Geometry Questions

If mCW 180 and m Q 58 find mSJ S W Q

What is the value of x G X X 82 X 37 X 43 E F F

Write the equation in standard form for the ellipse with vertices 0 12 and 0 12 and covertices 3 0 and 3 0

4 Jack is planting a triangular rose garden The lengths of the sides of the plot are 6 feet 7 5 feet and 10 feet Find the area of the garden to the nearest tenth of a square foot out

Question 4 10 8 6 4 a 20 v y b 2 15 10 I M 3 10 15 20 NT dapat X Identify a and b for the hyperbola with equation 6 8 1 a 62 1

A polar equation is given r 10 3 2 cos 0 a Find the eccentricity Use this information to determine the type of the conic section b Find the equation of the directrix c Sketch the curve Show the exact rectangular coordinates of the vertices and the y interrents Showt

1 Points A and B are on opposite sides of the Grand Canyon Point C is 200 yards from Point A on the same side of the canyon Angle B measures 87 and angle C measures 67 What are the distances between the points

find sin2x cos2x and tan2x if sinx 4 5 and x terminates in quadrant IV

function is defined for all real numbers as follows 10 x if 4 x 4 x 10 if x24 1 x Graph the function Then determine whether or not the function is continuous 12 10 13 10 6 8 10 V X

Given LV and KV are tangents of circle D find coordinate of point V L 3 6 D 9 2 K 1 4

Perform the indicated operation 3 cos 190 i sin 190 8 cos 229 i sin 229 Give your answer in polar form cos i sin

For problems 1 4 use the diagram below A O 60 7 B Find the area of OO Round your answer to the nearest tent

Find the area of the shaded segment Round your answer to the nearest tenth 3

What is the surface area of this rectangula pyramid 4 mm 7 mm 4 mm

Find the surface area and volume of the following solids Rour 1 5 cm

7 AHGFALKJ 18 F 36 24 H 8 G S 70 55 132 E 60 R F 144

Triangle Similarity Find the missing length The triangles in each pair are similar 1 ASTU ALKJ 2 S H 24 D L 3 ATSR ATGH C 45 G 27 5 ARQP ACDE K T Q 56 E ZV 59 42 U P 59 98 110 4 AWVU AWCD 168 A A 8 T 16 140 60 R T U E 15 30 6 AUTS AABC B 41 U T 41 110 20 F 10 D A S V C

3 SAT Question The equation below defines a circle in the xy plane What are the coordinates of the center of the circle a 20 16 b 10 8 c 10 8 d 20 16 x 20x y 16y 20

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