2D Geometry Questions and Answers

T By O cy B This is a vector with components 10 12 A

A ala va tu l n B C D E F 49 35 30 53 33 B D E F 49 35 30 53 33 24 18 43 8 55 34 2 36 17 44 24 18 55 43 8 34 36 2 17 44 ww The weights of edges in a graph are shown in the table above Apply the sorted edges algorithm to the graph Give your answer as a list of vertices starting and ending at vertex A Example ABCDEFA

000000000 D CD CE AE AB 14 BE BC BD AC AD 15 B 12 E Q Find the minimum cost spanning tree on the graph above using Kruskal s algorithm Which of the edges below are included in the minimum cost tree 10 A

C 15 00000 ABCDE D 8 14 13 12 B 7 E a Apply the repeated nearest neighbor algorithm to the graph above Starting at which vertex or vertic produces the circuit of lowest cost A

Find the total area of the composite figure Round all calculations to the nearest ter 38 mm Cepatic WILL BE 15 mm

Matt was converting the polar equation into an equivalent rectangular coordinate equation First Matt listed all the true relationships between polar coordinates and rectangular coordinates Analyze his work Step 1 Since tan and tan 1 substituting tan 11 for tan 1 2 4 Step 2 Using the definition of tan 1 tan Step 3 Since tan 1 1 Step 4 x y Matt is in his reasoning

Point Y is a centroid for every problem Solve for the missing segment 1 Find TY TW 18 2 Find TW TY 20 3 YV 7 Find XV 4 UZ 6x 3 UY 3x 10 Find UY T X Z W V

Test Final Exam Study Guide Question list O Question 1 Question 2 Question 3 PASAU K An agent for a residential real estate company in a suburb goal the agent would like to use the size of an apartment Complete parts a through f b Use the least squares method to determine the regress bo h Round to one decimal place as needed Bound to one decimal place as needed

While waiting for your sister to finish her bungee jump you decide to figure out how tall the platform she is jumping off is You are standing 200 feet from the base of the platform and the angle of elevation from your position to the top of the platform is 62 degrees How many feet tall is the platform

The table shows the number of goals made by two hockey players Player A Player B 2 1 3 8 2 1 4 3 1 2 3 1 3 2 2 1 3 6 Find the best measure of variability for the data and determine which player was more consistent O Player A is the most consistent with an IQR of 2 5 O Player B is the most consistent with an IQR of 1 5 O Player A is the most consistent with a range of 7 O Player B is the most consistent with a range of 5

MA 912 GR 3 2 X 7 2 Y 6 4 and Z 3 1 Part A Graph triangle XYZ Part B Find the lengths of the sides Cl

An equilateral triangle is inscr a circle We draw a line through the midpoints of two sides of the triangle Show that the ratio AB BC is the golden Ratio Hint Use the following Axiom If two chords of a circle intersect in a point that divides the first chord into the lengths a and b and the second into the lengths c and d then ab cd A 0 C B C

If x 3 is a factor of x kx 2k where k is a 1396 constant what is the value of k

x 3x 5x 15 0 What real value of x is a solution to the above equation fith

One angle of a right triangle measures a where 3335 What is sin 90 a cos a

2 3i If the expression above is rewritten in the form a where a and b are real numbers what is the value c a Note i 1 A 2 B 1 C 1 17

The scores eamed in a flower growing competition are represented in the stem and leaf plot 0 5 10 3 7 24 6 8 32 34 4 5 8 Key 518 means 58 What is the appropriate measure of variability for the data shown and what is its value O The range is the best measure of variability and it equals 18 5 O The IQR is the best measure of variability and it equals 45 O The range is the best measure of variability and it equals 45 O The IQR is the best measure of variability and it equals 18 5

S T R In quadrilateral PQRS above PS QR and PQ is parallel to SR If PQ and SR were both decreased by 75 and PT were quadrupled how would the area of PQRS change A The area of PQRS would be quadrupled B The area of PQRS would be increased by 75 C The area of PQRS would be decreased by 75 D The area of PQRS would be unaffected

h m t 4 9t For an object thrown straight upward the formula above gives the relationship between v the initial speed in meters per second t the time in seconds after the object was thrown h the height after t seconds and m the initial height from which the object was thrown Which of the following expresses h in terms of v t and m A h 4 9t vt m B h 4 9t vt m C h 4 9t vt m D h 4 9t2 vt m

10 400 350 300 250 200 150 100 50 Distance miles 1 2 Distance Traveled 3 4 Time hours 5 6 7 The scatterplot above shows the distances and times spent traveling for 22 trips by a driver What is the time in hours of the trip represented by the data point farthest from the line of best fit not shown A 4 B 6 C 8 D 10

The line plot displays the number of roses purchased per day at a grocery store 2 Roses Purchased Per Day 3 5 7 Number of Rose Bouquets 8 O The mean is the best measure of center and it equals 8 Which of the following is the best measure of center for the data and what is its value O The median is the best measure of center and it equals 7 3 The mean is the best measure of center and it equals 7 3 9 O The median is the best measure of center and it equals 8 10

2x 3y 6 x 4y 194 Which ordered pair satisfies the system of equations shown above A 9 4 B 3 4 C 1 5 D 3 4

T R S U Note Figure not drawn to scale Triangle PQR is isosceles with PR QR and PQ 64 If the ratio of ST to SU 5 3 what is the length of SQ A 8 B 24 C 32 D 40

zas 8 slices On a certain day the pizzeria sold a total of in individual slices or in pies of 364 slices 84 of which were sold as individual slices Which of the following shows the number of pies n sold on that day A n B n n C n 364 84 8 364 8 364 8 84 84 364 84 8

What is the volume of this sphere Use 3 14 and round your answer to the nearest hundredth 6 cm cubic centimeters

8 A h The formula above models the productivity index q in barrels per day of an oil well with a pressure differential of p P a permeability of k a pay zone thickness of h a viscosity of and a drainage factor of d Which of the following gives h in terms of q p Pwk u and d B h C h D h uqd k 9 k uqd qd Pe Pwf k Pe Pwf uqd Pe Pwf k d h S 110 4C The equation above is used to model the relationship between the number of scoops s of ice cream sold per day at a particular ice cream shop and the temperature C in degrees Celsius According to the model what is the meaning of the 4 in the equation A For every increase of 1 C four more scoops of ice cream will be sold B For every decrease of 1 C four more scoops of ice cream will be sold C For every increase of 4 C one more scoop of ice cream will be sold D For every cream will be sold decrease of 4 C one more scoop While sa Stephan money h amount save 14 during how th month of ice A St m B S e C S D 10 V t

Buster estimates the expected profit in dollars from one week s operation of his family s chocolate covered banana stand using the expression 4bd 200 where b is the number of bananas expected to be sold at the banana stand each day and d is the number of days the banana stand will be open during that week Which of the following is the best interpretation of the number 4 in the expression A There will be 4 chocolate covered bananas sold at the stand each day B The price of a banana increases by 4 every day C The number of customers will increase by a factor of 4 every day D The banana stand charges 4 for each chocolate covered banana

0 What is the measure of each exterior angle of a regular 30 gon Type your answer 1 point What is the sum of the measure of the interior angles of an octagon

3 B 1 point Find the missing value for x 87 Type your answer 105 1 point Find the missing value for x 136 132 129 X 135 124 141 158 116 92

Find the simple interest paid on a 690 loan at 4 9 annual interest for 18 months Enter an integer or decimal number more

Draw the reflection of the image over the y axis SEGMENT 10 9 8 7 6 5 4 3 2 8 7 6 5 4 3 2 1 OF 1 0 2 3 4 5 6 1 2 3 4 5 6 7 8 9 10 11

SEGMENT 10 9 8 7 6 5 4 3 2 8 7 6 5 et 3 2 T 1 0 1 2 3 4 5 D 1 2 3 4 5 6 7 8 9 10 11

Mutually Exclusive and Inclusive Events Two standard 6 sided dice are rolled How would you describe the following events of having their sum be EVEN OR GREATER THAN 9 Independent Inclusive Mutually Exclusive 2 1 3 1 5 1 6 1 1 2 22 3 2 42 5 2 B 6 2 1 3 3 3 5 3 1 4 2 4 54 3 2 5 3 5 4 5 5 5 65 1 6 2 6 RE 3 6 4 6 5 6

E Reflections Practice QUESTIONS Item 1 O Item 2 OItem 4 Item 5 Osten 5 Draw the reflection of the image o SEGMENT 9 8 7 6 BO 5 4 3 2

4 Graph the image of S 7 8 after a reflection over the x axi CLICK TO SELECT POINT S 11 10 9 8765 4 3 2 1 11 10 9 8 7 6 5 4 3 2 1 0 5 2 3 4 1

NS 1 2 6 Graph the image of points A and B after a reflecti CLICK TO SELECT POINT A POINT B

7 3 1 point The following triangles are similar 4x 6 G True False F 30 in 2x 18 18 in 1 point Given AKGHAFED what is the value of x 3x 33 G 5x 9 F F 10x 78 K E 21 in 3x 6 H 20 in Z 12 in K

S 3 Find the coordinates of the image of J 8 7 0 4 10 8 6 4 2

A Venn Diagram represents a teacher putting her students into categories Group A represents students that drive themselves to school Group B represent students that have a part time job What is the probability of randomly selecting a student that drives that also works part time P BIA 0 294 0 416 0 375 robability 0 583 7 5 B 3 2

Inscribed Angles State if each angle is an inscribed angle If it is name the angle and the intercepted arc 1 C B O 3 W 2 4 K M Date M

For 5 and 6 remember that the bearing is the angle that the line of travel makes with due north 90 measured clockwise 5 An airplane is flying on a bearing of 170 at 460 mph Find the component form of the velocity of the airplane I

Use the accompanying graph of y f x shown to the right to sketch a graph of ea a y f 3x 3 1 b y 3f 3 3 3 c y f x 3 OA O B Q o o O C pc FI

K Determine which ordered pairs x 5y 18 3 3 lect all ordered pairs that s

Two security cameras on a wall are viewing the same object at point Q on the ground The angle of depression from camera T is 24 and the angle of depression from camera N is 44 Camera N is mounted 33 feet above camera T 33 ft 44 24 Q We want to find how far the object Q is from the wall and how high above the ground camera T is positioned Q Let z represent the distance between the wall and object Q and let y represent how high camera T is above the ground Write an equation that uses the tangent function the lengths and y and the 24 angle Be sure to include the symbol when you write your angle 33 tan 44 tan 24 X

13 The graph of a piecewise defined function is given Write a definition for the function that best describes this graph 16 61

18 A roller coaster has a track that drops at an angle depression of 25 from a height of 14 9 m When it reaches the ground in travels horizontally for 8 m It then rises at an angle of elevation of 47 to a height of 26 8 m 5 14 9 m 7 25 32 35 3 25 X 36 47 24 26 8 m a What is the total horizontal distance covered by this portion of track 64 b What is the total distance travelled by a car on this portion of the roller coaster track 79 9

the equation of the polynomial function in the graph below

12 6 Quadric Surfaces Make a labelled sketch of the slices traces of the surface y 2 4 x 2 z 2 1 n the planes and for x 0 2 0 y k k 0 11 12 Then sketch the surface

Problem 54 Match the trigonometric function with one of the graphs I VI 1 f x tan 2 1 2 f x sec 2r 5 f x tanz 3 f x cot 2x 6 f r 1 csc z 4 f x 2 secr MA 11 U mir ith U 0 TI VI P

x 4y 4x y 2 x y x 4 y y 2 x 2 y x 4 y x 2 y x 2 y 4x y x 2 y x 2y x 4 Drag the function given above into the appropriate area below to match the gra A 0 27 G