2D Geometry Questions and Answers

IN 2 byly What value of a is the solution to the equation above

1 Determine the number of radians in the three angles shown in the circle DATSagal 2997gabynent voll ansibsi DATA wolad mus y 180 di l F 20 gradi R

1 If there are 2 54 centimeters in 1 inch how many inches is 10 centimeters Hint Set up a proportion bel

OW 2 SPIRAL Unit 2 Solve for the below tem y 23 63 2x 17

O O A B C Question 22 20 72 6 12 16

Round to the nearest whole number Find the area of the shaded region A 60 ho area of the 8 in B PC

Find the measure of angle BAD D A A A 73 B 107 C 146 36 5 B C 73 F

D Four chords are drawn in the figure below creating a quadrilateral with every vertex on the circle 3x 8 5x 4 A B Using the special properties of this figure determine the measure of Angle A Chow your work for full credit

Question 19 Look at the figure shown below in which O is the center of the circle X O 15 What are the values of the angles at vertices X and Y Angle X measures 30 60 120 120 210 Y degrees and angle Y measures degre

Use the diagram to complete the statement Given AJKL sin 38 equals K 52 D A B C J cos 38 cos 52 tan 38 tan 52 38 L

Questivi 120 points Which is the graph of the function f x 4 x 2 3 O O O 10 8 10 8 6 4 2 10 8 6 4 2 05 2 21 4 61 8 10 81 61 4 2 2 4 4 61 8 10t 101 8 6 T 2 4 6 8 10 2 4 6 8 10

K What is the measure of angle LKJ Round to the nearest whole degre L O 7 7 cm X B C A D 41 45 49 55 8 9 cm J

Q C What additional information is needed to prove that the triangles are congruent using the ASA congruence theorem K OB D A P M NL MP NK MQ N 4M 4L 4P N

A sphere has a radius r 12 inches What is its approximate volume O A O O B C D G 602 9 in 904 3 in 1 808 6 in 7 234 6 in

A A semi circle with points A and B is shown below When the semi circle is rotated about the side AB which of the following three dimensional figures is creat O A B C D cone cylinder cube B sphere

A right circular cylinder is shown below D Which of the following could be a two dimensional figure that results when a plane intersects this right circular cylinder Select three that apply C A B 80 cm circle ellipse triangle 60 cm rectangle

P In the figure below point O is the center of the circle and mRQ What is mZPOQ A B C OD O 125 135 145 70 Q R 35

A circle and a point are shown below Enter the maximum number of tangents that could be constructed to the circle from the point outside the

In circle O which term correctly identifies line XY D B A C D R X B S tangent chord secant diameter C A W

In the figure AXYZ AMNL Find m Y 33 Y m Y L 12 N 124 Z 8 M

A B E J D C If AEDE then 4 Select the theorem used to find the answer O Base Angles Theorem Converse of the Base Angles Theorem A D ABE

Set up and evaluate an integral to find the volume of the solid generated by revolving the region in the first quadrant and the x axis X Infinite region between the curve yoe y about the x axis y e

5 Give the area of a circle that has a circumference of 157 units

1 The circumference of a circle is 647 cm Find the diameter the radius and the length of an arc of 190 A 32 cm 64 cm 16 97 cm C 128 cm 32 cm 185 cm B 64 cm 32 cm 33 87 cm D 64 cm 128 cm 16 97 m 2 Find the measure of CDE

ne I x if x 3 for each valu 1 X 4 2 X 3 3 x 0 4 x 7 Su 2x 1 3 X 2 43 F XZ2

Graph g z 2 1 3 given the graph of the parent function f x 5 4 3 2 3 2 1 Clear All Draw 4 3 2 1 2 3 4 5 2 3 4

The graph f 2 is shown below Let g z be a transformation of f x shifted up 3 and right 3 Draw the graph of g x and write its formula below 7 6 7 6 5 4 3 2 1 5 4 3 2 1 1 2 3 4 5 6 1 2 3 4 5 6 7 Clear All Draw Write the formula for of g x below Be sure to use proper function notation

Part 2 Draw your own city block Your block must o Have clearly labeled coordinates 1 point Be a rectangle Provide evidence in a coordinate proof that the quadrilateral you drew is a rectangle Note There are many correct ways to do this but you may need to prove it s a parallelogram first 4 points Part 1 9 8 7 6 5 4 3 2 1 3 Self Assessment I proved that the city block is a parallelogram 3 points I proved that the city block is not a rhombus 2 points 2 1 1 1 2 3 4 5 6 7 8 9 A 6 1 B 5 6

e S Question 3 2 pts Explain the difference between a minor arc major arc and a semi circle

Question 5 Arcs UT and TS are congruent Find the measures of arcs UT and TS 86 U P 60 154 2 pts R

Question 6 Find the measure of the unknown arc 155 120 2 pts

Explain in your own words what an arc is 12pt IUA Paragraph B I

Question 2 Identify three minor arcs 3 pts

Find the value of x K J 6 11x 43 H 22x 1

Find points on the straight line segment joining 3 1 and 3 2 where the function f x y xy 1 attains its maximum value 4 points

Part 1 A city block is designed using a grid and a computer program The corners of the city block are represented by the points A 5 6 B 6 7 C 8 2 and D 3 3 One of the designers says that the city block is a rhombus Another designer says that the city block is a rectangle 5 63 6 4 3 3 8 2 1 16 3 133 y Show that both designers are wrong by proving The city block is a parallelogram 3 points Wes It is not a rectangle 2 points It is not a rhombus 2 points yes 11 AB 7 6 6 5 DC 2 3 8 311 Ap 3 6 3 5 y This is la paralelogran BC 2 7 9 8 6 9 8 7 6 5 4 3 2 A 2 51 8 8 1 2 3 YZ AC 8 5 2 6 15 3 D 987 654 3 3 6 79 DR T 6 3 1 3 113 51 3 2 1 1 2 3 4 chin 789 7 8 X1Y1 6 7 8 2 9 1 2 3 B 4 5 6 7 8 9 diaga congrevent X 6 3 2 7 11 11 N76 52 67 6 11 11 M 3 54 3 6 19 21

45 14 mm 20 mm Find the area of the sector to the nearest whole number Find the area of the triangle to the nearest whole number mm mm Find the area of the segment to the nearest whole number using the area of the sector and triangle

The circumference of a circle is 64 cm Find the diameter the radius and the length of an arc of 190 64 cm 128 cm 16 9 cm O 64 cm 32 cm 33 8 cm O 32 cm 64 cm 16 9 cm A O 128 cm 32 cm 185 cm

PQRS is a cyclic quadrilateral If P 2S 65 find ZQ and ZR 4Q 110 R 110 O4Q 120 LR 110 4Q 65 R 115 4Q 115 R 115

Triangles Directions Decide whether the pairs of triangles are congruent If so say whether they are congruent by SSS SAS ASA AAS or HL and then write the congruency statement If not congruent write not congruent 1 B 3 A ADA AA 4 7 M W R J D P L K B 2 5 8 B AAAA D B 11 6 E 9 BD N 12 C MAA B M J K D B

d The water temperame 2 Based on the graphs below which of the following substances has the highest specific heat capacity Assume each experiment began with 200 g of the substance at 100 C mixed with 500 of water at 20 C 1001 75 50 25 25 0 100 75 50 25 0 25 Temperature C A Final temperature 25 66 C Substance A Temperature C C Final temperature 22 78 C Substance C 100 75 50 25 0 25 50 Temperature C 1001 75 50 25 0 25 50 B Final temperature 20 95 C Substance B Temperature C D Final temperature 20 54 C Substance D reasoning needed to determine your answer

ow do we prove that two triangles are congruent In other words what is true about two congruent triangle Given AD bisects BE BE bisects AD AB DE ZA ZD Prove AABC ADEC B

Jessie does a lot of traveling for business When he travels he likes to run to stay in shape He has noticed that the amount of time he is able to keep running impacts the maximum distance he can run and also that the elevation of the city he s visiting impacts how long he is able to keep running Max distance Jessic can run miles 5 4 3 2 0 10 Max time Jessie can run min 30 40 50 20 50 40 30 20 10 Max time Jessie can run min timo Jessic 1000 2000 3000 Elevation feet 4000 a If Jessie is visiting a city with an elevation of 4000 feet how long is he able to keep running minutes 5000 b Based on your answer to part a what is the maximum distance Jessie can run in that city miles c If Jessie is visiting a city with an elevation of 0 feet what is the maximum distance Jessie can run in that city miles d If Jessie is visiting a city with an elevation of 5200 feet what is the maximum distance Jessie can run in that city

Area of Composite Figures Find the area of each figure Round to the nearest tenth if necessary 1 6m 10 m 6 ft 5 ft 4 ft 3 ft 2 12 yd 12 yd 6 cm 5 cm 3 3 5cm 5 cm 7 cm 4 in 6 cm h 14 cm 3 5 cm 9 in 5 in 6in 6 in 10 cm 18 in 4 in 10 in 8 in

9 10 11 12 13 14 Study Year 0 1 2 3 4 5 6 7 8 refer to the following information Artic Sea Ice Extent million km 5 98 6 18 6 08 5 59 5 95 4 32 4 73 5 39 4 81 4 22 3 63 5 35 5 29 4 68 4 72 Extent million km 76547 0 a 0 The predicted decrease in extent in millions of square kilometers of Arctic sea ice per year during the period predicted extent in millions of square meters of Arctic sea ice at the end of the nd The function a defined by a t c dt where c and d are constants models the extent in millions of square kilometers of Artic sea ice t years after the start of he study during a period in which the change is pproximately linear What does d represent The predicted total decrease in extent in millions of square kilometers of Arctic sea ice during the period 1 he predicted extent in millions of square ometers of Arctic sea ice at the beginning of period 2 Arctic Sea Ice Extent Over Time 3 6 7 8 9 10 Year A team of research climatologists conducted a 14 year study to determin the change in the area of the Arctic sea covered with ice termed the Ar sea ice extent The graph and table above model the extent a in million square kilometers of Arctic sea ice t years after the study began yer 12 4 5 13 destiny u To date LO 11 12 13 14 am 08 T CATOR ORSIN The rate of decrease of Artic sea ice extent from 7 to Year 10 is nearly constant On this interva of the following best models the extent a in m of square kilometers of Arctic sea ice t years study began A a 5 0 21t B a 7 0 13t C a 10 0 64t D a 15 1 82t Over which time period is the average Arctic sea ice extent the greatest A Year 4 to Year 5 B Year 7 to Year 8 C Year 9 to Year 10 D Year 12 to Year 13

Questions 17 19 refer to the following information box width w 17 box height h total height Note Figure not drawn to scale When designing stacked displays of different types of crackers for sale a manufacturer can use the box size formula h 3w 30 where h is the height of each box of crackers in inches and w is the width of each box of crackers in inches For any given stacked display the height and width of each box displayed is the same The height of each level in the stacked display is equal to the height of the boxes of crackers in the display For example there are 2 levels in the figure above each with a height of h The total height of the stacked display is the sum of each level s height as shown in the figure Some cracker manufacturing companies require that for wheat crackers the box height must be at least 12 inches and the box width must be at least 3 inches According to the box size formula which of the following inequalities represents the set of all possible values for the box width that meets this size quirement 06 w 12 3 w 6 18 A manufacturer wants to use the box size formula to design a stacked display that has a total height of 7 feet holds boxes with a height between 8 and 10 inches and contains an even number of levels With the manufacturer s constraints which of the following must be the width in inches of the box 1 foot 12 inches A 6 8 B 7 2 8 4 19 C D 10 Which of the following expresses the box width terms of the box height A w 30 30 h 30 30 h B W w C w 30 h D w 30 30 h

2014 is trigine so 7c 5d 10 ULLT For the solution c d to the system of equatio above what is the value of c d C A B 14 U 5 7 5 6 5

Year which lions er the 15 A B C D W following is equal to the ratio 62 Triangle WXY is shown above Which of the WZ WX N N N N XZ XY XY XZ X XZ YZ Z 28 Y

An office supply vendor that delivers printer ink to companies charges a subscription fee of 230 for its services plus x dollars for each carton of ink If a company paid 1 364 for 18 cartons of ink including the subscription fee what is the value of x A 46 B 52 C 63 D 78

The board of directors at a natural history museum decided to survey all of its scientists to determine if the new wing in the museum should feature an aquatic exhibit The board met with a sample group of 30 marine biologists The majority of the sample group were in favor of featuring an aquatic exhibit in the new wing Which of the following is true about the board s survey A The sample group should have included more marine biologists B It concludes that a majority of the scientists are in favor of featuring an aquatic exhibit in the new wing C The sample group is biased because it is not representative of all scientists D The sample group should have consisted only of scientists who are not marine biologists