Geometry Questions

of the lake WX MATHEMATICS You can measure the width of the lake using a surveying technique as shown in the diagram Find the wid V 104 m W WX m 6 m Z Y Not drawn to scale 8 m

COMPLETE THE SENTENCE For two figures to be similar the corresponding angles must be and the corresponding side lengths mu

Determine whether the triangles are similar If they are select the correct similarity statel 40 AV 55 N O similar ALMN AWXY O similar ALMN AYXW Osimilar AMNL AXYW not similar 3

Complete the table of values for the equation y 5 0 Then plot the ordered pairs X 0 11 3 2 6 Simplify your answers Type integers or fractions

7 Find the volume of the given prism Round to the nearest tenth if necessary 6 4 cm 4 8 cm 11 5 cm Not drawn to scale

shown Describe the transformation Example 4 L 0 0 L 0 0 M 4 1 N 1 3 N 1 3 M 4 1

Express the following as a function of a positive acute angle 4 tan 96

4 The graph of polygon the image of FGHI after a reflection across the line y 1 Include the line of reflection Then write the coordinates of the image Example 2 G

Progress The movement of the progress bar may be uneven because questions can be worth more or less including zero depending on your answer A rectangular prism has the following dimensions find the volume of the rectangular prism O 10a6 30a 10a O 10a 30a 10a O 10a 30a 10a 10a 3a a 5a w 2a and h Question ID 982 a 3a a Use the formula V 1 w h

A triangular prism has base edges 3 cm 5 cm and 7 cm long Its lateral area is 225 cm What is the height of the prism The height of the prism is Simplify your answer cm

What is the surface area of the solid The surface area of the given solid is cm Do not round until the final answer Then round to the nearest whole number as needed T 3 cm 6 cm L 4 cm

Use a net to find the surface area of the prism 5 ft Answer 4 ft 6 ft

Find the surface area of the cylinder 5 in 15 in The surface area of the given cylinder is in Simplify your answer Type an exact answer in terms of Use integers or decimals for any numbers in the expressi

Find the surface area of the prism The surface area of the prism is in L 11 in 6 in 5 in

Find the lateral area of the cylinder The lateral area of the given cylinder ism Round to the nearest whole number as needed 10 m 14 m

Find the surface area of the cylinder The surface area of the cylinder is cm Simplify your answer Type an exact answer in terms of 6 cm 9 cm

For the polyhedron use Euler s Formula to find the missing number faces edges 14 vertices 7 The number of faces is Tyne a whole number

Use Euler s Formula to find the number of vertices in the given polyhedron 8 faces 2 hexagons and 6 rectangles There are vertices in the polyhedron

4 1 8 Triangle ABC has vertices A 1 3 B 0 1 and C 4 0 Under a translation A the image point of A is located at 4 4 Under this same translation point C is located at

6 translation x y x y 4 y R S Q X

12 reflection across y 1 D E X

10 translation x y x 1 y 2 Ay H X

11 reflection across y 1 T U y X

3 reflection across the y axis Y y X

3 reflection across the y axis Y X

4 reflection across the x axis y F X

A 3 C 5 4 W B Z Y Triangle ABC is similar to triangle WYZ 3 Select all angles whose cosine equals 5

C 26 True False 12 B W 5 Z Triangle ABC is similar to triangle WYZ Determine whether the following statement is true or false sin B sin Y

the length of AB Round to the nearest hundredths place C 10 in 150 B Use 3 14 for pi LITE

S4 Segments that Meet Outside the Circle Solve for x Assume that lines which appear tangent are tangent X X 9 15 1 of 10

T t B C TT T Tt Using the diagram what is the percent chance that the offspring are homozygous dominant for the trait A 25 50 75 t Tt tt

A n double napped hyperbola O circle parabola ellipse is a conic section formed when a plane intersects both nappes of a cone

Five years after 650 high school seniors graduated 400 had a college degree and 310 were married Half of the students with a college degree were married What is the probability that a student does not have a college degree or is married A 31 65 B 56 65 O 5 13 9 13

Use the information and table to answer the following question The table shows the results of a random survey of students in Grade 9 and Grade 10 Every student surveyed gave a response Each student was asked if he or she exercised less than 5 hours last week or 5 or more hours last week Grade 9 Students Grade 10 Students A For this question choose TWO answers Based on the results of the survey which of the following statements are TRUE B C Less Than 5 Hours 5 or More Hours 63 51 D 49 58 More 10th grade students were surveyed than 9th grade students More than 50 of the students surveyed exercised less than 5 hours last week Less than 50 of the 10th grade students surveyed exercised 5 or more hours last week A total of 221 students were surveyed E A total of 107 9th grade students were surveyed

Events M and N have probabilities such that P M 0 4 P N 0 28 P M U N 0 56 and P Mn N 0 12 Are event M and event N independent A Yes because P M P N P M U N B No because P M P N P Mn N C Yes because P M P N P M U N D No because P M P N P Mn N

8 The two way table shows the classification of studenin a mathematics class by gender and dominant hand A student who is ambidextrous uses both hands equally well Male Female Total A 12 30 B D What is the probability that a randomly selected student in the class is female given that the student is right handed 12 23 C 23 30 Right handed 11 12 23 1 Left handed 4 2 6 Ambidextrous 1 0 1 Total 16 14 30

Use the Venn Diagram to complete the following sentence Club Membership Chess Club There are 5 Select One 2 8 Science Club Select One 3 4 Math Club 3 2 students in both the math club and the science club but not the chess club Save

Given set P 5 1 3 and set Q 4 2 1 2 3 What is Pn Q A 1 2 3 B 5 4 2 1 2 3 C 1 3 D do not have an intersection

Use the graph of y f x to graph the function g x f x 3 4 y f x Ay 16 A Show Transcribed Text G Choose the correct graph of g below OA U OB oo

Eliminate the parameter t Then use the rectangular equation to sketch the plane curve represented by the given parametric equations Use arrows to show the orientation of the curve corresponding to increasing values of t x 2 3 cost y 1 2 sint 0sts Choose the correct equation and then select the correct choice for the restrictions below filling in the answer box es to complete your choice if necessary Simplify your answers The rectangular equation is A x B A C x OD There are no restrictions on the values of x and y Choose the correct graph below b F yz x sys 3 AY with restrictions Q O B 6 3 Ay 3 Q G Q O C H 3 Ay H H Q Q O D W of To X

Which point is on the circle centered at the origin with a radius of 5 units Distance formula x x V V O 2 21 O 2 23 O 2 1 O 2 3

4 What is the 3D figure that is produced when the triangle below is continuously rotated a h m What is the height of the 3D figure formed What is the diameter 3

Which equation represents a circle that contains the point 2 8 and has a center at 4 0 Distance formula x x V V1 O x 4 y 100 O x 4 y 10 O x y 4 10 O x y 4 100

U Which equation represents a circle with the same radius as the circle shown but with a center at 1 1 O x 1 y 1 16 O x 1 y 1 4 O x 1 y 1 4 O x 1 y 1 16

Which equation represents a circle with a center at 4 9 and a diameter of 10 units O x 9 2 y 4 25 O x 4 y 9 25 O x 9 2 y 4 100 O x 4 y 9 100

In the diagram a circle centered at the origin a right triangle and the Pythagorean theorem are used to derive the equation of a circle x y2 2 Q 0 0 X A P x y E S If the center of the circle were moved from the origin to the point h k and point P at x y remains on the edge of the circle which could represent the equation of the new circle O h x k y P O x h y k 1 k x h y O x k y h 7

What is the center of a circle represented by the equation x 9 2 y 6 2 10 O 9 6 O 6 9 O 6 9 O 9 6

102 DE GN 0 0 N 3 0 5 stance formula x x V V Does the point 2 6 lie on the circle shown Explain O Yes the distance from 3 0 to 0 0 is 3 units O Yes the distance from 0 0 to 2 6 is 3 units O No the distance from 3 0 to 2 6 is not 3 units O No the distance from 0 0 to 2 6 is not 3 units

9 reflection across y 3 Ay K L X

6 Which object is formed when right triangleKST is rotated around leg RS a A pyramid with a square base b An isosceles triangle c A right triangle ng R d A cone S