COMMON CORE MATH II NCFE EXAM REVIEW · C. Laila’s ramp is about 6 inches taller than Casey’s...

COMMON CORE MATH II NCFE EXAM REVIEW

Name: Date:

1. Lily designed the package below to hold the barsof soap she makes.

Lily’s Package

What is the shape of Lily’s package?

A. cone

B. pyramid

C. rectangular prism

D. triangular prism

2. Which figure is a right prism with a hexagonalbase?

A.

B.

C.

D.

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3. Which of the following figures does not have arectangular cross section?

A. right circular cylinder

B. right triangular prism

C. right square pyramid

D. right circular cone

4. A cube is shown below.

A cross section of the cube passes through exactly3 vertices.

Which of the following shapes represents the crosssection?

A. hexagon

B. pentagon

C. triangle

D. square

5. A triangular right prism is cut perpendicular to thebase. What is the shape of the cross section?

A. hexagon

B. rectangle

C. trapezoid

D. triangle

6. An isosceles right triangle is placed on acoordinate grid. One of its legs is on the x-axisand the other on the y-axis. Which describes theshape created when the triangle is rotated aboutthe x-axis?

A. cone

B. cylinder

C. pyramid

D. sphere

7. A plane intersects a right rectangular pyramid,producing a cross section. The plane is parallel tothe base. What shape is the cross section?

A. trapezoid

B. triangle

C. rectangle

8. Jamal wants to make a box with no top out of a24 inch square piece of cardboard. She plans tocut smaller squares of equal size from the cornersof the cardboard and fold up the resulting sides.

To the nearest inch, what size of square cutoutswill create a box with the largest volume?

page 2 COMMON CORE MATH II NCFE EXAM REVIEW

9. Sam put an empty ice cream cone upside down ona table. Then he stood over the cone and lookeddirectly down on the point of the cone. Whichpicture shows what Sam saw?

A.

B.

C.

D.

10. A square is circumscribed about a circle. What isthe ratio of the area of the circle to the area ofthe square?

A.1

4

B.1

2

C.2

π

D.π4

11. Steve has a wall in his room that measures 13 feetlong and 81

2 feet high and is totally bare. Hewants to hang automobile posters that are 3 feetlong and 2 feet high. What is the greatest numberof posters he can hang so that the posters do notoverlap?

12. A square tile measures 6 inches by 6 inches.What is the least number of tiles needed to covera rectangular floor area of 9 feet by 12 feet?

A. 3 tiles

B. 108 tiles

C. 216 tiles

D. 432 tiles

13. A piece of fabric measures 37 inches by 38 inches.A triangular scarf with a height of 29 inches anda base of 25 inches is cut from the fabric. Howmuch is left over?

A. 340.5 in.2

B. 521.75 in.2

C. 681 in.2

D. 1043.5 in.2

14. A rectangle is divided into sections with the areasshown. What is the value of X?

24 40

21 X

A. 25

B. 28

C. 32

D. 35


15. A square with a side of x is inside a square witha side of 4, as pictured below. Which expressionrepresents the area of the shaded region in termsof x?

A. 16 + x2

B. 16 − x2

C. 16 − 2x

D. 16 − 4x

16. The dimensions of a rectangle are given in thediagram below.

If x =p7, what is the perimeter of the rectangle?

A. 3 + 7p7

B. 10p7

C. 6 + 14p7

D. 20p7

17. Jeremy plans to construct a storage building thatwill have a square-shaped floor. In his plans, eachside is represented by the expression (4x + 4) feet.

If the plans show that the perimeter of the floorof the building is 64 feet, what is the value of x?

A. 3

B. 5

C. 15

D. 16


18. The area, in square inches, of the top of arectangular shelf is given by 4x2 + 46x + 60. Apiece in the shape of a right triangle will be addedto the existing shelf, increasing the area of theshelf by 50%.

Which figure, with dimensions given in inches, canbe used to justify the area of the triangular piece?

A.

B.

C.

D.

19. What is the approximate area of the shadedregion?

A. 8.57 square units

B. 8.70 square units

C. 9.13 square units

D. 11.28 square units

20. Jasmine drew a rectangle with the followingproperties.

• The area is 32 square centimeters.

• The length is twice the width.

What is the perimeter of Jasmine’s rectangle?Show your work or explain how you know.

21. The perimeter of square HJKL is 2 times theperimeter of square WXYZ.

The area of square HJKL is how many times thearea of square WXYZ?

A. 16

B. 8

C. 4

D. 2


22. Which of these could be the area of a perfectsquare?

A. x2 − 9x + 6

B. x2 − 6x + 9

C. x2 − 5x + 6

D. x2 − 6x + 5

23. The area in square units of a certain rectangle isequal to the expression 15x2 − 32x + 16 . Which ofthese expressions could not be equal to one sideof the rectangle?

I. 5x + 2

II. 3x − 4

III. 5x − 4

A. I only

B. II only

C. III only

D. I and III only

24. The area of a rectangular field is represented by(2k2 + 27k + 70) feet, and the width of the fieldis represented by (k + 10) feet. Which expressionrepresents the length, in feet, of the rectangularfield?

A. k + 60

B. 2k + 7

C. 2k + 70

D. 2k2 + 26k + 60

25. A regular tetrahedron is a triangular pyramid.What is the total surface area of a regulartetrahedron with base edges of 7 cm?

A. 7p3 cm2

B. 14p3 cm2

C. 28p3 cm2

D. 49p3 cm2

26. In the figure below, if sin x = 513 , what are cos x

and tan x?

A. cos x =12

13and tan x =

5

12

B. cos x =12

13and tan x =

12

5

C. cos x =13

12and tan x =

5

12

D. cos x =13

12and tan x =

13

5


27. In the figure below, sinA = 0.7.

What is the length of−−−AC?

A. 14.7

B. 21.7

C. 30

D. 32

28. If a = 3p3 in the right triangle below, what is the

value of b?

A. 9

B. 6p3

C. 12p3

D. 18

29. The figure below shows a house with an attic,represented by ÂBC with AC = BC. Thedistance from A to B is 42 feet. The slope(commonly referred to as the pitch) of the roof is23 .

What is the height, h, of the attic?

A. 14 feet

B. 28 feet

C. 32 feet

D. 63 feet


30. Look at the diagram below.

Note: The figure is not drawn to scale.

What is the length of−−−−WX?

A. 15 units

B. 26 units

C. 30 units

D. 52 units

31. Which equation can be used to find AC in thetriangle below?

A. AC = 5 sin(40◦)

B. AC = 5 cos(40◦)

C. AC =sin(40◦)

5

D. AC =cos(40◦)

5

32. A dead tree was struck by lightning, causing it tofall over at a point 10 ft up from its base.

If the fallen treetop forms a 40◦ angle with theground, about how tall was the tree originally?

A. 13 ft

B. 16 ft

C. 23 ft

D. 26 ft

33. A water tower is located 410 feet from a building.From a window in the building, it is observed thatthe angle of elevation to the top of the tower is42 degrees and the angle of depression to thebottom of the tower is 25 degrees. Approximatelyhow tall is the water tower?

A. 191 feet

B. 369 feet

C. 448 feet

D. 560 feet


34. Laila and Casey both built bike ramps. Laila’sramp has a base that is 6 feet long and is slantedat an angle of 20.5◦ from the ground. Casey’sramp has a base that is 8 feet long and is slantedat an angle of 16◦ from the ground. Whichstatement is true?

A. Laila’s and Casey’s ramps are similartriangles.

B. Laila’s ramp is about 6 inches shorter thanCasey’s ramp.

C. Laila’s ramp is about 6 inches taller thanCasey’s ramp.

D. Laila’s and Casey’s ramps are approximatelythe same height.

35. Suppose that for each foot of land along the street,the annual tax is $25 per foot. The diagram belowshows a plot of land.

About how much is the annual tax for the plot?

A. $1,238

B. $1,293

C. $1,321

D. $1,411

36. The hypotenuse of each right triangle shown belowrepresents a ladder leaning against a building.

Which equation can be used to find h, the distancebetween the base of the building and the pointwhere the shorter ladder touches the building?

A. h = (sin 44◦)(15 sin 26◦)

B. h = (sin 44◦)(15 cos 26◦)

C. h = (tan 26◦)(15 sin 44◦)

D. h = (tan 44◦)(15 sin 26◦)


37. Reggie tosses a coin three times in a row. Thetree diagram below shows all possible outcomes,where H represents heads and T represents tails.

What is the probability that Reggie will toss twoor more heads?

A. 18

B. 38

C. 48

D. 78

38. Beth chooses from the following to decorate aroom.

• 4 choices of paint colors (blue, green,pink, white)

• 2 choices of borders (flowers, cats)

• 3 sets of curtains (white, pink, blue)

Beth will randomly choose 1 paint color, 1 border,and 1 set of curtains. What is the probability thatBeth will pick blue paint, a flower border, andwhite curtains?

A. 124

B. 19

C. 14

D. 12

39. A box contains 4 red pencils, 3 blue pencils, and3 yellow pencils. What is the probability thata student randomly selects a blue pencil, keepsit, and then a second student randomly selects ayellow pencil?

A.1

10

B.3

10

C.6

10

D.9

10


40. Tara plays a game using 2 bags of game pieces.One bag has 6 blue game pieces and 6 red gamepieces. The other bag has ten game piecesnumbered 1 through 10. On her turn, Tara mustdraw one game piece from each bag. What is theprobability that she draws a red game piece andan even-numbered game piece?

A. 12

B. 14

C. 130

D. 160

41. In a simulation designed to represent families withtwo children, two coins are tossed to model thegender of each child. The results of 50 trials areshown in the table below.

GENDER SIMULATION

First Child Second Child Frequency

boy boy 15

boy girl 14

girl boy 8

girl girl 13

Based on the results in the table, what is theprobability that a family with two children have atleast one boy?

A. 0.30

B. 0.44

C. 0.58

D. 0.74

42. Brittany can choose to travel by bus or train.

• The probability of the bus arriving late atBrittany’s destination is 33%.

• The probability of the train arriving late atBrittany’s destination is 10%.

• Because the price of a bus ride is cheaper,Brittany chooses the bus 80% of the time.

What is the approximate probability that Brittanytook the bus, given that she did not arrive late toher destination?

A. 0.67

B. 0.75

C. 0.80

D. 0.93

43. The frequency table below shows the agedistribution of people at a park.

0–19 years 20–39 years 40–59 years 60–70 years 80–99 years

Male 50 18 12 4 2

Female 42 18 14 6 1

What is the probability a randomly selected personat the park is a female, given that the person isunder 40 years old?

A. 60167

B. 1532

C. 12

D. 6081


44. Which pair of statements describes mutuallyexclusive events?

A. Jan has a pet cat. Jan has a pet dog.

B. Jan likes country music. Jan likes pop music.

C. Jan plays soccer in the fall. Jan plays tennisin the spring.

D. Jan passes her final math test. Jan fails herfinal math test.

45. A 5-character key code is randomly generated bya computer using the 26 letters of the alphabetand the 10 digits 0–9. What is the probabilitythat the 5 characters in a key code, listed asthey are randomly generated, will spell the word“GREAT”?

A.1

60, 466, 176

B.1

45, 239, 040

C.5

60, 466, 176

D.5

45, 239, 040

46. Line ` is parallel to line m. Line t is a transversalwith angle measures as indicated below.

Note: The figure is not drawn to scale.

What is the value of x?

A. 16

B. 20

C. 25

D. 32

47. Parallelogram ABCD was translated toparallelogram A’B’C’D’.

How many units and in which direction were thex-coordinates of parallelogram ABCD moved?

A. 3 units to the right

B. 3 units to the left

C. 7 units to the right

D. 7 units to the left


48. Joanne and Christopher are designing a quilt. They start by creating a triangle shape in the lower left quadrant asshown below.

They transform it by rotating the triangle shown above 90◦ clockwise about the origin. What does the new designlook like?

A. B.

C. D.


49. Polygon A will be rotated counter-clockwise 90◦ about point P to form polygon A0.

A.

B.

C.

D.


50. Which figure shows the triangle below reflected over the x-axis, then reflected over the y-axis?

A.

B.

C.

D.


51. Triangle PQR is shown.

What are the coordinates of P0 when ^PQR isdilated by a scale factor of 3 using the origin asthe center?

A. (6, 18)

B.

(3,

2

3

)

C.

(2

3, 3)

D. (18, 6)

52. If triangle ABC is rotated 180 degrees about theorigin, what are the coordinates of A0?

A. (−5,−4)

B. (−5, 4)

C. (−4, 5)

D. (−4,−5)


53. Use the illustration below to answer the followingquestion.

As a result of a transformation, the image of thepoint A(2, 1) is A1(1, 2). This transformation isdescribed as a reflection across the

A. line y = x.

B. line y = −x.

C. x-axis.

D. y-axis.

54. Use the graph to answer the question.

Which pair of transformations moves quadrilateral 1to quadrilateral 2?

A. reflect it over the line y = −3, then rotate it90◦ counterclockwise about the origin

B. reflect it over the x-axis, then rotate it 180◦

about the origin

C. rotate it 90◦ counterclockwise about point(−3,−3), then translate it 8 units to the right

D. translate it 8 units to the right, then reflect itover the line y = −3

55. Two angles of a triangle have measures of 55◦

and 65◦. Which of the following could not be ameasure of an exterior angle of the triangle?

A. 115◦

B. 120◦

C. 125◦

D. 130◦


56. In the figure below,−−−AB and

−−−CD are perpendicular.

What is the perimeter of ÂBC?

A. 13

B. 28

C. 42

D. 84


57. Four holds on one of the rock climbing walls are labeled on the diagram below. Matthew first climbs vertically10 feet from Hold A to Hold B, horizontally 25 feet from Hold B to Hold C, and then vertically 15 feet fromHold C to Hold D.

How many fewer feet would Matthew have climbed if he had climbed directly from Hold A to Hold D? Providethe work that shows how you arrived at your answer.


58. Which theorem of congruence should be used toprove ^QRS ∼= ^TUV?

A. Angle-Side-Angle (ASA)

B. Angle-Angle-Side (AAS)

C. Side-Angle-Side (SAS)

D. Side-Side-Side (SSS)

59. In the diagram below,−−−RT intersects

−−−−QU at point S.

Which postulate should be used to prove that^RQS ∼= ^TUS?

A. Side–Side–Side

B. Angle–Side–Angle

C. Angle–Side–Side

D. Side–Angle–Side

60. In the diagram below, O1 ∼= O4.

Which of the following conclusions does not haveto be true?

A. O3 and O4 are supplementary angles.

B. Line l is parallel to line m.

C. O1 ∼= O3

D. O2 ∼= O3


61. Use the proof to answer the question below.

Given:−−−AB ∼= −−−

BC ; D is the midpoint of−−−AC

Prove: ÂBD ∼= ^CBD

Statement Reason

1.−−−AB ∼= −−−

BC; D is the midpoint of−−−AC 1. Given

2.−−−AD ∼= −−−

CD 2. Definition of Midpoint

3.−−−BD ∼= −−−

BD 3. Reflexive Property

4. ÂBD ∼= ^CBD 4. ?

What reason can be used to prove that the trianglesare congruent?

A. AAS

B. ASA

C. SAS

D. SSS

62. In the figure below,−−−AC ∼= −−−

DF and OA ∼= OD.

Which additional information would be enough toprove that ÂBC ∼= ^DEF?

A.−−−AB ∼= −−−

DE

B.−−−AB ∼= −−−

BC

C.−−−BC ∼= −−−

EF

D.−−−BC ∼= −−−

DE

63. Given: E is the midpoint of−−−CD; OC ∼= OD

Which of the following statements must be true?

A. OA ∼= OD

B. OB ∼= OC

C.−−−CE ∼= −−−

BE

D.−−−AC ∼= −−−

BD


64. Parallelogram WXYZ and diagonal−−−−WY are shown

in the diagram below.

Which of the following statements best proves thatOXWY ∼= OZYW ?

A. If two parallel lines are cut by a transversal,then corresponding angles are congruent.

B. If two parallel lines are cut by a transversal,then complementary angles are congruent.

C. If two parallel lines are cut by a transversal,then alternate interior angles are congruent.

D. If two parallel lines are cut by a transversal,then alternate exterior angles are congruent.


65. Which statement and reason complete the proof below?

Statements Reasons

1)−−−AB k −−−

DE; C is a midpoint−−−AE 1) Given

2)−−−AC ∼= −−−

CE 2) Definition of a midpoint

3) OBAC ∼= ODEC 3) If two parallel lines are cut by atransversal, then alternate interiorangles are congruent.

4) OACB ∼= OECD 4) Vertical Angle Theorem

5) 5)

6)−−−BC ∼= −−−

CD 6) Corresponding parts of congruenttriangles are congruent.

A. ÂBC ∼= ÊDC; SAS

B. ÂBC ∼= ÊDC; ASA

C. C is the midpoint of−−−BD; definition of a midpoint

D.−−−AB ∼= −−−

ED; corresponding parts of congruent triangles are congruent


66. Given:−−−AD k −−−

EC,−−−AD ∼= −−−

EC

Prove:−−−AB ∼= −−−

CB

Shown below are the statements and reasons forthe proof. They are not in the correct order.

Statement Reason

I. ÂBD ∼= ^CBE I. AAS

II. OABD ∼= OEBC II. Vertical angles are congruent.

III.−−−AD k −−−

EC,−−−AD ∼= −−−

EC III. Given

IV.−−−AB ∼= −−−

CB IV. Corresponding parts of congruenttriangles are congruent.

V. ODAB ∼= OECB V. If two parallel lines are cut bya transversal, the alternate interiorangles are congruent.

Which of these is the most logical order for thestatements and reasons?

A. I, II, III, IV, V

B. III, II, V, I, IV

C. III, II, V, IV, I

D. II, V, III, IV, I

67. Given: k k m k n

Which statement justifies the conclusion thatO1 ∼= O2 ∼= O3?

A. If k k m k n and are cut by transversal t, thenalternate interior angles are congruent.

B. If k k m k n and are cut by transversal t, thenvertical angles are congruent.

C. If k k m k n and are cut by transversal t, thenalternate exterior angles are congruent.

D. If k k m k n and are cut by transversal t, thencorresponding angles are congruent.

68. The point (−3, 2) lies on a circle whose equationis (x + 3)2 + (y + 1)2 = r2. Which of the followingmust be the radius of the circle?

A. 3

B.p10

C. 9

D. 10


69. In the diagram below, point M is the midpoint of−−−JK.

What are the coordinates of point J?

A. (−4, 1)

B. (−8, 2)

C. (−10,−4)

D. (−10,−8)

70. A circle has a center at (2,−3). One end point ofa diameter is at (4,−2). What are the coordinatesof the other endpoint of that diameter?

A. (6,−1)

B. (−2, 4)

C. (1,−5)

D. (0,−4)

71. Two students started at the coordinate (0, 0).Student A walked 7 units east and 5 units south.Student B walked 4 units west and 1 unit south.How many units apart are the students?

A. 11

B.p137

C.p153

D.p157


72. Which is the graph of a circle with equationx2 + 4x + y2 − 6y = 3 ?

A.

B.

C.

D.

73. The endpoints of a diameter of a circle are (−4, 7)and (2,−1). What is the equation of the circle instandard form?

A. (x − 1)2 + (y + 3)2 = 25

B. (x + 1)2 + (y − 3)2 = 25

C. (x − 1)2 + (y + 3)2 = 100

D. (x + 1)2 + (y − 3)2 = 100

74. Which circle has the smallest area?

A. x2 + y2 = 12

B. (x − 2)2 + y2 = 8

C. (x + 1)2 + (y + 3)2 = 6

D. (x + 8)2 + (y − 9)2 = 3

75. When walking your dog, what can you not do?

A. Chew Gum

B. Sleep

C. Talk

76. To find the image length L of a 4-foot tall objectin a spherical mirror with a focal length of 2 feet,

L = 4(2

o − 2)2 can be used, where o is the distance,

in feet, of the object from the mirror. What is theimage length of the object when it is 1.5 feet awayfrom the mirror?

A. 256 feet

B. 128 feet

C. 64 feet

D. 32 feet


77. The principle wants to read the list of candidatesfor prom queen. There are 6 candidates. Howmany ways can the principle introduce thecandidates?

A. 2160

B. 720

C. 21

D. 6

78. Brenda must create a password according to theserules:

• The password must consist of 2 lettersfollowed by 2 digits.

• There are a total of 26 letters and 10 digitsthat she may use.

• The letters may be repeated.

• The digits may not be repeated.

How many different passwords are possible?

A. 4680

B. 5148

C. 60,840

D. 66,924

79. An object is launched at an initial velocity of19.6 meters per second from a 58.8-meter tallplatform. This situation can be modeled by thefunction f (x) = −4.9x2 + 19.6x + 58.8 where xrepresents the time, in seconds, that the object isin motion, and f (x) is the height of the object.

a) Find the average rate of change from0 seconds to 1 second. Find the averagerate of change from 1 second to 2 seconds.Explain what each average rate of changemeans based on the problem. Compare thetwo average rates of change to explain whatis happening with the object.

b) Find the average rate of change from3 seconds to 5 seconds and explain itsmeaning.

c) What is the maximum height of the object?When does the object reach its maximumheight?

d) When does the object hit the ground? Howdo you know?

e) What is the average rate of change between1 second and 3 seconds? Why?

f) How would the function and graph of thefunction change if the object were launchedfrom a platform which is 63.8 meters tall?Explain your reasoning.

80. The Just for Fun t-shirt company used the functionP(q) = −100 + 0.5q+ 0.01q2 to determine the profitP(q), in dollars, of selling q t-shirts.

a) Compare the average rate of change between100 t-shirts and 200 t-shirts to the averagerate of change between 200 t-shirts and300 t-shirts.

b) Alison thinks the average rate of changebetween 0 t-shirts and 50 t-shirts is negative.Do you agree or disagree? Explain yourreasoning.


81. The height, in meters, of a rock as it falls at agiven time (x), in seconds, can be found using theexpression −5x2 + h0 , where h0 is the startingheight where the rock falls.

a) A rock falls from a starting height of80 meters. Write a function, f (x), thatmodels the height of the rock as it falls.Make sure to use proper function notation.

b) Using the function from part A, what is thevalue of f (3)?

c) Ahmed states that the domain for thisfunction in the given context is x ≤ 4.Explain why Ahmed is incorrect, and providea correct domain.

82. Use the piecewise function below to answer eachquestion.

h(x) =

8<

:

−2x2 + 5x + 10 for -4 <= x < 3 Step 13x + 2 for 3 <= x < 7 Step 2p2x − 5 for 7 <= x < 16 Step 3

a) What is the range for step 1?

b) What is the domain for the entire function?

c) What is h(10.5)?

83. Suppose that Kyle has $1,500 to invest. Hisinvestment will earn an interest rate of 8.25%compounded continuously.

a) To the nearest cent, what will be the valueof Kyle’s investment after 6 years?

b) To the nearest tenth, how long will it takefor Kyle’s investment to grow to $3,000?

c) To the nearest tenth, what interest rate wouldbe needed to triple Kyle’s investment in15 years?

84. The function P(t) = 300e(0.038t) models the numberof bacteria in a population after t minutes.

a) What is the meaning of the coefficient of ein the context of the problem?

b) What is the meaning of the coefficient of tin the context of the problem?

85. The table below shows the height of a rocket atdifferent times.

Time (seconds) 0 0.5 1.5 2.5 3.5

Height (feet) 0 28 60 60 28

a) Write a function that gives the height of therocket, y, after x seconds.

b) At what time does the rocket begin itsdescent?

c) What is the rocket’s total flight time?

86. The function V(t) = 1, 000(1.06)2t models thevalue of an investment after t years.

a) What was the initial value of the investment?

b) As a percent, what interest rate is theinvestment earning each year?


87. Interest rate

A bank offers an interest rate of r compoundedn times per year. The formula for the amount ofmoney, A, in an account at the end of t years, is:

A = P(1 +

rn

)nt

where P is the amount of money in the account atthe beginning of the year (assuming no deposits orwithdrawals).

a) If at the beginning of the year Joe had $1,000in an account with 2% interest compoundedsemiannually, how much money would hehave in the account at the end of the year?Show your work or provide an explanationfor your answer.

b) The effective interest rate, R, is the percentincrease in the account over one year. Whatis the effective interest rate for Joe’s account?(Do not round your answer.) Show your workor provide an explanation for your answer.

c) Joe had x dollars in his account at thebeginning of the year. Describe how todetermine the amount of money Joe wouldhave in his account after 1 year using theeffective rate you found above.

88. If x2 is added to x, the sum is 42. Which of thefollowing could be the value of x?

A. −7

B. −6

C. 14

D. 42

89. Carter is solving this equation by factoring.

10x2 − 25x + 15 = 0

Which expression could be one of his correctfactors?

A. x + 3

B. x − 3

C. 2x + 3

D. 2x − 3

90. Eric’s T-shirt Shop

Eric owns a T-shirt shop. Eric has been selling 50T-shirts each day at a price of $20. He finds thatfor each $1 reduction in price, he can sell 5 moreeach day. At what price (in dollars) should he sellthe T-shirts in order to maximize his daily incomefrom their sales?

91. Jamie wants to solve this equation:

x − 6 =p3x

Which statement is true?

A. The solutions of Jamie’s equation are thesolutions of x2 − 3x − 6 = 0.

B. The solutions of Jamie’s equation are thesolutions of x2 − 15x + 36 = 0.

C. The solution of Jamie’s equation is one of thesolutions of x2 − 3x − 6 = 0.

D. The solution of Jamie’s equation is one of thesolutions of x2 − 15x + 36 = 0.


92. Consider these two equations:

y = 3x + 2

y = −x2 − 4x + 10

Here are the first steps to solving this system ofequations:

3x + 2 = −x2 − 4x + 10x2 + 7x − 8 = 0

(x − 1)(x + 8) = 0

What is one solution to the system of equations?

A. (1,−8)

B. (−1, 8)

C. (1, 5)

D. (−1,−1)

93. When solving a system of equations, Ben came upwith the graph shown.

Which of the following is the system of equationshe solved?

A. − 2x + y = 5

(x − 3)2 + (y − 5)2 = 36

B. − 2x + y = 5

(x + 3)2 + (y + 5)2 = 36

C. − 2x + y = 5

(x − 5)2 + (y − 3)2 = 36

D. − 2x + y = 5

(x + 5)2 + (y + 3)2 = 36

94. Solve: y = 3x2 + 3y = 5 − 5x

A.{( 13 ,

103 ), (2, 15)

}

B.{( 13 ,

103 ), (−2, 15)

}

C.{(−13 , 20

3 ), (2,−5)}

D.{(−13 , 10

3 ), (−2,−5)}


95. What is the nature of the roots of the equation5n2 = 4n + 6?

A. two imaginary roots

B. one real, rational root

C. two real, irrational roots

D. two real, rational roots

96. The equation x2 + bx + c = 0 has exactly 1 realsolution when b and c are real numbers. Whichequation describes b in terms of c?

A. b = c2

B. b =pc

C. b = 2c

D. b = 2pc

97. What is the solution to the equation 5x = 17?

A. x = 2

B. x = log10 2

C. x = log10 17 + log10 5

D. x =log10 17

log10 5

98. Which equation is equivalent to log319 = x?

A. 139 = x3

B.(19

)3= x

C. 3x = 19

D. 319 = x

99. A certain radioactive element decays over time

according to the equation y = A(1

2

) t300

where

A = the number of grams present initially and t =time in years. If 1000 grams were present initially,how many grams will remain after 900 years?

A. 500 grams

B. 250 grams

C. 125 grams

D. 62.5 grams

100. Bacteria in a culture are growing exponentiallywith time, as shown in the table below.

Which of the following equations expresses thenumber of bacteria, y, present at any time, t?

A. y = 100 + 2t

B. y = (100) · (2)t

C. y = 2t

D. y = (200) · (2)t

101. In 1997 the population of a small town was 700.If the annual rate of increase is about 0.8%, whichvalue below expresses the population five yearslater?

A. 5(700)(0.008)

B. 5(700)(1.008)

C. (700)(0.008)5

D. (700)(1.008)5


102. What is the value of log3 27?

A. 2

B. 3

C. 6

D. 9

103. Use the equation below to answer the followingquestion.

As the value of x becomes negative and continuesto decrease, what happens to the value of y?

y = 2x

A. y becomes negative

B. y gets closer to 1

C. y gets closer to 0

D. y gets closer to x

104. What is the solution to the equation?

log2 8 + log2 32 = x

A. 4

B. 8

C. 40

D. 256

105. The equation c = 523, 430(1.193)t models UnitedStates copper prduction in pounds from 1987-1992.Which statement best interprets the coefficient andbase of this equation?

A. The copper production in 1987 was 523,430ounds, and it had been increasing at a rate of1.93% per year during that period.

B. The copper production in 1987 was 523,430ounds, and it had been increasing at a rate of19.3% per year during that period.

C. The copper production increased by a factorof 523, 430 × 1.193 pounds per year duringthat period

D. The copper production at the beginning of1987 was at 1.193 pounds, and it had beenincreasing by a factor of 523,430 ounds peryear during that period.

106. Which of the following is the logarithmic form of

the equation y = 20−32 ?

A. log 20y = −32

B. log 3220 = y

C. − log 32y = 20

D. log 20(−32 ) = y


107. What are the real roots of the function in thegraph?

A. 3

B. −6

C. −1 and 3

D. −6, −1, and 3

108. The relationship between the distance d, in feet,required to stop a vehicle and s, the speed in milesper hour that the vehicle was traveling, is given bythe equation

d =0.0155s2

f

where f represents the coefficient of frictionbetween the tires and the road.

It took a car 205 feet to stop. What speed was thecar traveling? Use f = 0.3 and round your answerto the nearest mile per hour.

109. A quadratic function, f , has zeros P and Q, such

that P + Q = 5 and1

P+

1

Q= 8. Which choice

describes f ?

A. f (x) = 8x2 − 40x + 5

B. f (x) = 8x2 − 40x − 5

C. f (x) = 2x2 − 10x + 5

D. f (x) = 2x2 − 10x − 5

110. What is the volume of the figure below?

A. x3 + 10x2 + 34x + 24

B. x3 + 11x2 + 34x + 24

C. x3 + 10x2 + 24x + 24

D. x3 + 11x2 + 24x + 24

111. What is the degree of the polynomial12xy3 − 7y2z5 + 5x6y − 2x2y2 ?

A. 22

B. 11

C. 7

D. 4


112. What are the zeros of f (x) = x4 − 7x3 + 15x2 − 9x?

A. x = 1, x = 3

B. x = 0, x = 1

C. x = 0, x = 1, x = 3

D. x = 0, x = 1, x = 2, x = 3

113. Which is the polynomial for the given graph?

A. P(x) = (x − 2)(x − 8)(x + 1)(x + 4)

B. P(x) = (x − 2)(x + 1)2(x + 4)

C. P(x) = (x + 2)(x + 8)(x − 1)(x − 4)

D. P(x) = (x + 2)(x − 1)2(x − 4)

114. Which of the following is an irrational number?

A.p16

B.p144

C.p4

D.p3

115. Which of the following is equivalent to theexpression below for all real values of n and k ?

5n · 5k

A. 5n+k

B. 5n−k

C. 5nk

D. 5n÷k

116. Convert the following to radicals:

52/3


Problem-Attic format version 4.4.210c_ 2011–2014 EducAide SoftwareLicensed for use by Kyra Bernat

Terms of Use at www.problem-attic.com

COMMON CORE MATH II NCFE EXAM REVIEW 05/08/2014

1.Answer: D

2.Answer: A

3.Answer: D

4.Answer: C

5.Answer: B

6.Answer: A

7.Answer: C

8.Answer:

9.Answer: A

10.Answer: D

11.Answer: 16 posters

12.Answer: D

13.Answer: D

14.Answer: D

15.Answer: B

16.Answer: C

17.Answer: A

18.Answer: A

19.Answer: D

20.Answer: 24 (cm)

21.Answer: C

22.Answer: B

23.Answer: A

24.Answer: B

25.Answer: D

26.Answer: A

27.Answer: C

28.Answer: A

29.Answer: A

30.Answer:

31.Answer: A

32.Answer: D

33.Answer: D

34.Answer: D

35.Answer: A

36.Answer: D

37.Answer: C

38.Answer: A

39.Answer: A

40.Answer: B

Teacher’s Key Page 2

41.Answer: D

42.Answer: B

43.Answer: B

44.Answer: D

45.Answer: A

46.Answer:

47.Answer: D

48.Answer: B

49.Answer: D

50.Answer: D

51.Answer: D

52.Answer: A

53.Answer: A

54.Answer: A

55.Answer: C

56.Answer: C

57.Answer: 15 or 14.64 feet

58.Answer: B

59.Answer: B

60.Answer: A

61.Answer: D

62.Answer: A

63.Answer: D

64.Answer: C

65.Answer: B

66.Answer: B

67.Answer: D

68.Answer: A

69.Answer: D

70.Answer:

71.Answer: B

72.Answer: A

73.Answer: D

74.Answer: D

75.Answer: B

76.Answer: C

77.Answer: B

78.Answer: C


79.

Answer: –f (1) − f (0)

1 − 0= 14.7 Meters per second.

f (2) − f (1)2 − 1

= 4.9 meters per second. The

average rate of change during the secondinterval is slower than the first because asthe object is traveling upward it will startto slow down as it reaches its maximumheight and begin its descent. The averagerate of change is still positive.

–f (5) − f (3)

5 − 3= −19.6. Object is falling

at an average of 19.6 meters per second.

– max height: 78.4 meters at 2 seconds

– 6 seconds

– The average rate of change between1 second and 3 seconds is 0 meters persecond because the object reached itsmaximum height at 2 seconds whichmeans it traveled the same distance from1 to 2 seconds as it did from 2 to3 seconds, only in opposite directions.

– f (x) = −4.9x2 + 19.6x + 63.8

80.Answer:

81.Answer: – f (x) = −5x2 + 80

– 35 meters

82.Answer: – [−42, 13.125]

– [−4, 16)– 4

83.Answer: – $2,460.75

– 8.4 years

– 7.3%

84.Answer:

85.Answer: – Student writes a function that gives the

data in the table

– 2 seconds or any equivalent roundedvalue

– 4 seconds or any equivalent roundedvalue

86.Answer: – $1,000

– 12% or any equivalent rounded

87.Answer: – $1,020.10 1, 000

(1 + 0.02

2

)2= 1, 020.10

– 2.01% 20.101,000 = 0.0201

– x × 1.0201

88.Answer: A

89.Answer: D

90.Answer:

91.Answer: D

92.Answer: C

93.Answer: C

94.Answer:

95.Answer: C

96.Answer: D

97.Answer: D

98.Answer: C

99.Answer: C

100.Answer: B

101.Answer: D

102.Answer: B

103.Answer: C

104.Answer: B

105.Answer:

106.Answer:

107.Answer: C

108.Answer:


109.Answer: A

110.Answer: B

111.Answer: C

112.Answer:

113.Answer:

114.Answer: D

115.Answer: A

116.Answer:

3p52

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