Geometry Questions

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

Find the equations of the tangent lines at the point where the curve crosses itself Enter your answers as a comma separated list of equations x t 3 2t y t 2

O 1 3 1 2 1 6 O 1 4 Question 2 If a six sided die is rolled find the odds that the number will be a multiple of 2 2 1 2 p 2 6

Maggie used a standard deck of 52 cards and selected a card at random She recorded the suit of each card she picked then replaced the card The results are in the table below 1 4 13 50 1 2 Diamonds 7 10 Hearts What is the theoretical probability of selecting a heart Spades Clubs JK TILL JY JY I

Billy rolled a six sided die Each time he recorded the number rolled in the table below 1 3 5 18 5 12 Number on Die 7 15 1 2 3 4 5 6 Frequency 8 3 9 What is the experimental probability for rolling a number greater than 4 6 4 6

sweepstakes 1 500 499 1 1 499 499 500 Question 6 Maggie used a standard deck of 52 cards and selected a card at random She recorded the suit of each card she picked then replaced the card The results are in the table below O 7 10 Diamonds 3 10 Hearts Spades Clubs 2 pts JY HY HY I What is the experimental probability of selecting a heart

16 A tank is in the shape of a pyramid The base of the tank is a rectangle with length 3 feet and width 7 feet It is 9 feet high Find the volume of the tank

15 Popcorn is served in a conical container that has a radius of 3 inches and a height of 6 inches What is the volume of the small container

13 Find the volume of a cylindrical pool if the diameter is 20 feet and the depth is 6 feet

14 A fish tank is in the shape of a cylinder The tank is 22 feet deep and 40 feet in diameter Find the volume of the tank

The number of males and females enrolled in Oddability High School are listed per class in the table below Grade 9 10 11 12 107 207 20 207 35 207 Male 16 69 120 100 130 150 Female 150 If a student is chosen at random what is the probability that the student is female 100 110 175

Find the volume of the following 1 4 2 ft 11 cm 3 ft 11 cm 11 cm

1 6 Find the measure of the arc 1 AB A E D 40 B C AC L BE 2 ABC 3 ABD 4 BC

A ferris wheel is 19 meters in diameter and boarded from a platform that is 5 meters above the ground The six o clock position on the ferris wheel is level with the loading platform The wheel completes 1 full revolution in 6 minutes The function h f t gives your height in meters above the ground t minutes after the wheel begins to turn What is the amplitude What is the equation of the Midline What is the period The equation that models the height of the ferris wheel after t minutes is f t meters minutes meters How high are you off of the ground after 11 minutes Round your answer to the nearest meter meters

Rodrigo is organizing his CD collection He has 5 pop CDs and 85 other CDs If Rodrigo randomly selects one of his CDs what is the probability that it will be a pop CD Write your answer as a fraction or whole number P pop

Dwayne is making a gift during a pottery class at school He knows how to make 8 different items and there are 8 kinds of clay with which to make it How many different gifts can Dwayne make ich

20 You are planning to start a home business You decide to build a workroom in the shape of a rectangular prismin the backyard It will give you solitude to work and a place for cus tomers to see your products without disturbing your family in the house You price the mate rials needed and decide that the perimeter of the floor can be 64 ft in total Maximizing the floor area inside the workshop is your only objective What dimensions would you choose for the floor rounded to the nearest whole numbers You may know the answer already but provide a fully documented algebraic solution 5 marks

Oliver is deciding what to wear to school today There are 7 tops to choose from and 4 different pants How many different outfits can Oliver create outfit

Ken is buying a new set of DJ equipment Ken can afford one mixer and one turntable and is trying to decide among 3 different mixers and 8 different turntables There are 4 different speaker setups in Ken s price range How many different sets of DJ equipment can Ken buy sets

5 6 7 D Play Station B 8 00 Xbox 16 Nintendo 9 10 11 H 2 12 13 14 15 16 17 18 19 20 REQUIRED 1 A Video Game store Game Go is conducting a survey and asking each customer which current video game systems they own A customer named Justin said he only owns the latest Play Station and the latest Nintendo consoles In which region or regions would this place Justin in the VENN diagram 21 22 23

8 Find the area of the shapes below using addition or subtraction y a b 60 12 10 Wy 0 Seef X 3