR ≅ ∠SRP

3.

4. 4. Opposite sides of a parallelogram are congruent

5. SRT ≅ QPT 5.

6. PT Ä RT

ST Ä QT

6. Corresponding parts of congruent triangles are congruent.

7. PQ = RT

ST = QT

7. Definition of congruent line segments

Enter the statement and reasons into the boxes to complete the proof.