2D Geometry Questions and Answers

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

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

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

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

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

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

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

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

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

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

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

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

Use for questions 8 11 A bag contains 20 slips of paper individually numbered 1 20 If a slip of paper and a letter in the word PENNSYLVANIA is chosen at random find each probability 8 P less than 15 then a vowel 9 P multiple of 4 then V 10 P at least 11 then N 12 Bella guessed on the last three questions on her science test If each question has five answer choices what is the probability she got all three correct 11 P a prime number then a consonant 13 It has rained two out of the past nine days Based on this data what is the probability that it will not rain for the next four days

Question 5 1 point For the diagram below which primary trigonometric ratio would you pick to solve for the unknown value 3 8 cm R 37 a sin b cos c tan Question 6 1 point For the diagram below which primary trigonometric ratio would you pick to solve for the unknown value 2 8 m W 58

From the given figure find the length h Show all your steps to get full marks h 3 98cm 0 48cm R1 00cm 2 84cm

Expo sin 2u cos zu sin u 4 5 37 2 u 27t tan 2u

You roll a 6 sided die What is P 6 or 1 Simplify your answer and write it as a fraction or whole nun

Check for Understanding 7 The triangle shown has vertices at A 3 1 B 1 2 and C 4 2 Find the area of triangle ABC 3 4 1 2 7 A A 22 8 4 A 16 2 A 4 4 7 14 unite16 4 12 unit 3 4 A T B 4 2 C 172

Practice 8 Find the area of the shapes below using addition or subtraction a b 60 putty A b h A R 11 66 11 R 66 89 unit c P A R A 9 4 18 9 4 18 31an 25 Z d WAY W 10 0 2 Y A 1 6 4 12 679 12 27 unit 2 32 7 A8 4 N A b h 4 8 1 8 34 A 32

All four sides of quadrilateral tangents of a circle then ABCD are PTET Nov 2011 1 AC AD BD CD 2 AB CD BC AD 3 AB CD AC BC 4 AC AD BC DB

The drawing for a right triangular roof truss represented by AABC is shown in the accompanying diagram If LABC is a right angle altitude BD 4 meters and DC is 6 meters longer than AD find the length of base AC in meters A B D C

In the diagram below QM is an altitude of right triangle PQR PM 8 and RM 18 Solve for QM 8 M 18 R

Triangle RST is similar to AXYZ with RS 3 inches and XY 2 inches If the area of ARST is 27 square inches determine and state the area of AXYZ in square inches

1 The base of an isosceles triangle is 5 and its perimeter is 11 The base of a similar isosceles triangle is 10 What is the perimeter of the larger triangle

Homework The university administration has asked a g for improvement over the next year The cho summarized in the preference table

You are painting a jewelry box in the shape of a square pyramid How much paint will you need 10 in 13 in

4TH i area of the triangle Round your ans 70 C 45

1 Choose the partially colored map that could be color

Universal Set U 3 5 6 7 10 11 12 Subset B 10 What is the complement of Set B in Set U 10 3 5 6 7 10 11 12 3 5 6 7 11 12 O 5 6 10 11

Given Universal Set U 1 2 4 6 11 12 Subset B 2 What is the complement of Set B in Set U 1 4 6 11 12 1 2 6 11 1 2 4 6 11 12 2

Given Universal Set U Subset B 2 3 6 10 11 12 2 10 11 What is the complement of Set B in Set U 2 10 11 2 3 6 10 11 12 O 3 6 12 2 6 10 11

Set A Set B 1 8 10 1 7 8 10 1 1 8 10 8 10 7 8 10 What is the intersection of sets A and B

Given Set A Set B 2 3 11 12 1 4 5 7 11 What is An B 11 1 4 5 7 O 1 2 3 4 5 7 11 12 2 3 5 7 11 12

Set A 2 3 5 6 7 11 Set B 1 3 8 9 11 12 What is AU B 1 2 3 5 6 7 8 9 11 12 2 5 6 7 3 11 O 2 3 6 7 8 9 11 12