Honors Math 3 Recovery Packet Spring 2015

10

TRIANGLE PROOFS!

NOTICE~ All of the pictures are the same and we are trying to prove the same thing each

time but we will use different methods based on the givens!

Make no assumptions, only draw conclusions from what you are given!

1.) Given: ∆ABC with AC≅BC

CD bisects <ACB

Prove: ∆ACD ≅∆BCD

2.) Given: Isosceles triangle ABC with CA CB D is the midpoint of AB

Prove: ACD BCD

3.) Given: Isosceles triangle ABC with CA CB CD is the Altitude to AB

Prove: ACD BCD

A D

C

B

A D

C

B

A D

C

B

11

MORE TRIANGLE PROOFS!

1.)Given: BA bisects CD

AC⊥CD

BD⊥CD

Prove: ∆ACE≅∆BDE

2.) Given: BA≅DA

CA bisects ∡BAD

Prove: ∆CBA≅∆CDA

3.) Given: BC and AE bisect each other at D

Prove: ∆ABD≅∆ECD

D C

B

A

E

12

CPCTC

C_________________________________ P__________________________ of

C___________________________ T ________________________________ are C___________________________

You can use CPCTC AFTER you have proven two triangles are congruent

to get that any additional parts are congruent!

Examples:

#1: HEY is congruent to MAN by ______. What other parts of the triangles are congruent by CPCTC?

______ ______

______ ______

______ ______

#2:

CAT ______, by _____

THEREFORE:

______ ______, by CPCTC

______ ______, by CPCTC

______ ______, by CPCTC

#3:

Given: ARAC and 21

Prove: 43

M

A

N

Y

E

H

L

C

S

R

4 3

2 1

C

T P

A

R

A

13

#4:

Given: LNONLM and MNLOLN Prove: OM

#5

Given: BCAC and BXAX Prove: 1 2 #6

Given: 1 2 and 3 4

Prove: ZWXY

M

N O

L

C

X B A

1 2

4 3

W

X Y

Z

1

2 3

4

14

PROOFS WITH PARALLEL LINES AND

PROVING MORE THAN 1 PAIR OF TRIANGLES CONGRUENT

If you are given that two lines are parallel then you should always look for Alternate Interior Angles.

Draw Alternate interior angles:

Example:

1.) Given: AE bisects BD

AB∥DE

Prove: AC≅EC

2.) Given: ∡ABE≅ ∡CDE

AB≅CD

Prove: AD≅CB

Cent ra l Ang le Worksheet 06 Not e:

A minor ar c is less t han 180q ; a major ar c is great er t han 180q , you must use t hree point s t o name a major ar c. When only t wo point s are used t o name an arc i t must be a m inor arc but a m inor arc can be named using t hree point s. I n t he f igure below HK is a m inor arc but i t can a lso be ca lled HJK .

Given: ~P wit h JK = 50q & diamet er NJ Find t he measure of each arc: 1) HJ = 2) JK =

PN

H

J

K

50

3) HK = 4) HNK = 5) HNJ = 6) NHJ = 7) NKJ = 8) JKH = 9) NK = Using t he let t ers in t he above diagram, name: 10) 2 equal cent ra l ang les 11) 2 equal m inor arcs 12) Any 2 major arcs

Î

2

I nscr ibed Ang le Worksheet 20 1) BC = 42q , � 1 =

A

B

C1

Problem s 1 t hrough 10

2) BC = 63q, � 1 = 3) � 1 = 42q , BC = 4) � 1 = 37q , BC = 5) BC = pq , � 1 = 6) � 1 = hq , BC =

7) � 1 = (7x + 3)q, BC = (15x + 1) q , x = 8) BAC = 242q , � 1 = 9) BAC = sq , � 1 = 10) � 1 = pq , BAC =

11) � 1 = 24q , BD = 124q, � 2=

A

B

C

D1

2

Problem s 11 t hrough 14

12) � BAD = 62q, BC = 24q, � 2= 13) BC : BD = 2: 5 , � 1 = 14q , � 2 =

14) � 1 = (x + 5)q , � 2 = (3x – 8) q, BD = (9x – 16) q x =

Î

9

12-3 Practice B Sector Area and Arc Length

Find the area of each sector. Give your answer in terms of π and rounded to the nearest hundredth. 1.

2.

sector BAC _______________________ sector UTV _______________________ 3.

4.

sector KJL _______________________ sector FEG _______________________ 5. The speedometer needle in Ignacio’s car is 2 inches long. The needle

sweeps out a 130° sector during acceleration from 0 to 60 mi/h. Find the area of this sector. Round to the nearest hundredth. ____________

Find the area of each segment to the nearest hundredth. 6.

7.

_________________________________________ ________________________________________

8.

9.

_________________________________________ ________________________________________

Find each arc length. Give your answer in terms of π and rounded to the nearest hundredth.

10. 11.

_________________________________________ ________________________________________

12. an arc with measure 45° in a circle with radius 2 mi _________________

13. an arc with measure 120° in a circle with radius 15 mm _________________

12-3 Problem Solving Sector Area and Arc Length

1. A circle with a radius of 20 centimeters has a sector that has an arc measure of 105°. What is the area of the sector? Round to the nearest tenth.

_________________________________________

2. A sector whose central angle measures 72° has an area of 16.2π square feet. What is the radius of the circle?

________________________________________

3. The archway below is to be painted. What is the area of the archway to the nearest tenth?

_________________________________________

4. Circle N has a circumference of 16π millimeters. What is the area of the shaded region to the nearest tenth?

________________________________________

Choose the best answer.

5. The circular shelves in diagram are each 28 inches in diameter. The “cut-out” portion of each shelf is 90°. Approximately how much shelf paper is needed to cover both shelves? A 154 in2

B 308 in2

C 462 in2 D 924 in2

6. Find the area of the shaded region. Round to the nearest tenth.

F 8.2 in2 H 71.4 in2 G 19.6 in2 J 78.5 in2

7. A semicircular garden with a diameter of 6 feet is to have 2 inches of mulch spread over it. To the nearest tenth, what is the volume of mulch that is needed? A 2.4 ft3 C 14.1 ft3 B 4.8 ft3 D 28.3 ft3

8. A round cheesecake 12 inches in diameter and 3 inches high is cut into 8 equal-sized pieces. If five pieces have been taken, what is the approximate volume of the cheesecake that remains? F 42.4 in3 H 127.2 in3 G 70.7 in3 J 212.1 in3

Trigonometry Self Check Exercises (Radians and Degrees)

Convert the following degree measure into radians 1. 30° 2. 60° 3. 90° 4. 180° 5. 270° 6. 360° 7. 36° 8. 45° 9. 70° 10. 22° Convert the following radian measure into degrees. 1. 2

π 2. 4

π− 3. 3

2π 4. 4

5π 5. 3

11π 6. 2

5π 7. 7

4π 8. π 9. π7 10. 9

5π

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Kuta Software - Infinite Algebra 2 Name___________________________________

Period____Date________________Exact Trig Values of Special Angles

Find the exact value of each trigonometric function.

1) tan

θ

x

y

60°

2) sin

θ

x

y

225°

3) sin

θ

x

y

90°

4) cos

θ

x

y

150°

5) cos

θ

x

y

90°

6) tan

θ

x

y

240°

7) cos

θ

x

y

135°

8) tan

θ

x

y

150°

-1-

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9) cos

θ

x

y

270°

10) tan

θ

x

y

225°

11) cos 270° 12) sin 0

13) cot

7

π

414) csc

2

π

3

15) csc 225° 16) sin 300°

17) csc 90° 18) tan 240°

19) sin

π

4

20) tan 120°

21) tan

−13

π

6

22) cos −630°

23) cos 990°24) csc

−31

π

6

25) csc

−5

π

626) cos

−17

π

3

27) sin

29

π

6

28) sec 945°

29) cos

−11

π

2

30) sin −2

π

-2-

1. A buoy in the ocean is bobbing up and down in harmonic motion. At time = 2 seconds, the buoy is at its high point and returns to that high point every 10 seconds. The buoy moves a distance from 3.6 feet from its high point to its low point. (hint: you decide what height represents sea level without the waves and continue accordingly). Draw a graph and write an equation that describes this motion.

a) How high is the buoy at time = 30 seconds? Is it rising or falling at that time?

b) How many times in the 2 minutes will the buoy be at sea level?

2. The inside of a bicycle wheel whose diameter is 25 inches is 3 inches off the ground. An ant is sitting on the inside of the wheel. Steve starts riding the bicycle at a steady rate. In 1.2 seconds the ant reaches its highest point on the wheel. The wheel makes a revolution every 1.6 seconds. Draw a graph and write an equation that describes the motion of the ant.

a) What will be the height of the ant 25 seconds into the ride?

b) Within the first 10 seconds, how many times will the ant be at its starting height?

3. John is bouncing up and down on a trampoline which is 4 feet off the ground. The highest he gets off the trampoline is 11 feet which he reaches in 2 seconds. He completes a bounce every 3 seconds. Draw a graph and write an equation that describes this motion.

a) In 45 seconds, what will be his height? Is he going up or down at this time?

b) Within the first 45 seconds, how many times does he reach his peak?

!

Trigonometry Worksheet 8

1. Given sin ✓ =

35 in quadrant II, find

cos ✓.

2. Given cos ✓ = �23 in quadrant III, find

sin ✓.

3. Given cos ✓ =

35 in quadrant IV, find

tan ✓.

4. Given sin ✓ = �67 in quadrant III, find

tan ✓.

5. Given cos ✓ =

14 in quadrant IV, find

sin ✓.

6. Given tan ✓ =

p3 in quadrant III, find

cos ✓.

7. Given tan ✓ = �1 in quadrant II, find

sin ✓.

8. Given sin ✓ = � 110 in quadrant IV, find

cos ✓.

9. Given cos ✓ =

12 in quadrant I, find

tan ✓.

10. Given cos ✓ = �25 in quadrant II, find

sin ✓.

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Graphing Quadratics in Vertex Form

If not in vertex form use completing the square to get in vertex form.

!

!!!

!!!

f(x)=(x - 4)2 - 3! f(x)=-(x - 1)2 - 3!

f(x)=2(x + 3)2 - 6! f(x)= -2(x - 1)2 - 2!

!!!

!!

f(x)= x2 + 4x - 5!

!f(x)= x2 + 4x + 7!

f(x)= 2x2 + 8x + 2!

!!

f(x)= 2x2 -12x + 9

9

9

Write an equation of each graph below in the form f (x) = a(x ! h)2+ k .

33. f (x) = 34. f (x) = 35. f (x) =

36. f (x) = 37. f (x) = 38. f (x) =

39. f (x) = 40. f (x) = 41. f (x) =

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Algebra 2 - Task 2.6ID: 1

Name___________________________________

Period____Date________________©X w2p0B1j3m 4KKuDtKaD zSmolf6tvwVa2rmea cLrLfCf.G y 8AMlnlh PrSiOgSh7tesk ur6eZsjeqrdvbebdt.9Solving Quadratics - All MethodsSolve using the Quadratic Formula - Level 2

1)

n2 + 9

n + 11 = 0 2)

5

p2 − 125 = 0

3)

m2 + 5

m + 6 = 0 4)

2

x2 − 4

x − 30 = 0

Solve using the Quadratic Formula - Level 3

5)

b2 − 12

b + 10 = −10 6)

6

r2 − 5

r − 4 = 7

7)

7

x2 − 16 = 6 8)

6

n2 − 10

n − 16 = 3

Solve using the Quadratic Formula - Level 4

9)

4

a2 − 22 = −10

a 10)

n2 − 45 = 12

n

11)

5

v2 − 2 −

v = −

v 12)

4

x2 − 5

x − 3 = 2

x2

Solve by Factoring - Level 2

13)

p2 + 6

p + 5 = 0 14)

k2 − 8

k = 0

15)

x2 − 7

x = 0 16)

a2 + 5

a = 0


17)

6

n2 + 5

n − 25 = 0 18)

2

x2 − 11

x − 21 = 0

19)

10

r2 + 75

r + 140 = 0 20)

60

m2 + 4

m − 160 = 0


21)

4

x2 − 17

x + 10 = −5 22)

2

n2 + 13

n + 19 = 4

23)

5

v2 + 3 = −16

v 24)

20

b2 − 40

b = 25

Solve by completing the square - Level 2

25)

a2 + 8

a + 11 = 0 26)

k2 − 14

k − 19 = 0

27)

n2 + 16

n − 17 = 0 28)

x2 − 20

x + 64 = 0


29)

x2 + 20

x + 70 = 6 30)

x2 + 12

x + 30 = −5

31)

7

n2 − 14

n − 73 = 9 32)

9

m2 + 18

m − 8 = 5


33)

6

x2 − 48 = −12

x 34) 3

p2 =

−12

p − 9

35)

5

n2 + 19

n =

3

n + 92 − 3

n2 36)

2

b2 + 17

b =

14 + 5

b

Honors Math 3 Recovery Packet Spring 2015

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