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12/22/13 Final Exam Review Questions

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Name: ____________________________________

1.

Jordan got a new water bottle to use for soccer. Approximatelyhow much water can Jordan fit in the water bottle?

A. 1,728 cm3

B. 5,429 cm3

C. 1,356 cm3

D. 21,703 cm3

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2.

The area of a rectangle is represented by x2 − 5x − 24. If thewidth of the rectangle is represented by x − 8, express thelength of the rectangle as a binomial.

A. x – 3B. x – 16C. x + 3D. x + 32

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3.

Which point lies on the line whose equation is 2x − 3y = 9?

A. (−1,−3)B. (−1, 3)C. (0, 3)D. (0,−3)

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4.

Students in Ms. Nazzeer’s mathematics class tossed a six-sidednumber cube whose faces are numbered 1 to 6. The results arerecorded in the table below.

Based on these data, what is the empirical probability of tossinga 4?

A.

B.

C.

D.

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5.

The solution set for the equation x2 – 5x = 6 is

A. {1,–6}B. {2,–3}C. {–1,6}D. {–2,3}

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6.

When factored completely, x3 - 9x is equivalent to

A. x(x - 3)B. x(x + 3)(x - 3)C. (x + 3)(x - 3)D. x(x + 3)

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7.

The gas tank in a car holds a total of 16 gallons of gas. The car travels 75 miles on 4 gallons of gas. If the gas tank is full at thebeginning of a trip, which graph represents the rate of change in the amount of gas in the tank?

A.

B.

C.

D.

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8.

Select all expressions from the list below that share a commonfactor with the expression 14x2 + 21x.

Select all that apply:

12x + 8 20x – 30 28xy – 35x 10x2 + 15x 42x – 35

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9. Sam and Odel have been selling frozen pizzas for a classfundraiser. Sam has sold half as many pizzas as Odel. Togetherthey have sold a total of 126 pizzas. How many pizzas did Samsell?

A. 21B. 42C. 63D. 84

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10. In the next Olympics, the United States can enter four athletesin the diving competition. How many different teams of fourdivers can be selected from a group of nine divers?

A. 36B. 126C. 3,024D. 6,561

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11.

Figure 1

In the diagram, ≅ , ⊥ , and ⊥ .Which statement can be used to prove that ΔPQR ≅ ΔSRQ?

A. AAS ≅ AASB. SAS ≅ SASC. HL ≅ HLD. SSS ≅ SSS

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12.

Vince buys a box of candy that consists of six chocolate pieces,four fruit-flavored pieces, and two mint pieces. He selects threepieces of candy at random, without replacement.

Calculate the probability that the first piece selected will befruit-flavored and the other two will be mint.

A.

B.

C.

D.

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13.

The expression is equivalent to

A. 2w5

B. 2w8

C. 20 w5

D. 20 w8

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14. What are the vertex and the axis of symmetry of the parabolashown in the diagram below?

A. The vertex is (-2,-3), and the axis of symmetry is x = -2.B. The vertex is (-2,-3), and the axis of symmetry is y = -2.C. The vertex is (-3,-2), and the axis of symmetry is y = -2.D. The vertex is (-3,-2), and the axis of symmetry is x = -2.

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15.

What is the equation of the graph shown below?

A. y = 2x

B. y = 2–x

C. x = 2y

D. x = 2–y

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16.

The graph of y = x3 − 4x2 + x + 6 is shown below.

What is the product of the roots of the equation x3 − 4x2 + x +6 = 0?

A. −36B. −6C. 6D. 4

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17.

Maria has a set of 10 index cards labeled with the digits 0through 9. She puts them in a bag and selects one at random.The outcome that is most likely to occur is selecting

A. an odd numberB. a prime numberC. a number that is at most 5D. a number that is divisible by 3

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18.

At a wedding, there are 456 people spread out amongst 45tables. There are no empty seats. The reception hall has tablesthat sit 12 people or 8 people. Write a system of equations thatcan be used to find the number of each type of table therestaurant has.

A.

B.

C.

D.

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19.

What is the solution set for the equation x2 - 5x + 6 = 0?

A. {-6,1}B. {6,-1}C. {-2,-3}D. {2,3}

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20.

Figure 2

In the diagram of right triangle ABC, AB = 4 and BC = 7. Whatis AC, to the nearest hundredth?

A. 5.74B. 5.75C. 8.06D. 8.08

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21.

What is an equation of the circle whose center is (−3, 1) andwhose radius is 10?

A. (x + 3)2 + (y − 1)2 = 10B. (x + 3)2 + (y − 1)2 = 100C. (x − 3)2 + (y + 1)2 = 10D. (x − 3)2 + (y + 1)2 = 100

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22.

Jon has thirteen coins consisting of quarters and dimes. Thesum of money Jon has is $2.20. Write a system of equationsthat could be solved to determine how many of each coin Jonhas.

A.

B.

C.

D.

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23.

The diagram shows a rectangular prism with edge lengths of 2

inches, 1 inch, and 1 inches. It also shows a green cube

with edge lengths of inch.

At most, how many green cubes will fit into the rectangularprism?

A. 3 green cubes

B. 30 green cubesC. 15 green cubesD. 5 green cubes

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24. Which value of x is in the solution set of the inequality - 4x + 2> 10?

A. -2B. 2C. 3D. -4

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25.

What is the sum of and ?

A.

B.

C.

D.

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26.

What is the product of and expressed in

simplest form?

A. x

B.

C. x + 3

D.

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27.

If 2x + 5 = -25 and -3m - 6 = 48, what is the product of x and m?

A. -270B. -33C. 3D. 270

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28.

Solve for x:

A. 1B. −1C. −4D. 4

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29.

Which ratio represents sin x in the right triangle shown below?

A.

B.

C.

D.

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30.

What is the sum of the roots of the equation 2x2 – 3x + 9 = 0?

A. 2/3B. 9/2C. 3/2D. –3/2

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31.

A cellular telephone company has two plans. Plan A charges $11a month and $0.21 per minute. Plan B charges $20 a month and$0.10 per minute. After how much time, to the nearest minute,will the cost of plan A be equal to the cost of plan B?

A. 1 hr 22 minB. 1 hr 36 minC. 81 hr 8 minD. 81 hr 48 min

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32.

What are the coordinates of the image of point (-1, 2) under a dilation of 3 with respect to the origin?

A. (-6, 3)B. (6, -3)C. (3, 6)D. (-3, 6)

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33.

In the diagram, the slope of the ascent of an aircraft is 7/50.

Find m∠x, the angle of elevation, to the nearest degree.

A. 6°B. 8°C. 12°D. 15°

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34.

Express the product of in simplest form.

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35.

The length of a side of a square window in Jessica’s bedroom is represented by 2x - 1. Which expression represents the area ofthe window?

A. 2x2 + 1B. 4x2 + 1C. 4x2 + 4x - 1D. 4x2 - 4x + 1

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36.

If cos 72° = sin x, find the number of degrees in the measure of acute angle x.

A. 18°B. 36°C. 72°D. 108°

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37.

Given the real valued function , , which number is

in the domain of f(x)?

A. –1B. 2C. 3D. 7

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38.

The graph below shows and its image, , after atransformation.

Which transformation would map onto ?

A. translationB. glide reflectionC. rotation centered at the originD. reflection through the origin

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39.

Figure 3

Which equation defines the graph in the diagram?

A. y = x2 + 6x + 1B. y = -x2 + 6x + 1C. y = x2 + 3xD. y = -x2 + 3x - 1

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40.

What is the product of the roots of the equation 2x2 – x – 2 =0?

A. 1B. 2C. –1D. –2

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41.

Explain how to find the solution(s) to a quadratic equation bygraphing.

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42.

In triangle ABC, is extended through C to D. If m∠BCD= 2x + 35, m∠BAC = x − 3, and m∠ABC = 3x − 20, what is thevalue of x?

A. 28B. 29C. 30D. 31

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43.

Which is equivalent to the expression after it has

been simplified?

A.

B.

C.

D.

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44.

In the diagram of right triangle ABC, b = 40 centimeters, m∠A= 60, and m∠C = 90.

Find the number of centimeters in the length of side c.

A. 40B. 60C. 80D. 80

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45.

A ball is thrown straight up at an initial velocity of 54 feet persecond. The height of the ball t seconds after it is thrown isgiven by the formula h(t) = 54t - 12t2. How many seconds afterthe ball is thrown will it return to the ground?

A. 9.2B. 6C. 4.5D. 4

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46.

A pentagon is drawn on the set of axes below. If the pentagonis reflected over the y-axis, determine in what quadrant theimage lies and whether this transformation is an isometry.

A. Quadrant II, not an isometryB. Quadrant III, is an isometryC. Quadrant II, is an isometryD. Quadrant IV, is not an isometry

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47.

Which inequality is represented by the graph below?

A. y < 2x + 1B. y < -2x + 1

C. y < x + 1

D. y < - x + 1

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48.

In which figure is ΔA' B' C' a reflection of ΔABC in line l?

A.

B.

C.

D.

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49.

The graph of y = f(x) is shown below.

Which set lists all the real solutions of f(x) = 0?

A. {−3, 2}B. {−2, 3}C. {−3, 0, 2}D. {−2, 0, 3}

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50.

The function is undefined when the value of x is

A. 0 or 3B. 3 or –3C. 3, onlyD. –3, only

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51.

Timothy brought an oatmeal container to math class today fora group project. His group has to figure out how much oatmealwill fit inside of the container. What is the approximate volumeof the oatmeal container?

A. 2,010 in3 B. 503 in3 C. 251 in3 D. 50 in3

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52.

Dwayne purchased a computer from Techtronics, Inc. for$2,600 in 2007. The rate of depreciation is 7%. Which wouldbe the best estimate for the value of the computer in 2010?

A. $1,945B. $2,091C. $2,577D. $2,593

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53.

The diagram below shows right triangle ABC.

Which ratio represents the tangent of ∠ABC?

A.

B.

C.

D.

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54.

What is the maximum value for the function y = sin 5x?

A. –

B.

C.

D. –5

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55.

A committee of three is to be chosen from 10 teachers. Howmany different committees can be formed?

A. 30B. 120C. 720D. 1,000

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56.

If tan A = , what is the measure of ∠A to the nearest

degree?

A. 79°B. 60°C. 30°D. 27°

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57.

In which of the accompanying figures are segments and perpendicular?

A. figure 1, onlyB. figure 2, onlyC. both figure 1 and figure 2D. neither figure 1 nor figure 2

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58.

The value of the expression is

A. 50B. 102C. 740D. 750

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59.

In isosceles triangle ABC, AC = BC = 20, m∠A = 68, and is the altitude to side . What is CD to the nearest tenth?

A. 49.5B. 18.5C. 10.6D. 7.5

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60.

Nancy’s rectangular garden is represented in the diagram below.

If a diagonal walkway crosses her garden, what is its length, infeet?

A. 17B. 22

C.

D.

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61.

What is the amplitude of the graph of the equation y = 2 sin

x?

A.

B. 2C. 3πD. 2π

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62.

Is a triangle with sides measuring 24 cm, 25 cm, and 7 cm a righttriangle?

A. YesB. NoC. Cannot tell

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63.

If ΔABC ∼ ΔZXY, m∠A = 50, and m∠C = 30, what is m∠X?

A. 30B. 50C. 80D. 100

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64.

If the vertex angles of two isosceles triangles are congruent,then the triangles must be

A. acuteB. congruentC. rightD. similar

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65.

Figure 4

In the diagram of isosceles triangle ABC, ≅ andaltitude is drawn. If BD = 4 and AD = 3, find the perimeterof ΔABC .

A. 13B. 15C. 16D. 18

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66.

Which equation could be used to find the measure of one acuteangle in the right triangle shown below?

A. sin A =

B. tan A =

C. cos B =

D. tan B =

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67.

The bull’s-eye of a dartboard has a radius of 2 inches and theentire board has a radius of 9 inches, as shown in the diagrambelow.

If a dart is thrown and hits the board, what is the probabilitythat the dart will land in the bull’s-eye?

A.

B.

C.

D.

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68.

Campsite A and campsite B are located directly opposite eachother on the shores of Lake Omega, as shown in the diagrambelow. The two campsites form a right triangle with Sam’sposition, S. The distance from campsite B to Sam’s position is1,300 yards, and campsite A is 1,700 yards from his position.

What is the distance from campsite A to campsite B, to thenearest yard?

A. 1,095B. 1,096C. 2,140D. 2,141

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69.

Given the following number line:

Figure 5

Find the probability that a point chosen at random from isalso on and .

A.

B.

C.

D.

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70.

In ΔABC, a = 6, b = 5, and c = 8. Cos A equals

A. 75/80B. 53/80C. -3/80D. 53/60

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71.

In ΔABC shown below, P is the centroid and BF = 18.

What is the length of ?

A. 6B. 9C. 3D. 12

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72.

Which of the following points in the diagram below is theincenter of triangle ABC?

A. HB. OC. DD. F

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73.

The accompanying diagram shows a ramp 30 feet long leaningagainst a wall at a construction site.

If the ramp forms an angle of 32° with the ground, how highabove the ground, to the nearest tenth, is the top of the ramp?

A. 15.9 ftB. 18.7 ftC. 25.4 ftD. 56.6 ft

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74.

Julius’ dad bought a traffic cone to place at the end of theirdriveway. He hopes it will notify drivers to be cautious sincechildren play in the area. He wants fill the cone with cement soit won’t fall over. Approximately how much cement will he needto fill the traffic cone?

A. 942 in3

B. 14,130 in3

C. 1,571 in3

D. 4,710 in3

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75.

The roots of the equation 2x2 - 8x - 4 = 0 are

A. imaginaryB. real, rational, and equalC. real, irrational, and unequalD. real, rational, and unequal

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76. The roots of the equation 2x2 - 5 = 0 are

A. imaginaryB. real, rational, and equalC. real, rational, and unequalD. real and irrational

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77.

The discriminant of a quadratic equation is 24. The roots are

A. imaginaryB. real, rational, and equalC. real, rational, and unequalD. real, irrational, and unequal

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78.

Jeff says, “I know exactly how many solutions a quadraticfunction will have just by analyzing the discriminant!” How isJeff able to prove this?

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79.

What are the roots of the equation x2 + 9x + 12 = 0?

A.

B.

C.

D.

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80.

What is the smallest integer value of k that makes the solutionsof 3x2 – 7x + k = 0 imaginary?

A. 4B. 5C. 6D. 7

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81.

What is the positive root of the equation x2 – 3x – 6 = 0?

A.

B.

C.

D.

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82.

The table below shows the results of the golf team’s fundraising efforts selling small and large sizes of Cookie Dough and ItalianHoagies at SF high School.

PART A:Define the variables.

PART B:Write a system of equations to model the situation.

PART C:What does each equation of the system represent?

PART D:Determine the best method to solve the system of equations. Explain your reasoning.

PART E:Solve the system of equations, and explain what the solution represents.

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83.

Describe the strategies you use to solve a system of linear equations. Try to incorporate all of the methods that can be used tosolve a system of equations in your answer.

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84.

A card-collecting store sells individual packs for one price or an entire hobby box for another. Jaycee purchased 12 packs and 3hobby boxes for $196.50. Jeremiah paid $403.50 for 8 packs and 7 hobby boxes.

PART A:Define the variables.

PART B:Write a system of equations to model the situation.

PART C:What does each equation of the system represent?

PART D:Determine the best method to solve the system of equations. Explain your reasoning.

PART E:Solve the system of equations, and explain what the solution represents.

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85.

Max and Crystal are solving a system of equations. Is either of them correct? Explain your reasoning.

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86.

Factor completely: 2x2 - 18

A. 2(x - 3)2

B. 2(x + 3)2C. 2(x + 3)(x - 3)D. 2(x + 9)(x - 9)

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87.

Solve for the positive value of x: x2 – 64 = 0

A. –8B. 8C. 16D. 64

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88.

How is the graph of y = x2 + 4x + 3 affected when thecoefficient of x2 is changed to a smaller positive number?

A. The graph becomes wider, and the y-intercept changes.B. The graph becomes wider, and the y-intercept stays the

same.C. The graph becomes narrower, and the y-intercept

changes.D. The graph becomes narrower, and the y-intercept stays

the same.

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89.

Factor completely: 2x2 - 50

A. (x + 5)(2x - 5)B. (2x + 5)(x - 5)C. 2(x - 5)2D. 2(x + 5)(x - 5)

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90.

Which statement below is true about the graph of y = ax2 if achanges from 3 to –5?

A. The graph becomes wider and opens up.B. The graph becomes narrower and opens up.C. The graph becomes wider and opens down.D. The graph becomes narrower and opens down.

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91.

How does changing the sign of the leading coefficient in anequation of the form y = ax2 affect its graph?

A. The graph becomes narrower.B. The graph is reflected over the x-axis.C. The graph becomes wider.D. The graph shifts up or down.

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92.

Which equation represents a quadratic function?

A. y = x + 2B. y = |x + 2|C. y = x2

D. y = 2x

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93.

Which graph below shows the equations y = |x| and y = 3|x| forthe interval −3 ≤ x ≤ 3?

A.

B.

C.

D.

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94.

The parallel lines in the diagram are:

A. and B. and C. and D. and

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95.

The area of a circle is 25π. What is the length of a radius of thecircle?

A. 5B. 2C. 12.5D. 25

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96.

In the diagram below, m and ⊥ at R.

If m∠1 = 63, find m∠2.

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97.

Willy ate three slices of pizza from a full pie. If each piece hada central angle of 45 degrees, what fraction of the area of theentire pie was left for the rest of Willy’s family?

A.

B.

C.

D.

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98.

As shown in the diagram below, lines m and n are cut bytransversal p.

If m∠1 = 4x + 14 and m∠2 = 8x + 10, lines m and n are parallelwhen x equals

A. 1B. 6C. 13D. 17

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99.

The diagram below shows the graph of y = |x - 3|.

Which diagram shows the graph of y = -|x - 3|?

A.

B.

C.

D.

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100.

Which is the best example of parallel lines?

A. the rails of train tracksB. the edges of a cloudC. the tires on a carD. a 4-way traffic intersection

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recorded in the table below. - Iredell-Statesville Schools ... triangle ABC, is extended through C...

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