Geometry Questions

3 In the diagram above of circle 0 m AOC 3x 5 and m ABC x 15 What is the mAC 5 b 20 C 25 d 40 80 a e A B

Kira looked at some boxes of cereal in the grocery store For each one she recorded the size and whether or not it contained a prize Mini size Regular size Prize No prize 3 3 3 1 What is the probability that a randomly selected box of cereal is regular size or contains a prize Simplify any fractions

Myra is packing a lunch box to take to school Myra can make 6 kinds of sandwiches and there are 6 kinds of fruit in the house There are 7 flavors of juice boxes in the refrigerator Assuming Myra packs one of each item how many different lunches can she pack lunches

4 In the circle above mzQ 3x mLU 2x 12 mzA 2x and mzD 2y Detern U

2 Find the value of x K 83 M L 9x 40

a EF b GD C CB d DB intercepts which arc C A D E B LL F INSCR 2

You spin the spinner once 3 1 2 What is P less than 2 Write your answer as a percentage rounded to the nearest t

Alec attended his town s annual Worm Charming Competition Contestants are assigned to a square foot of land where they have 30 minutes to charm worms to the surface of the dirt using a single technique Alec observed contestants charming techniques and kept track of how many worms surfaced 5 10 worms 11 20 worms 21 30 worms Tapping the ground Raking the ground 6 5 5 8 10 4 What the probability that a randomly selected contestant charmed 11 20 worms or 5 10 worms Simplify any fractions

Gordon is a physical therapist who specializes in pediatric leg injuries His patients differ in age and type of injury 0 12 years old 13 19 years old Knee pain Ankle pain 3 3 4 5 What is the probability that a randomly selected patient is 13 19 years old or suffers from knee pain Simplify any fractions

Nellie and her brother are at a store shopping for a beanbag chair for their school s library The store sells beanbag chairs with different fabrics and types of filling Velvet Suede Foam 4 5 Beads 4 3 What is the probability that a randomly selected beanbag chair is made from suede and is filled with foam Simplify any fractions

2 Using circle O determine mzPQR and mPR 90 R a mzPQR 90 mPR 90 b mzPQR 180 mPR 90 mzPQR 45 mPR 90 mzPQR 90 mPR 45 radius is 9 cm

3 Solve for the value of x 4 G F 21 x 2 38x 5 A H

2 Use the Zero Product Property to identify the x intercepts Find the y intercept line of symmetry vertex and draw a sketch graph for each function a y x 4x 32 x intercepts y intercept line of symmetry vertex product sum 5 15 20 25 30 35 9 10x

b y 3 x 5 48 Step 1 Convert to standard form standard form Step 2 Factor standard form and use Zero Product Property to find x intercepts product S 10 10 vertex 20 30 40 50 Step 3 Use the information below to graph x intercepts y intercept line of symmetry 19 16 10

4 Convert the equations to standard form from vertex form then use the Zero Product Property to identify the x intercepts Find the y intercept line of symmetry vertex and draw a sketch graph for each function a y x 5 9 Step 1 Convert to standard form standard form Step 2 Factor standard form and use Zero Product Property to find x intercepts product sum 10 5 Step 3 Use the information below to graph x intercepts y intercept line of symmetry vertex

trapezoid rhombus or kite shown below 36 in b 7ft c 19 ft 9m 21 ft 14 ft 45 m 24 In A A

A college professor asked his psychology students to complete a personality test He paid special attention to his students career goals and their greatest fears Social worker Therapist Psychiatrist Fear of snakes Fear of heights 8 6 2 7 4 3 What is the probability that a randomly selected student wants to be a therapist or psychiatrist Simplify any fractions

11 One sector has an area of 8 27 square millimeters and an arc measure of 82 What is the area of the circle that contains the same sector A 13 Find the area of the regular polygon shown below Assume the perimeter of the polygon is approximately 121 4 m 18 mm 12 Find the area of the circle shown below 5H T 14 mm 14 Find the total area of the pool shown below 20 mm A 32 mm

Nina likes to go on canoe trips and on each trip she purchases oars to keep as souvenirs Her collection of oars is organized by decade and type of wood 2010s 2020s Spruce wood Ash wood 6 2 6 4 What is the probability that a randomly selected oar was purchased in the 2010s or was made from ash wood Simplify any fractions

Regan joined a book club to spend more quality time with her cousin At the first meeting club members recorded how many hours a week they typically read and whether they preferred e readers or paperback books E readers Paperback books About 1 hour per week About 3 hours per week 6 4 6 4 What is the probability that a randomly selected club member prefers e readers or reads about 1 hour per week Simplify any fractions

His grandparents Jamie found a box with a surprising number of spare keys Jamie figured that the color of the sticker on each key must indicate what the key was for When Jamie tested the keys he was surprised to find that this was not the case Blue sticker Green sticker Front door of the house Back door of the house 4 3 3 2 What is the probability that a randomly selected key is labeled with a blue sticker or opens the front door of the house Simplify any fractions

8 Find the indicated measure a Find the radius of a circle with an area of 153 94 square millimeters r b The area of a circle is 12 57 square miles Find the diameter of the circle

5 Regular pentagon ABCDE is inscribed in circle G B a FG is a n A apothem B radius side of the pentagon b CD is a n A apothem B radius side of the pentagon 6 What is the area of the shaded region 5 in 10 in 4 in 3 in 7 in 6 in 15 in A 10 in

4 Find the area of the trapezoid shown below 11 cm 21 cm 18 cm

A wilderness retail store asked a consulting company to do an analysis of their hiking shoe customers The consulting company gathered data from each customer who purchased hiking shoes and recorded the shoe brand and the customer s level of happiness Displeased Pleased A Footlong shoe A Toes Knows shoe 3 3 3 3 What is the probability that a randomly selected customer is pleased or purchased a Toes Knows shoe Simplify any fractions TELEP C O 2 55

7 Find the area of the regular polygon 32 cm

3 Find the area of the circle shown below 20 5 in

journalist attended a crossword puzzle competition The competition ends when a contestant has accurately completed five different crossword puzzles For his story the journalist recorded the home country and final score of each contestant United States Canada Up to 100 points Over 100 points 6 7 3 3 What is the probability that a randomly selected contestant is from Canada or scored over 100 points Simplify any fractions

IEEL A historian is constructing a model of a wagon wheel used on the Oregon Trail If the wagon wheel has a diameter of 10 feet and is divided into 12 congruent segments what is the area between each pair of spokes 10

missing piece of information in each problem below a If the area of a kite is 130 square inches and the length of the long diagonal is 13 inches what is the length of the short diagonal d b The area of a trapezoid is 342 square feet If the length of one base is 41 feet and the height is 12 feet what is the length of the other base

9 Find the area of the shaded sector A 7 ft 102 B

Pythagorean Theorem 3 points 1 The end of a dog s leash is attached to the top of a 5 foot tall fence post as shown in the diagram below The dog is 7 feet away from the base of the fence post How long is the leash to the nearest tenth of a foot 5 ft 7 ft Leash Dog

Chef Henderson baked her famous casseroles for a company holiday party The casseroles have different shapes and different delicious fillings Rectangle Circle Spinach 2 4 Cheese 4 4 What is the probability that a randomly selected casserole is shaped like a circle and is filled with cheese Simplify any fractions

Isabelle designs bow ties for a local boutique store The store manager counted the ties currently on display tracking them by material and shape Cotton Suede 3 4 Butterfly 5 Batwing 6 What is the probability that a randomly selected bow tie is shaped like a butterfly and is made of suede Simplify any fractions

At a science museum visitors can compete to see who has a faster reaction time Competitors watch a red screen and the moment they see it turn from red to green they push a button The machine records their reaction times and also asks competitors to report their gender Male Female 5 2 Less than 0 3 seconds 3 0 3 to 0 7 seconds 5 What is the probability that a randomly selected competitor reacted in less than 0 3 seconds and was female Simplify any fractions

The probability that a number cube lands on 3 is The probability that a coin lands on heads is 6 What is the probability that the number cube lands on 3 and the coin lands on heads B 12

A science teacher presented a balloon to her class and posed the question If I keep this balloon in the freezer overnight what will occur She followed up with How certain are you of your answer The teacher recorded her students responses Certain Uncertain Shrink Expand 4 5 6 4 What is the probability that a randomly selected student was certain and believes the balloon will expand Simplify any fractions

The probability that Randy likes yellow is 0 75 The probability that Sandy likes red and that Randy likes yellow is 0 3 If these events are independent then what is the probability that Sandy likes red 0 4 80 35 0 45 0 225

The probability of event A is 0 9 The probability of event A and event B is 0 45 If these events are independent then what is the probability of event B A 0 9 B 0 45 C 0 5 D 0 405

Part B Dilations Use the trapezoids to answer questi 8 1 What is the ratio of the perime trapezoid

5 Write the equation of the graph below in polar Polar form

urriculum 2 0 Honors mative Assessment I NO CA 4 Two of the equations below have graphs that Select the two equations that apply r 5 cos 8 r 2 2 sin 8 r 4 cos 26 in 30

2 Find an ordered pair of polar coordinates to represent the point whose rectangular coordinates are Find the equivalent polar equation of the curve x y 9 writing r as a function of 8 Show the work that leads to your answer 4 Find the equivalent rectangular equation of the 3seco writing y as a function of x Show the work that leads to your answer curve r

1 Use spherical coordinates to evaluate JIS E where E lies between the spheres 22 y 22 4 and x y 9 x y dV

The given graph shows vertical traces of a surface defined by z f x y for x 1 x 0 and a 2 6 5 4 3 2 1 a 6 5 4 3 2 1 3 4 5 6 N x 2 Identify the equation of the surface Of x y x y Of x y x y Of x y y x Of x y y r 3 x 1 x 0 4 5 J 6

1 Write the equation of the hyperbola centered at the origin with length of the horizontal transverse axis 8 and the curve passes through the point 7 8 2 The equation of the hyperbola that has a center at 9 1 a focus at 4 1 and a vertex at 12 1 is x C A where A B C D y D 1 B

Achilles is piloting a 65 meter tall giant death robot looking ahead he sees another giant death robot scanner indicates that the angle of elevation from the top of Achilles robot to the top of the opposing robot is 4 degrees and the angle of depression to its feet is 30 degrees Give answer in exact vaules in terms of trig functions How far from Achilles robot is the other robot how tall is the other robot

The goal of this problem is to sketch the curve associated with the following equation in polar coordinates r 3 sin 20 First use a separate page to make a table of r and values satisfying the equation or else make a plot for the above equation using Cartesian coordinates and use this information to sketch the graph of the curve in polar coordinates a Use the linked page of curves and points to identify the curve that you ve sketched in the space below Two letter code for your curve b Write the polar coordinates of the points P and Q shown on the linked page Coordinates for P r 0 Coordinates for Q r 0 Important Because of nonuniqueness of polar representations for each point pick the coordinates r 0 satisfying the equation where 00 is the smallest possible nonnegative

The equation of the hyperbola that has a center at 9 1 a focus at 4 1 and a vertex at 12 1 is x C A where 4 B D y D B 1

18 Triangle ABC is similar to triangle XYZ Solve for r C P 13 5 19 5 12 B N 4 5 X 4 t