Review – Unit 1 Milestone Geometry Name ____________________________________Date __________________________ Period ____

Fill in the following blanks to complete the proofs.

1. Given: ∠ A≅∠E , AB≅ BE

Prove: ∆ ABC ≅∆ EBD

2

.

3. Given: ∠EDG≅∠FDH

Prove: m ∠1 = m ∠3

4. Figure A’B’C’ is a dilation of figure ABC 5. Which transformation results in a figure that is similar to

by scale factor of 13 . The dilation is centered at (4, 4). to the original figure but has a larger area?

a. a dilation of ∆ QRS by a scale factor of 0.5

b. a dilation of ∆ QRS by a scale factor of 12

c. a dilation of ∆ QRS by a scale factor of 1.5 d. a dilation of ∆ QRS by a scale factor of 2

Which statement is true?

Statements Reasons∠ A≅∠E GivenAB≅ BE Given∠B≅∠B a.∆ ABC ≅∆ EBD b.

Statements Reasons∠EDG≅∠FDH Givenm∠EDG = m∠FDH a.m ∠EDG = m ∠1 + m ∠2m ∠FDH = m ∠2 + m ∠3

b.

m∠1+m∠2 = m∠2+m∠3

c.

m∠1 = m∠3 d.

a. ABA ' B' =

B' C '

BC b.

ABA ' B' =

BCB' C '

c. AB

A ' B' =BC

D' F ' d. ABA ' B' =

D' F '

BCSolve for the missing variables and classify the quadrilateral.

6. x = ___________ 7. x = ___________

y = ___________ y = ___________

Classify: ___________________________________ Classify: ________________________________

8. 9. x=¿ ___________ x=¿ ___________

y=¿ ___________ y=¿ ___________

Classify: ____________________________________ Classify: ____________________________________

10. Answer the following questions with:ALWAYS, SOMETIMES, or NEVER

11. ____________________ A trapezoid has 2 congruent angles.

x=¿ _________ y=¿ ___________ z = ___________ 12. _____________________ A rhombus is a square.

Classify: ____________________________________ 13. _____________________ A square is a rhombus.

14. Dilate the line y=2 from the point (0, -1) with a 15. Use the following points and scale factor to dilate scale factor of k=3. the figure.

A = (0, -3)

B = (9, 9)

C = (-6, 3)

k=13

16. Triangle FGH was reflected across the x - axis to 17. In the diagram, ∠J ≅∠K and ∠O≅∠L.to form triangle F’G’H’. Triangle F’G’H’J’ wasthen reflected about the y - axis to obtaintriangle F”G”H”.

Which additional information is sufficient to prove that ∆ JOM is congruent to ∆ KLN?

a. NM ≅ MLb. PN ≅ PM

Which statement is true? c. ON ≅ LMa. The figures are both similar and congruent. d. JP≅ PM Answer: ___________b. The figures are neither similar nor congruent.c. The figures are similar but not congruent.d. The figures are congruent but not similar.

Answer: ___________

18. Which triangle congruence theorem can be used 19. Which triangle congruence theorem can be usedto prove these triangles are congruent? to prove these triangles are congruent?

Answer: ___________ Answer: ___________

The following figures are similar. Set-up a proportion and solve for x.

20. 21.

22. 23.

24. 25.

26. In the triangles shown, ∆ ABC is dilated by a factor 27. Write an algebraic expression to represent the

of 14 to form ∆ XYZ. Total angle measure inside the kite.

Given that m∠ A=45º and m∠B=95º, what is ∠Z ?Answer: _______

28.

x = __________

29. Dilate the line y=3 from the point (0, -2) with a 30. Use the following points and scale factor to dilate scale factor of k=2. the figure.

A = (0, -4)

B = (8, 0)

C = (4, -8)

k=14

Unit2Find the value of each variable.

1. 2.

x = _________ x = _________

y = _________ y = _________

Describe and correct the error in finding the length of the hypotenuse.

3. 4.

5. Complete the table.

Find the value of x.

6. 7.

x = _________ x = _________

Complete the table.

8.

9. sin ∠X = ______________ cos ∠X = ______________

sin ∠Y = ______________ cos ∠Y = ______________

sin ∠L = ______________ cos ∠L = ____________

sin ∠M = ______________ cos ∠M = ______________Find the value of each variable. Round decimals to 4 places.

10. 11. 12.

a = ___________ c = ___________ x = ___________

b = ___________ d = ___________

13. Quadrilateral LMTP is an isosceles trapezoid.

What is the length of LP ?

Find the value of each variable. Round decimals to 2 places.

14. 15.

16. Andre uses an angle-measuring device on a 3-foot tripod to find the height, h, of a weather balloon above groundlevel, as shown in the diagram below.

The balloon is at a 40º angle of elevation. A radio signal from theballoon tells Andre that the distance between the tripod and the balloon is 15,000 feet.

Write the equation in terms of height and find the height of the balloon.

17. Use the diagram of a cone to answer the question.

The base of the cone has a radius of 6 cm.

What is the slant height, in cm, of the cone?

18. Find the area. 19. Find the perimeter.

20. The Triangle UGA is a right triangle.What is the best approximation for m∠U?

21. In right triangle ABC, angle A and C are complementary angles. The value of tan C = 3512 . What is the value of sin A?

22. In a right triangle HJK, ∠J is a right angle and sin ∠H = 12 .

What is true about the cosine of K?

Unit 3a

Name the following parts of the circle:

1. Chord 2. Tangent Line 3. Radius4. Secant 5. Center 6. Diameter

7. Point of Tangency

BE and CF are diameters of the circle ⊙A. Find the measure of the indicated arc.

8. m FE = _____________ 9. mCD = _____________

10. m BF = _____________ 11. mCF = _____________

12. mCFD = ____________ 13. m EBC = ____________

14. mCE = _____________ 15. m BDF = _____________

16. AB and CB are both tangent to circle ⊙D.AB = 3x – 7 and CB = 8x + 3Find the value of x.

Find the measure of the indicated angle or arc in circle ⊙A.BC is a diameter of ⊙A, and m BE = 52, and m DF = 162.

17. m∠BDC = ___________ 18. m∠EDB = _____________

19. m∠BFE = ___________ 20. m∠DBF = _____________

21. m∠DGF = ___________ 22. m BDC = _____________

23. m EC = _____________ 24. m BFE = _____________

25. m∠CDE = ___________

Solve for the missing angle.

26. 27.

28. How many common tangents do two circles have if they are touching? How many tangents do two circles have if they are not touching?

3x - 7

8x +3

29. Draw each of these common tangent lines.

In the following circle, the 2 chords intersect at a right angle.m AE=53º and m BD=18.

30. m AB = ______________ 31. mCD = ______________

32. mCDE = _____________

33. Solve for x. 34. Solve for x.

35. Find the value of x. 36. Find the value of x.

Solve for the missing angle or arc measure.

37. 38. 39.

40.

CD = _____________

m DBC = _____________

Unit 3b

SHOW ALL WORK. WRITE IN PENCIL.Points will be deducted work is not in pencil or if work is not shown for EVERY problem needing work.

Use the following figure to answer questions 1-2.

1. Circumference of ⊙ A 2. Length of BC

Use the following figure to answer questions 3-10.In ⊙B, ∠ ABE≅∠DBE.

4. Length of AE 3. m AE = ___________

6. Length of DE 5. m DE = ___________

8. Length of ADE 7. m ADE = ___________

9. m AD = _______ 10. Length of AD

11. Find the length of the outer edge of the figure.

12. Find the area of a circle with a radius of 21 cm. 13. Find the volume of a sphere with a radius of 18 cm.

A small pizza has an area of 35π in2. The pizza is cut into 8 even slices. Find the following:

14. Radius of the pizza 15. Circumference of the pizza

16. Area of 1 slice of pizza 17. Length of crust on 1 slice

18. Find the area of the 2 sectors formed by ∠ ABC.

19. The diameter of a baseball is 3.25 inches. 20. If the radius of a sphere doubles, how does volume Find the volume of the baseball. of the sphere change?

21. The diagonal of the base in a square-based pyramid is 6√5 feet and the height of the pyramid is 6 feet. What is the volume of the pyramid?

For numbers 22, 24, and 26, solve for x. For numbers 23, 25, and 27, solve for the segment. 22. x = ______________ 23. PF = _______________

24. x = ______________ 25. SU = _______________

26. x = ______________ 27. UW = _______________

Unit 4a

Simplify each expression.

1. (−5 x4−3 x2+1 )+(2x2+8 x4+4) 2. (2m3+5 m4−9 m )−(12 m4−5 m3+3m)

Find each product.

3. −2 x4(x2+4 x+9) 4. (6 x+2 )(x−4)

5. (4 n−2 )2 6. (−2 x+6 )(−2 x+3)

Find the area of the following figures.

7. 8.

Find the perimeter of the following figure. Find the perimeter of a triangle twice as big as this one.

9. 10.

X+3

8x+4

X+3

3X+2

Find the volume of the following figure.11. 12. The box below has a volume of

V=60 x3+48 x2−12 x. What is the height of the box?

13. Fill in the area model to find the area. 14. Fill in the dimensions of the area model.

__________ __________

______

Write each of the following as an imaginary number.

15. √−225 16. √−324

Fill in the following chart.

17.

2X+1

X+4

3x+1

x

3x + 3

8

5x

6x

Simplify the following imaginary numbers.

20. −3−9 i+7+9 i−4+8 i 21. 8+2 i−(9−7 i )−(−4+4 i)

22. (−4 i )3 23. (4 i ) (−3 i )(4+i)

24. If r=2+4 i and s=3−i, 25. If m=7+2i and n=5−i, what does r2−s equal? what does (m+n )2 equal?Unit 4b:

1. Which expression has a value that is a rational number? a. √11+16b. 4 (√5+√7 )c. √16+√4d. √5+0 Answer: ____________

2. Which statement is true about the value of (√7+4 ) ∙ 3 ? a. It is rational because the product of two rational numbers is rational. b. It is rational because the product of a rational number and an irrational number is rational.c. It is irrational because the product of two irrational number is irrational.d. It is irrational because the product of an irrational number and rational number is irrational.

Answer: ____________3. Let a be a nonzero rational number and b be an irrational number.

Which of these MUST be a rational number?

a. b+0b. a+ac. a+bd. b+b

Answer: ____________

4. Which expression is equivalent to √32−√8 ? 5. Which expression is equivalent to √ 1627

?

a. 2√2 a. 4 √33

b. 2√33

b. 6√2

c. 2√6 c. 3√34

d. 4 √39

d. 2√10Answer: ____________ Answer: ____________

Simplify the following radicals.

6. 4√625 x6 y−2 z4 7. 3√729 a2 b−4 c15

Simplify the following radicals.

8. 2√5+3√45+3√45−√25 9. 2√5 (√30−3√5 ) 10. (−√3 ) (4 √2 ) (2√3 )

11. (3+2√6 ) (1−4√3 ) 12. 2+√14

√313.

25−√3

Rewrite the following radicals as exponents. Simplify if necessary.14. 5√m 15. 3√ x9 16. √√√3125

Rewrite the following exponents as radicals. Simplify if necessary.

17. m17 18. x

1512 19. (644 )

114

20. Which expression is equivalent to √xx3 ? 21. Which expression is equivalent to 3√64 x

67 ?

a. x52 b. √ x5 a. 4 x

27 b. 4 x

187

c. 1

√x5 d. 1

x√ x c. 64 x

27 d. 64 x18

Simplify. Your answer should only contain positive exponents.

22. (2 xy )4 ∙ x−3 23. u4 v3

4 u−3 v2 24. (uv3 )3

¿¿

25. 2 y74 ∙3 x

32 y

−32 26. (a−2

3 b12 )

32 27.

4√x ∙ 6√x3√x

Unit 5a:

SHOW ALL WORK. WRITE IN PENCIL.Points will be deducted work is not in pencil or if work is not shown for EVERY problem needing work.

Factor out a GCF from the following expressions.

1. 2 m3+40 m6 2. 3 x6 y2−6 y5+12 xy

Factor the following quadratic expressions using the Area Method3. x2+5 x+6 4. 3 x2+11 x+6

Solve the following quadratic equations by Factoring.

5. x2−5 x−14=0 6. 3 x2+14 x+15=0

Solve the following quadratic equations by Completing the Square.

7. x2+6 x−27=0 8. x2−4 x−32=0

Solve the following quadratic equations by using the Quadratic Formula.

9. 12 x2−8x−3=0 10. 3m2=−4+8m

Find the discriminant then tell how many and what kind of solutions the following quadratic equations have.

11. 4 x2−4 x+1=0 12. −7n2+6 n−2=3 13. x2−10 x+16=7

Tell how many and what kind of the solutions the following functions would produce.

14. 15. 16.

17. A bird in a tree dropped a worm 128 feet to the ground. The number of seconds, t , it took for the worm to reach the ground is modeled by this equation. −16 t 2+128=0 How many seconds did it take the worm to reach the ground?

18. A rectangle’s length is 5 m longer than it is wide. The area of the rectangle is 36 m2. Find the length and width of the rectangle.

19. Write and solve a quadratic equation given that the builder only has enough concrete to cover 60 square feet to find the width of the sidewalk.

Solve the following system of equations.

20. y=x2−6 x+11 y=−2 x+8

Unit 5b:

SHOW ALL WORK. WRITE IN PENCIL.Points will be deducted work is not in pencil or if work is not shown for EVERY problem needing work.

1. Convert the following function in to Standard Form. 2. Convert the following function in to Vertex Form.

f ( x )=−143

( x−3 )2+8 f ( x )=4 x2−16 x+4

3. Which function has a domain of Rand a range of y ≥−3 ? 4. Which function’s graph has its minimum value at x = 7?

a. y= (x+1 )2+3 a. y=−3 (x−7 )2+7b. y=−2 ( x+2 )2+3 b. y=5 ( x+7 )2+7c. y=3 ( x+1 )2−3 c. y=3 ( x−7 )2−7d. y=−4 ( x+2 )2−3 d. y=−5 (x+7 )2−7

5. Which function’s graph has an axis of symmetry of x = -3? 6. Which function’s graph is increasing on the interval (−∞,2 ) and decreasing on the interval (2 , ∞ )?

a. y=−3 (x−4 )2+5 a. y=−2 ( x−2 )2+5b. y=4 ( x+3 )2+5 b. y=5 ( x+4 )2+2c. y=3 ( x−5 )2−4 c. y=2 ( x−4 )2−2d. y=−5 (x+4 )2−5 d. y=−5 (x+2 )2−5

7. Solve the following System of Equations Algebraically.

y=x2+8 x−312

( y−2 )=x+1

8. Solve the following System of Equations Graphically.

y=x2−4 x−12 y=−4 x+4

9. Use this graph to answer the question. 10. Use this graph to answer the question.

Which function is shown in the graph? Which function is shown in the graph?a. f ( x )=x2+3 x−10 a.f ( x )= (x+4 )2+4 b. f ( x )=x2−5 x−8 b.f ( x )= (x+4 )2−4 c.f ( x )=x2−3 x−10 cf ( x )=−( x+4 )2−4. d.f ( x )=x2+x−12 d.f ( x )= (x−4 )2+4 For the following functions, describe the transformation(s) taking place from the parent function f ( x )=x2.

11. f ( x )=34

x2+4 12. f ( x )=−( x−2 )2

13. f ( x )=(x+4)2−3 14. f ( x )=5 x2

15. What is the end behavior of the graph of 16. Which statement BEST describes the graph of f (x+6)? f ( x )=0.25 x2−7 x−1

a. As x increases, f (x) increases. a. The graph is f (x) is shifted up 6 units. As x decreases, f (x) decreases. b. The graph is f (x) is shifted left 6 units.

c. The graph is f (x) is shifted right 6 units.b. As x increases, f (x) decreases. d. The graph is f (x) is shifted down 6 units. As x decreases, f (x) decreases.

c. As x increases, f (x) increases. As x decreases, f (x) increases.

d. As x increases, f (x) decreases. As x decreases, f (x) increases.

Write EVEN, ODD, or NEITHER, to describe each of the following functions.

17. 18. 19.

20. Which statement BEST describes the comparison of the function values for f (x) and g(x )?

x f(x) g(x)0 0 -101 3 -72 6 -43 3 -14 12 -2

a. The values of f (x) will always exceed the values of g(x ).b. The values of g(x ) will always exceed the values of f (x).c. The values of f (x) exceed the values of g(x ) over the interval [0 ,5 ].d. The values of g(x ) begin to exceed the values of f (x) within the interval [4 ,5].

Unit 6:

SHOW ALL WORK. WRITE IN PENCIL.Points will be deducted work is not in pencil or if work is not shown for EVERY problem needing work.

13. What is the equation of the circle with a center 14. What is the equation of the circle with a center at (-3, 6) and a radius of 4 in general form? at (11, -4) and a radius of 3√2 in standard form?

Convert the following equation into standard form, Convert the following equation into standard form.then answer the questions below. then answer the questions below.

x2+ y2+6 x−18 y−106=0 x2+ y2−2x−63=0

15. Standard Form: _____________________________ 16. Standard Form: _____________________________

17. Center: ___________________________________ 18. Center: ___________________________________

19. Radius: ___________________________________ 20. Radius: ___________________________________

21. Solve the following system of equations:

x2+ y2=40 y=−3 x

x y-2 -13-1 -10 41 -12 -133 -32

22. A circle is centered at the origin and has a radius of √17 units. A line has a slope of −4 and passes through the origin. At which points does the line intersect the circle?

23. A circle is centered at the origin and has a radius of 6 units. A horizontal line passes through the point (6, 0). In how many places does the line intersect the circle?

24. A circle is centered at the origin and has a radius of 3 units. A vertical line passes through the point (3, 0). In how many places does the line intersect the circle?

25. A circle is centered at the origin and has a radius of 4 units. A horizontal line passes through the point (0, 4). In how many places does the line intersect the circle?

Unit 7:SHOW ALL WORK. WRITE IN PENCIL.Points will be deducted work is not in pencil or if work is not shown for EVERY problem needing work.

Let set A be the names of kids who own a PS4.Let set B be the names of kids who own an Xbox1. Let set C be the names of kids who own a WiiU.

1. Find A ∩C2. Find B∪C .3. Find ( A∪C) '.

4. The set A ∩ B represents ____.5. The set B∪C represents ____.

A random survey was conducted about gender and eye color. This table records the data.

6. What is the probability that a randomly selected person has brown eyes, given that the person selected is female?

7. What is the probability that a randomly selected person is male, given that the person has hazel eyes?

8. Which of the following events are independent given P ( A ) , P ( B ) , and P( A∧B)?a. P ( A )=0.48; P (B )=0.25; P ( A∧B )=0.13

b. P ( A )=0.08; P (B )=0.2; P ( A∧B )=0.012c. P ( A )=0.6; P (B )=0.2; P ( A∧B )=0.35d. P ( A )=0.9; P (B )=0.3; P ( A∧B )=0.27

9. In a certain school, the probability that a student plays a sport is 55%. The probability that a student is a Senior is 28%. The probability that a student plays a sport and is a Senior is 15%. Are the events independent? How do you know?

10. In a particular state, the first character on a license plate is always a letter. The last character is always a digit from 0 to 9. If V represents the set of all license plates beginning with a vowel, and E represents the set of all license plates that end with an even number, which license plate belongs to the set V ∩ E ' ?

a. U23 PC6 b. LG4 3F8 c. ER8 8X5 d. H7M Z54

11. Assume that the following events are independent: The probability that the Braves won both games in a double header is 0.31. The probability that the Braves won the first game of the double header is 0.71.

What is the probability that the Braves won the second game, given that the Braves won the first game? a. 0.34 b. 0.40 c. 0.44 d. 0.22Use the following chart for questions 12 and 13.

12. What is the probability that a card is a king, given that the card is not a heart?

13. What is the probability that a card is a heart, given that the card is a face card?

In the movie X-Men Days of Future Past, there are 10 men and 6 women. Of these people, 8 men and 5 women are mutants.14. If a person is chosen at random from the group, 15. If a person is chosen at random from the group, what is the probability of choosing a woman or what is the probability of not choosing a mutant or a male mutant? a man?

Joe has a number cube with sides labeled 1 through 6. He rolls the number cube twice.16. What is the probability that the sum of the two rolls 17. What is the probability that the sum of the two rolls is an even number, given that at least one of the rolls is a composite number or at least one of the rolls is is a 6? a 5?

19. Each letter of the alphabet is written on a card using a red ink pen and placed in a container. Each letter of the alphabet is also written on a card using a black ink pen and placed in the same container. A single card is drawn at random from the container. What is the probability that the card has a letter written in black ink, the letter K, or the letter D?

For problems 20-22, use the following sets. Let A={2 , 3 , 4 , 5 ,6 ,7 }, B={prime numbers∈theinterval [5,10 ]}, and C={5 ,6 , 7 , 8 ,9 ,10 }.

20. Find A∪B . 21. Find B∩ C. 22. Find A ∩C.

23. A bag contains 8 red balls and 7 yellow balls. You randomly draw one ball, replace it, and randomly draw a second ball. What is the probability that the first ball is red and the second ball is red?

24. You write each of the letters of the word MISSISSIPPI on pieces of paper and place them in a bag. You randomly draw one letter, do not replace it, then randomly draw a second letter. What is the probability that the first letter drawn is an S and the second letter is an M?

25. A code consists of 2 prime digits followed by 2 different letters. What is the probability that the code is 73LY?