Geometry Questions

4 A circle is centered at C 1 3 and has a radius of 6 Where does the point P 6 6 lie a Inside the circle b Outside the circle c On the circle d Cannot be determined

Figure F is graphed 1 Transform figure F using the rule x y x y 8 Sketch it on the graph 2 Describe the transformation precisely Translation along the directed line segment from point to point rotation direction and degrees reflection across line 3 Does the transformation result in a figure that is congruent to the original similar to the original both or neither T 10 9 4 2 10 8 6 4 2 0 ON 2 4 6 8 X 8 F 2 4 S 8 10

Find the point that partitions segment AB is a 2 1 ratio Enter your answers and your explanation in the space provided You may also use the drawing tool to help explain or support your answer yf 10 9 8 7 6 5 4 3 A T 8 B S

a 6 3 b 0 9 3 0 d 2 4 wn in order to receive full credit ring all work and annotations Keep work organized and box C ation for circle A below Which point lies on the interior of circle A x 2 y 5 20 hat is the circumference of the circle given in 1

The image shows quadrilateral ABCD 1 Prove that quadrilateral ABCD is a square 2 Find the perimeter of ABCD Explain or show your reasoning 3 Find the area of ABCD Explain or show your reasoning Enter your answers and your explanation in the space provided You may also use the drawing tool to help explain or support your answer y 7 6 5 C 4 3 2 1 A 16 1 5 2 T B 3 X 8 D 4 HT 5 S 6 C 7 X

5 Write an equation and solve to find the volume of the cylinder T3X2 18 r 3 cm h 2 cm

994 8 YA EX 654 327 O T F X 8 1 2 3 4 5 6 7 8 9 X The parabola in the image has its focus at 4 3 Its directrix is the line y 1 The point 8 6 is on the parabola Select all of the statements that are true Select all that apply The equation x 4 y 3 y represents the parabola The equation x 4 y 3 y 1 represents the parabola The point 8 6 is the same distacne from the point 4 3 as it is from the line y 1 The point 2 3 is on the parabola The point 0 5 5 is on the parabola If point x y is on the parabola then the distance between x y and the point 4 3 is the same distance between x y and the y axis

The image shows a circle with center 4 6 and radius 10 units Select all points that lie on the circle Select all that apply 4 12 6 6 4 6 13 10 4 16 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 6 5 4 3 2 O 2 5 6 T 4 6 1 2 3 4 5 6 7 8 9 101112131415161

Find the center and radius of the circle by this equation 2 2 x 10x y 6y 30 0 Enter your answers and your explanation in the space provided You may also use the drawing tool to help explain or support your answer

Line m is represented by the equation 3 y 2 x 4 Select all equations that rpresent lines perpendicular to line m Select all that apply y 3x 4 0y x 4 y x 4 y x 4 y 1 x 5 6 3 y 1 x 5 2

The triangles below are similar What is the ratio larger to smaller of the areas 15 ft 9 ft Input answer as larger smaller

1 Determine the equation of the circle below 2 5 3 A N 1 B 0 2 b

3 Write a trigonometric equation and solve to find x 24 12 gjo X

The Venn diagram below not to scale shows a sample space S and two events A and B The area of the sample space is 1 Event A is represented by a square with a side length of 2 2 Event B is represented by a circle where the center of the circle is point O and the diameter is In2 1 Computer P A and P B II Prove that events A and B are independent III Prove that events A and B are not mutually exclusive A 0 B S

Which of the following points lies on the circumference of the circle x 3 y 12 29 sty 923 10 20 a 15 7 b 8 12 C 2 14 9 3 8 10 18

The areas of two similar octagons are 112 in 2 and 63 in 2 What is the ratio larger to smaller of their perime Input answer as larger smaller

What is the area of the figure below 10 m Select one O a 72 m O b 96 m O c 36 m O d 60 m 6m 12 m

What is the area of the figure below 7 5 in Select one 6 in O a 45 in O b 90 in O c 135 in 2 O d 180 in

What is the area of the parallelogram 4 5 m 6 m 4 14 m Select one O a 84 m O b 126 m O c 63 m O d 31 5 m

2 Determine whether the point 7 3 lies on the graphs of the following lines a 2x 4y 26 b x 7y 13 K

What is the area of the figure below 10 8 in 10 in O b 4 in 5 in Select one O a 52 in 54 in 2 O c 27 in O d 26 in 2 3 in

18 A month of the year and number from 1 40 is chosen at random What is the probability that the month begins with the letter A and the number is a perfect square 19 A coin is tossed four times What is the probability of getting tails each time

20 A jar contains 15 quarters 9 dimes 10 nickels and 6 pennies A coin is selected at random not replaced then another coin is selected Find the probability of each event a P dime then nickel b P quarter then penny c P both not dimes

Determine if a permutation or combination is appropriate find the number of possibilities 36 The number of ways that 18 runners can win first second and third place 37 The number of ways to choose 3 slices of pizza from a pizza cut into 16 pieces

40 The number of ways to form a 12 person jury 41 The number of 6 digit passcodes possible from a pool of 40 potential jurors using the digits 1 8 if digits cannot repeat

Find each probability using permutations or combinations whichever is appropriate 42 A class contains 12 girls and 16 boys If a 43 To enter a video call with their teacher each student must enter a unique group of 5 people is formed from this class what is the probability that they are all boys passcode that begins with 3 capital letters that do not repeat What is the probability that a student s passcode begins with ABC 44 There are 30 calculators numbered 1 30 in a case If 4 of the calculators are broken what is the probability that the numbers on the broken calculators are at least 16 45 Laura is filling three empty photo frames on her mantle by randomly using individual pictures of her eight grandchildren If Ben i her grandson what is the probability that his picture is used in the middle frame

25 Mr Howell teaches four geometry classes On the last fest he gave 95 of the students passed the test 60 studied for the test and 48 both studied and passed the test If a student is chosen at random what is the probability that they passed the test given that they studied 26 Ryan pitched for his baseball team in 5 8th of the games it rained for 3 10th of the games and he pitched and it rained for 1 4th of the games If a game is chosen at random what is the probability that it rained given that Ryan pitched

35 A bag contains three different colored marbles red blue and green Of these some are solid and some are striped If one of the marbles is chosen at random find each probability Red Blue Green Striped 6 15 12 Solid 10 8 9 a P green b P solid or blue c P striped green d P not blue solid

For questions 29 34 A group of boys and girls were surveyed and asked their eye color 29 The results are shown in the partial table below Complete the table Blue Brown Green Total Boy 126 157 Girl 21 64 8 Total 49 30 Create a relative frequency table by filling in all joint and marginal relative frequencies Blue Brown Green Total Boy Girl Total

21 A card is chosen from a standard deck not replaced then another is chosen What is the probability that both cards are spades 22 A letter from the word BOOKKEEPER is chosen at random not replaced then another letter is chosen What is the probability of choosing a K then an E

For questions 15 and 16 A point in the figure below is chosen at random Find the probability that the point lies in the shaded region Give each answer as a percent 15 16 12 cm 22 cm 10 ft 6 ft

38 The number of ways to arrange the letters in the word JOURNEY 39 The number of ways to create a 4 person committee from a group of 25 people

Use for questions 11 and 12 Of the 125 students enrolled at a dance studio 96 take ballet and 50 take jazz Of those that take ballet 28 also take jazz 11 Draw a Venn diagram to represent this information Ballet Jazz 96 28 50 125 13 If a point is placed at random on AE 12 If a dance student is chosen at random find each probability Give each answer as a fraction in simplest form a P ballet or jazz b P ballet but not jazz c P neither ballet nor jazz 14 A shuttle bus arrives at a hotel every 40 146 96 49

For questions 7 10 give each answer as a fraction simplest form decimal and percent 7 If a letter in the word MATHEMATICIAN is chosen at random what is the probability of choosing a vowel 9 If a card is selected at random from a standard deck what is the probability that it is a face card or an 8 8 A number from 1 30 is chosen at random What is the probability that the number is a two digit number and prime 10 If a card is selected at random from a standard deck what is the probability that it is an ace or a red card

Compound Events each answer as a fraction in simplest form 17 Each spinner below is spun once Find the probability of each event Green Blue Yellow Red Yellow 18 A month Blue Blue Green 9 8 7 10 6 1 2 4 3 a P blue then even b P not red then less than 7 c P green then at least 3

23 A number from 1 50 is chosen at random Find each probability as a fraction in simplest form a P odd less than 25 b P greater than 10 even 24 A letter in the grid below is chosen at random What is the probability that the letter is in the word BASKETBALL given that it landed in the shaded region ABCDE FGHIJ KLMNO PQRST

SU and VT are chords that intersect at point R S V x 6 x 1 n x 4 T What is the length of line segment VT O4 units 08 units 13 units O14 units

The circle is inscribed in triangle PRT P U 9 T S 5 R Which statements about the figure are true Select two options The perimeter of the triangle is 19 units TU TS PUTU The length of line segment PR is 13 units The length of line segment TR is 10 units

W 12 k 4 k N What is the length of line segment XZ O4 units 8 units 16 units 20 units

BD and AC are chords that intersect at point Y w 3 X Y 8 D S C What is the length of line segment AY O 2 units O 3 units O4 units O 6 units

Line segment BA is tangent to the circle 55 C A 120 What is the length of line segment BA Round to the nearest unit O 18 units O 65 units 88 units O 98 units

The circle is inscribed in triangle AEC A F B D C Which are congruent line segments Select two option OAB and CB OEF and ED ED and CD AF and EF CB and CD

R S T Line segment ST is congruent to which line segment OSK OKU OUT OTK

ndow elf Custom drapes are being fitted for a large circular window It is difficult to get these measurements but the window has an 8 ft horizontal shelf with a 2 ft brace that sits in the frame If the brace is extended upward it would go through the center of the shelf and the circle What is the diameter of the window Diameter feet

Circle O is inscribed in the given triangle 12 P 4 O R 6 What is the perimeter of the triangle O22 units O 30 units O 44 units O 60 units

What is the definition of postulate an assumption presumed to be true that is used as the basis for a logical argument B a statement that has been shown to be true by logical argument C a statement known to be false that is used as the basis for a logical argument D a statement that has been shown to be false by logical argument A

Use OP at the right to find the name of a minor arc whose measure is less than 82 D 829 P 68

A searchlight has a parabolic reflector that forms a bowl which is 13 in wide from rim to rim and 3 in deep If the filament of the light bulb is located at the focus how far from the vertex of the reflector is it round to at least 3 decimal places 13 3 Picture not to scale

Click here to watch the video Use the graph of y f x shown below to graph the function g g x f 2x y fix 8 0 CE KEE 4 5 0 0 SE DE 8 0yb

When a population grows past the ecosystem s carrying capacity what happens to the population OA The population starts to die off to return to carrying capacity OB Continues to grow OC The population grows then finds a new carrying capacity OD The population will go extinct due to lack of resources