Geometry Questions

If tan 0 2 a sin 20 3 0 3r find the exact value of each of the following 2 0 2 c sin b cos 20 c sin a sin 20 Type an exact answer using radicals as needed 0 2 b cos 20 Type an exact answer using radicals as needed 0 2 Type an exact answer using radicals as needed d cos 2 Type an exact answer using radicals as needed d cos

Question 3 25 points Hamilton Circuits Paths Which of the below descriptions shows a possible HAMILTON PATH EFADECBA FECBAD ADEFBC ADECBAFE A D F E C B

Simplify the logarithmic expression Express powers as factors log 5z7 log 5z Type an exact answer in simplified form

Hamilton Circuits Paths Which of the following is a Hamiltonian Circuit beginning at vertex A for the given graph ABCDA ACBDA ADBCA all of the above Question 3 25 points D A C B

Question 1 25 points Hamilton Circuits Paths Which of the below descriptions shows a possible HAMILTON CIRCUIT ADFECGBA ADFECBG ADFABGDECBA A D F E C B G

Rewrite cot 8 sec 0 in terms of sine and cosine cot 0 sec 8 Simplify your answer

Information is given about a polynomial f x whose coefficients are real numbers Find the remaining zeros of f Degree 4 zeros i 14 i The remaining zero s of f is are Use a comma to separate answers as needed

78 Name 2 At Pizza Pie Heaven a large pizza has a 16 in diameter and is cut into 8 equal slices Per What is the approximate length of the arc formed by the crust of one slice Be sure to show your work

Cuestion 3 Write the equation of each circle below in circle form Iden the center and radius Practice at least 1 of these a x 10x y 2y 20 0 b x 8x y 2y 8 0 c x 12x y 20y 8 0

Quiz 2 Target 78 Name 78 Calculate measurements of arcs sectors and circles using degrees and radians NM PT AT 1 Three friends bought a giant cookie cake and divided it into equal parts so that each of them got 1 piece The Cookie cake has a radius of 13cm Find the area of each person s piece Be sure to show your work 360 120 3 Per

120 B O 112 E A D C N What is the value of z O 52 O 104 O 116 O 208

9 F 10 8 B 2 15 3 G 16 11 12 14 17 21 13 18 20 4 6 19 C 5 D E Given G is the center of the circle AD is a diameter mAB 78 mFE 105 mED 27 mCD 42 m 1 m 2 m27 m 8 m 9 m 10 m 11 P D m 19 m 20 m 21 All Things Algebra 2015

54 32 D 4 1 112 Marcel is designing a circular necklace that will consist of 4 sections each with a different color of plastic Determine how he needs to cut the plastic by finding the measures of the angles m21 m22

or angles formed by two intersecting chords 1 The intersecting chords form vertical angles If mZDEB 105 then mZAEC 105 2 Find the sum of the angle measures mZDEB mZAEC 210 0 3 Find the sum of the arc measures mBD MAC Correct 0 mZDEB 105 mZAEC 105 mAC 130 mBD 80 B E C

Explore the properties of angles formed by two intersecting chords 1 The intersecting chords form vertical angles If m2DEB 105 then mZAEC 105 MIDA C 2 Find the sum of the angle measures mZDEB m2AEC D mZDEB 105 m ZAEC 105 B A C

Words to Know Write the letter of the definition next to the matching word as you work through the lesson You may use the glossary to help you A arc chord inscribed angle intercepted arc tangent to a circle Central Angles anangle whose vertex is on a circle and whose sides are chords B an arc in the interior of an angle that has its endpoints on the angle C a part of a circle between two given endpoints D a line line segment or ray that intersects a circle at exactly one point and contains no points inside the circle E a segment with both endpoints on a circle

C O A UU Which segment is both a chord and a diameter segment

Directions Determine whether a permutation or combination can be used Then solve 19 Three cards from a standard deck of 52 cards are chosen at random What is the probability that all three cards chosen are hearts 21 If the 3 digit security code on the back of a credit card using the digits 0 9 has no repeating digits what is the probability that the code does not contain any numbers less than 52 20 Marissa has a 50 20 10 5 and 1 bill in her wallet She takes the bills out and randomly line them up What is the probability that the first bill is greater than 5 22 There are twelve seniors and eight juniors on the prom committee If two students are chosen at random to decide on decorations what is the probability that one is a senior and one is a junior

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