2D Geometry Questions and Answers

each with an internal radius at the opening of A baking company produces ice cream cones 4 centimeters and an internal height between 14 75 centimeters and 15 centimeters What is one possible volume rounded to the nearest cubic centimeter of an ice cream cone produced by this company

On a number line two different points are both 5 units from the point with coordinate 6 The solution to which of the following equations gives the coordinates of both points A y 6 5 By 6 5 C y 5 6 D y 5 6

In circle N with m MNP m MQP Q M za N 74 find the P

3 4k 10 26 5k 21 What value of k satisfies the equation above

Robert Louis 3 9 h sch 6 1 4 5 Height feet 4 4 5 7 5 3 4 2 EPORTE 5 8 3 8 Robert and Louis each have five rose bushes and the heights of the bushes are shown in the table above The mean of the heights of Robert s rose bushes is 0 3 feet greater than the mean of the heights of Louis s rose bushes What is the value of h CA In the xy plane the graph of y 4x 25x intersects the graph of y x at the points 0 0 and c c What is the value of c 37 38 John is analyzing the monthly expenditures of his business to determine whether his expenses exceeded his predicted budget Of the money he spent this month 10 was for office supplies 40 was for employee salaries 35 was for rent and the remaining 450 was for utilities How much more money in dollars did John spend on rent than on office supplies An elementary school had k kindergarten students enrolled at the beginning of the 2011 school year The number of kindergarten students enrolled tripled each year until 2014 when the elementary school had 540 kindergarten students enrolled What is the value

Points P and Q lie on a circle with radius 2 and are PQ has length What fraction of the circumference is the length of arc PQ 2700 13

16 P 12 12 In the figure above PQ is parallel to RT What is th length of PS 3 R T 5

20 3 How many gallons of a juice mix that is 60 orange juice must be added to 5 gallons of a juice mix that is 30 orange juice to obtain a juice mix that is 40 orange juice Con

If r 64 for positive integers r and s what is one possible value of s 32

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