Geometry Questions

In the triangle below with right angle LE suppose that mLF 2x 37 and mL G 5x 4 Find the degree measure of each angle in the triangle G E 5x 4 2x 37 F m ZE m LF m LG 0 0 0

Directions Determine whether the examples Example 7 There are 15 students waiting at the bus stop If the bus can only fit 6 more students how many ways can the driver select the students to ride the bus 8 How many ways are there to make 5 letter arrangements out of the word DISCOVERY 9 A lock contains the numbers 0 39 The lock will open when the lock is spun to the correct 3 numbers in order How many different 3 number combinations are possible for the lock if the numbers cannot repeat 10 There are 18 baseball teams in a league How many ways can the league choose two teams to play each other on opening night 11 A multiple choice test contains 35 questions If the teacher allows the students to omit any 10 questions how many ways can a student choose which questions to answer 12 There are 45 golfers in a tournament How many ways can they win first second and third place P C 4 How many 7 digit phone numbers are possible using the digits 0 2 if the digits can not ropogt and the first C P P P C P 13 Alana has 17 dresses in her closet In how many ways can she select 4 to pack for a trip P Solve 156 15116 15 6 156 5005 ways 985 91 91 4 9 51 15 20 754443 45 45 45 3 42 85 140

4 The equation of the circle is x y 2x 6y 71 What are the coordinates of the center and the lengt of the radius of the circle 2 points a Radius 9 center 1 3 b Radius 9 center 1 3 c Radius 81 center 1 3 d Radius 81 center 1 3 O A O B O c C

5 The center of a circle is 1 15 and one point on the circle s circumference is 4 15 What is the length of the diameter 2 points a 5 b 10 c 25 d O O O 100 A OB O C

3 In a circle with center O central angle AOB has a measure of radians The area of the sector formed by central angle AOB is what fraction of the area of the circle 2 points a b C d 74 780 IN H 7 O A OB O C

2 In the diagram above AC and AD are tangent to circle B at points C and D respectively If CB 4 and AE 8 determine the length of AC in simplest radical form 2 points a 8 2 b 4 2 c 4 3 d 8 3 O A O B O C A E B

6 In the circle below LA 4x 4 mzB 7x mzC 5x 41 and m D 5y What is the value of y 2 points a 5 b 10 C 15 d 20 O A O O B C D B D

1 What is the value of x 2 points a 7 2 111232 b 1 c 5 d 10 O A OB O C 3x 6 10

3 1 1 point What is the measure of ZY 136 b X 68 Z Type your answer 1 point What is the measure of FGH 101 H

What is the measure of the arc RU R S 88 30 V 35 Type your answer U x 1 point What is the measure of x 27 T 18

JL and NL are secants to Circle O What is the value of angle L 125 N 92 Type your answer D K B 51 1 point What is the measure of E E M L 140 C

3 1 point What is the measure of x 16 14 2x 5 6 x 11 Type your answer 1 point What is the measure of x 15 Tyne your answer

9 10 1 point What is the value of x x 1 point Find CD G 12 Type your answer 18 2x 7 11 D E

2 What is the approximate length of the red arc Round your answer to the tenth place Type your answer U 4 1 point What is the area of the shaded section round you answer to the nearest centimeter 140 110 S 5 cm R T

2 1 point Demetrius wants to paint the cylinder shape cardboard cut out he made in art class shown below 3 inches 8 inches If he just wants to paint the lateral area of the cylinder approximately how many square inches of paint will he need Type your answer 1 point Coach Fox is getting a new swimming pool It has a diameter of 18 feet and had a depth of 4 5 feet shown below 1204

Look at the similar cones below Which statement must be true 15 36 25 60 The ratio to their volume must be 25 144 The ratio to their volume must be 27 125 The ratio to their height must be 1 3 The ratio to there surface areas must be 125 728 1 point The scale factor of two prisms is 7 3 Which could be the two surface areas 14 sq in and 6 sq in 147 sq in and 27 sq inches 49 sq in and 18 sq in 343 sq in and 27 sq in

By using C continuity combine two cubic B zier curve using 0 0 1 2 1 4 and 0 6 as control points for the first curve and 2 6 4 3 and 3 0 as the remaining control points of the second curve Calculate the first control points of the second curve

YZ is tangent to OX What is the value of x Y 2x 4 38 Z

Q3 Calculate the side or angle marked with a letter 11 51 2 9 31 Q4 B D D A 90 C D 32 4 B A 41 and AD 100 cm Calculate a the length of AB b the length of DC c the length of BD B A 32 4 100 cm 41 L

NAME Perimeter Problems page 2 of 2 3 Jacob and his dad are going to make a rabbit pen in the backyard They have 16 feet of fencing Help Jacob draw some plans Sketch and label at least 4 different rectangles with a perimeter of 16 centimeters on the centimeter grid paper below Write an equation under each sketch to show that the perimeter is actually 16 centimeters Put a star beside the sketch you think would be best for a rabbit pen 20 Op H

4 Using the function f x x 4 3 write a new equation for each transformation Each part is a new problem a Translated up 3 units b Shifted left three units c Opens down e The new vertex is located at 3 2 d Vertically stretched with a scale factor of 3 f Opens down shifted right 2 units shifted down 4 units

5 Let ABCD be a square of area 1 Let X Y Z W be random points on AB BC CD DA taken uniformly and independently of each other Let S be the area of the quadrangle XYZW D C We A Z a Find the expression of S in terms of X Y Z W Y B

e 5 Rewrite the equation of the given function in graphing form State the vertex a f x x 4x 6 b c f x x 4x 1 g x 2x 8x 7 d f h x 3x 18x 23 g x x 2 x 4 f x 2 x 3 x 4

3 Write an equation for the graphs in graphing form y a Equation 1 2 3 3 6 b NU d T 7 7 7

2 Use y x 4x 7 for the following questions a Write the equation in graphing form b Name the vertex and intercepts

M2 Chapter 9 1 Circle ALL the attributes that match the graph of f x 7 x 3 5 A vertex 3 5 F opens up B vertex 3 5 G opens down C vertex 3 5 H axis of symmetry at y 5 D wider than y x I axis of symmetry at x 3 E narrower than y x J no y intercept K y intercept at y 68 L y intercept at y 5 M no x intercept N x intercept at x 68 O x intercept at x 5 1

8 Express the quadratic in vertex form y x 20 9x

9 Write the term needed to create a perfect square trinomial m b p 6x a 81

y intercept axis of symmetry x intercepts solutions 4 Write the equation of the axis of symmetry REVIEW Equation y a x h k Vertex The turning point of a parabola Axis of symmetry The line that cuts the parabola into two symmetric pieces the x value of the vertex written as x vertex se the information above to answer the following questions given the graph below 1 What is the vertex of the parabola 2 How many solutions are there 0 1 2 3 3 What are the roots write as a coordinate point 5 Determine the equation in vertex form Roots solutions zeros x intercepts the x values where the parabola meets the x axis and y 0 6 5 4 3 2 0 5 6 B

f x x 6 142 f x x 6 34 f x x 6 38 f x x 6 34 Show all work

6 Determine the vertex and axis of symmetry o the graphed quadratic ertex 4y Axis of Symmetry

7 Write the equation that represents the graph 7 6 S 4 3 2 7 6 5 4 3 2 1 1 13 4 5 6 1 2 3 4 S 6 7

A steep mountain is inclined 68 from the horizontal and rises to a height of 3200 ft above the surrounding plain A cable car is to be installed running from a point 930 ft from the base of the mountain to the top of the mountain The shortest length of cable places You can round the distance from the top of the mountain to its base to 5 3 additional decimal places or use the Ans feature on your calculator ft Round the final answer to 2 decimal

3 Solve for x 5 20 IM2 20 22 Kuta Software LL C Test Similarity Find the missing length indicated 1 K X 16 10 25 4x 2 x 8 10 5 X 8 16 5 CX 8 12x 48 12 12 x 4 1 25 12 tho 10 5X 40 16 27 30 X 4875 145 91 40 Kate Spia 120 AT Ale 50F5X XE S rights reserved 3 SASCH 2 4 6 Name Guisom Ahmadal 4x y V 4 20 34 15 15 GX 35X 8e 35 21 9x 2 20 9x 2 12 25x 296 25 25 X 8 225 904x41 255 36X19 15 Period 20 21x3c9x 2 21 54 12 321 54 32 X 6 216 36x 36 36 35 140 20x 20 20

A bag contains eight red marbles and four blue marbles You randomly pick a marble and then pick a second marble without returning the marbles to the bag The first marble is red and the second marble is blue Determine if this scenario involves independent or dependent events O Independent Events

one marble from the jar After you put that marble back in the jar you randomly draw a second marble Use this information to answer the questions Round your answers to the nearest tenth of a percent Do NOT include the percent symbol Question 7 2 pts What is the probability that you draw a blue marble first and a red marble second Question 8 2 pts

answers to the nearest tenth of a percent Do NOT include the percent symbol Question 9 2 pts What is the probability that the spinner stops on purple first and red second Question 10 2 pts

There are 4 green 10 red and 6 yellow marbles in a bag You choose a marble without looking put it aside and choose another marble without looking Find the probability that you choose a red marble followed by a yellow marble Express all probabilities as simplified fractions

A bag holds 4 white marbles and 2 blue marbles You choose a marble without looking put it aside and choose another marble without looking Find the probability that you choose a white marble followed by a blue marble Express all probabilities as simplified fractions

A die has the numbers 3 5 6 8 10 and 12 on its faces You roll the die twice What is the probability that you roll an odd number on both rolls Enter your answer as a simplified fraction

4 5 9 CHAPTER 12 Find the volume of the figure Round your answer to two decimal places if needed 1 Quiz 2 18 cm 3 cm 14 in 12 ft 24 cm 4 cm 50 m 9 217 9 21 8 12 1005 3 8A V 6 0 12 2412 74 6 in 30 m 8 cm 4 cm

Find the perimeter of polygon ABCDE A E 1 04 9 CON 8 7 6 5 4 32 1 10 9 8 7 6 5 4 3 2 1 1 2 3 34567890 4 5 6 8 9 1 0 D B 1 2 3 4 5 6 7 8 9 10 C X

Find the measure each shaded Central Angle A B 9 120

21 L 18 14 X 20 Q 12 R The polygons are similar Find the value of x

x E X 20 D 16 F 15 H 18 G 12 J The polygons are similar Find the value of x

c46 N 8 M Find the scale factor of the figures Then list all pairs of congruent angles AABC ALMN k B ZAZ ZB Write the ratios of the corresponding side lengths in a statement of proportionality

Given the circle below with secant YXW and tangent VW find the length of YX Round to the nearest tenth if necessary Y X 15 7 W

2 Find the solutions to the quadratic below using completing the square x 10x 4 0

Proving the First Case of the Inscribed Angle Theorem Given AB is the diameter of a circle and is one side of the angle that intercepts AC Prove mzABC is half the measure of AC 180 2x B You can draw line segment CD by the unique Since the triangle isl x D Triangle BCD is isosceles since BD and CD are both circle and all radii of a given circle are congruent EFO x A postulate of the its base angles are congruent

4 ERROR ANALYSIS Describe and correct the error in solving x 8x 10 by completing the square X x 8x 10 x 8x 16 10 x 4 10 x 4 10 x 4 V 10