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EOCT Review- Unit 1

Find the center of dilation for the diagram below.

2. a) (0,2) b) (4,2) c) (0,0)

d) (6,4)

Find the center of dilation.

3.

4. Tell if the following scale factors make the image larger or smaller than the preimage.

2 ___________14 ___________

52

____________ .27_______________

5. Perform a dilation of 2 on the following figure, using the origin as the center of dilation.

6. Perform a dilation of 12 on the following

figure, using the origin as the center of dilation.

7.

8. For similar figures, corresponding angles are ______________ and corresponding sides are _________________.

9. Explain why the following two triangles are similar.

10.

∆ ABC ∆ XYZ . If m< A=500, m<Z=30°, AB=12 , XY =8 , YZ=10 ,∧AC=21 , find the following measures.

m<Y =¿¿ BC=_______________

m<C=¿¿ XZ= _______________

11.

A piece of a proof is given provided the diagram. Choose the missing justification.

12. A piece of a proof is given. Choose the missing justification.

13. What’s the difference in two figures being similar and two figures being congruent?

14. What are the four patterns that we studied that are sufficient in showing two triangles are congruent?

15. Mark up the diagram as you read through the proof. Which pattern should from #14 should go in the blank?

16. What does CPCTC stand for? What does it allow you to do?

17.

18.

19.

20.

If m<1=41° , find the measure of the other three angles.

21.

ABCD is a parallelogram. If CD = 24, AE = 11, and m< ADC=72°, find AB,AC, m<DCB ,∧m< ABC .

E

22.

If the lines that appear parallel are, write in the measure of all eight angles provided that x = 112o

23. Name two pair of alternate interior angles.

Name four pair of corresponding angles.

24.

Find the value of x.

What is the relationship of AC and DC ?

25.

26. Find x.

27. Find x.

28.

Other than measure, what else does TS and AC have in common?

29. ABCD is a rectangle.

If AC= 24, find BD and BR.

zw z

v

u z

t z s

30.

EOCT Review- Unit 2

31.

32.

33.

Using the diagram above, find the following:cosC=__________ sinC=_______________

tanA=__________ sinA= _______________

tanC=__________ cosA= ______________

34.

35.

36. <A and < B are complementary angles.

sinA=45 . cosB=¿¿

37. sin 33=cos ¿

sin ¿cos82

38.

39.

40. If sinθ= 941 , find cosθ and tanθ by drawing

your own triangle.

41. Find sinF in the diagram below.

EOCT Review- Unit 3

42. True or False: All circles are similar.

43.

AB is a radius and AC is a tangent. Find x if

m<BAC=(2 x−40 )°

44. Using the diagram from #43 to find the circumference and area of the circle if AB=9 meters.

45.

In the circle above, D is the center. If m< ADC=102°, find m AC and m< ABC.

46.

Find m AB if m< ABC=71°.

F

A

B

C

47.

If m AE=44°∧m CD=38° ,find m< ABE.

48.

If m AD=160°∧m AC=70° , find m<B .

49. Find the value of ?.

50. Find the value of x in the diagram below.

51. Find m<SPQ in the diagram below.

52. Find the value of ? in the diagram below.

53.

In the diagram below, find EC if AB=10 ,BC=12 ,∧CD=11.

54.

Find the value of AB if BC= 10 and CD=9.

55.

In the diagram above, find m<A if m<B=92° and m<C=85° .

56.

57.

58.

59.

60.

61. In the diagram below, if x= 42° and the diameter of the circle was 10 inches, find the area of the shaded sector.

62. Let x represent the length of the arc of the shaded region in the diagram below. Find x and the area of the shaded sector.

63. How many radians is 45 degrees?

64. How many degrees is 32

π radians?

65. Identify the right angle in the diagram and explain why it has to be a right angle.

66.

67. What does B stand for in the formula for the volume of a prism? (V =Bh)?

68. Find the volume for the cone pictured below.

69. Find the volume of a sphere that has a radius of 9 feet.

70. Find the volume of each cylinder.

71. Find the volume of the pyramid pictured below.

71.

72. To construct the following circle, what do you first construct from each vertex?

a) angle bisector b) perpendicular bisector

c) parallel line d) median

73. To construct the following circle, what do you first construct on each side of the triangle?

a) angle bisector b) perpendicular bisector

c) parallel line d) median

EOCT Review- Unit 4

74. When you add, subtract, or multipy a rational number(except zero) and a rational number together, the answer is always what kind of number?

75.

76.

77.

78.

79. Convert the following expressions containing rational exponents to radical form.

x52=¿¿

913 =¿¿

y47 =___________________

80. Convert the following expressions that contain radicals to rational exponent form.

5√ x=_____________________

4√93=¿¿

√ y9=¿¿

81. Simplify the following using exponent rules.

x2 ∙ x7=¿¿

8 x4 y2

12 x2 y5 =¿¿

(9 x3)2=¿¿

x−4=¿¿

100=¿¿

82. Simplify the following expressions containing radicals.

√24=¿¿

√ 925

=¿¿

3√5

=¿¿

√80−√45=¿¿

83. Simplify the expression containing rational exponents.

84. Simplify. Make sure your answer has positive rational exponents.

85.

86.

87.

88.

89.

90. Add, subtract, or multiply the following polynomials.

(7 x2−9 x−5 )+ (−2 x2−9 x+7 )

(−4 x2−3 x−9 )−(2 x2+19 x−2 )

(9 x−1)(4 x+5)

91. Find the perimeter and the area of the rectangle pictured below.

92.

93.

94. Evaluate each small power of i.

i0=¿¿

i1=¿¿

i2=¿¿

i3=¿¿

95. Using the previous problem as a guide, evaluate these larger powers or i.

i95=¿¿

i202=¿¿

i576=¿¿

i899=¿¿

_______________________________________96. Add or subtract the following expressions containing i.

(8−3 i )+ (2−9 i )=¿¿

2 i+ (7−2 i )+ (−4+3 i)=¿¿

(9−6 i )−(5+3 i )=¿¿

5 i−(4+2 i )−(3−9i )=¿¿

97. Simplify the following expressions by converting i2 to -1.

8−7 i+10 i2= _______________________

−14+12i−i2=¿¿

98. Multiply the following complex numbers.

(3−9 i ) (5−i )=¿¿

2 i (8+6 i )=¿¿

EOCT Review-Unit 5

99. Factor the following expressions.

9 x2+27 x

4 x2−81

x2+9 x+20

4 x2+4 x−3

100. Solve the following quadratic equation using factoring.

x2+10 x=24

101.Solve the following equation using the quadratic formula.

2 x2−x−4=0

102. Solve the following quadratic equation using any method.

5 x2+8 x=4

103. Solve the following quadratic equation that has complex solutions.

x2=−x−3

104.

How many solutions does the equation graphed above have? What is/are the solution(s)?

105.

How many solutions does the equation graphed above have? What is/are the solution(s)?

106.

How many solutions does the equation graphed above have? What is/are the solution(s)?

107. Solve using square roots: 9 x2+16=0

108.

109.

110. List the terms, degree, and coefficients of the expression. 8 x2+10 x−17

111.

112. Find the zeros of the quadratic function.

f ( x )=x2−7 x−18

113. Find the zeros of the quadratic function.

f ( x )=2(x−4 )2−10

114. Find the vertex in the quadratic functions.

f ( x )=2(x+7)2−5

f ( x )=−3 (x−1 )2−2

115.

116.

117.

118. Solve the following system of equations involving a line and a parabola.

119. Find the average rate of change for the function f ( x )=x2−9x−10 between -1 and 3.

120.

121.

122.

123. Using the graph, where does the solution to the system of equations appear to be?

124. Find the average rate of the quadratic function using the table.

125. Classify the following functions as odd,even, or neither.

f ( x )=7 x4−9 x2+11_________________

g ( x )=8 x−10 x5______________________

h ( x )=12 x3+x2−11 x−10____________

126. Put the types of sequences in order from largest to smallest if the sequences are allowed to be carried out far.

Exponential Linear Quadratic.

127. Write the first five terms of the sequnence whose explicit rule is f ( x )=2 x2−9 x+1.

128. Write out the gaps between the terms in your answer from #127 and write down the pattern you notice.

129.

130.

131.

132.

133.

134. The function f ( x )=−16 t2+64 t +5 models the height of a ball that was hit into the air, where t is measured in seconds and h is the height in feet. For how long will the ball be in the air?

135.

136.

137. Which explicit expression matches the sequence 2,11,26,47,…..

a) f ( x )=x+9 b) f ( x )=9 x−7

c ¿ f ( x )=3 x2−1 d) f ( x )=3x−1

138.

139.

140.

141.

142.

143.

Which function BEST models the graph above?

a) f ( x )=−x2+4 b) f ( x )=x2+4

c) f ( x )=x+4 d) f ( x )=−x+4

EOCT Review- Unit 6

144. Write the equation of a circle whose center is (-1,2) and whose radius is 5.

145. Graph the circle from #144.

146. What is the center and radius of the circle whose equation is (x−4)2+( y+3)2=49 ?

147. What is the center and radius of the circle whose equation is x2+4 x+ y2−8 y+19=0?

148.

149.

150.

151. Write the equation of the parabola whose focus is (-2,1) and whose directrix is x=2.

152.

153. Solve the following system of equations.

154. Find the distance between the points (-2,3) and(4,1) using the distnace formula.

155. Find the midpoint of the segment whose endopoints are (-2,3) and (4,1) using the midpoint formula.

EOCT Review- Unit 7

156.

Use the table above to find the probability of owning a car GIVEN that the student is a senior.

157. Using the same table, find the probability of being a junior GIVEN than the student does not own a car.

158. In a certain town, the probability that a person plays sports is 65%. The probability that a person is betweent he ages of 12 and 18 is 40%. The probability that a person plays sports and is between the ages of 12 and 18 is 25%. Are the events independent? How do you know?

159.

Let W= the set of characteristics of whales and F= the set of characteristics of fishes. List the characteristics in each set listed below.

W ∩ F=

F '=¿

W '∪F '=

160. In Mr. Mabry’s class, there are 12 boys and 16 girls. On Monday, 4 boys and 5 girls were wearing white shirts. A student is chosen at random. What is the probability that the student is a boy or is wearing a white shirt?

161. Staying with Mr. Mabry’s class, what is the probability that a student is a girl or is not wearing a white shirt?

162. A number cube containing the numbers 1 through 6 is rolled TWICE. What is the probability that the sum of the rolls is a prime number given that one of the rolls is a 3?

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171.