Fall 2014 Unit 1 Practice Exam Name___________________________________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Simplify the exponential expression. Assume that variables represent nonzero real numbers.1) (-4x5y-6)(2x-1y) 1)

A) -8x4

y5B) -8x4y7 C) -8x6

y7D) -2x4

y5

2) xy3

x3y

-22)

A) x4

y4B) 1

x5y7C) y4

x4D) 1

x8y8

3) 9x-4y-2z3

3xy-2z-3

-33)

A) x15y4

27z18B) 3x15

z18C) x9

27z18D) x15

27z18

4) 36x3/4

9x1/34)

A) 4x1/6 B) 27x1/6 C) 4x5/12 D) 4x5/4

Evaluate the expression.5) 25-3/2 5)

A) 1125

B) 125 C) -125 D) -1

125

Solve the equation.

6) x3

- 2 =x7

+ 3 6)

A) 154

B) 1054

C)2110 D) 3

4

7) -3x + 9 = -3 + 5x 7)

A)32 B)

23 C) 1

3D) -

23

8) -6x + 5 = -6 + 8x 8)

A) - 2 B) 1411

C) - 1411 D) 11

14

1

Solve the linear inequality. Write the solution set using interval notation and graph it.9) 6x - 1 > 5x - 4 9)

A) (-3, )

B) [-3, )

C) (- , -3]

D) (-5, )

10) 4 + 6y - 3 5y + 13 10)

A) (- , 6)

B) (- , 12]

C) [12, )

D) (6, )

Find the slope of the line that goes through the given points.

11) ( 45

, 1) and ( 45

, 2) 11)

A)25 B) Undefined C)

52 D) 15

2

12) (1, 4) and (-3, 2) 12)

A)35 B)

12 C)

53 D) 2

2

Use the given conditions to write an equation for the line in slope-intercept form.

13) Slope = 89

, y-intercept = 3 13)

A) f(x) = 98

x + 278 B) f(x) = 8

9x - 3 C) f(x) = -

89 x - 3 D) f(x) = 8

9x + 3

14) Passing through (8, 3) and (2, 7) 14)

A) y = mx + 253 B) y = -

23 x +

253 C) y = 2

3x +

253 D) y - 3 = -

23 (x - 8)

15) Slope = 2, passing through (-2, 2) 15)A) y - 2 = x + 2 B) y - 2 = 2x + 2 C) y = 2x - 6 D) y = 2x + 6

Use the given conditions to write an equation for the line in the indicated form.16) Passing through (5, 3) and parallel to the line whose equation is y = -2x + 3 ;

point-slope form16)

A) y - 5 = -2(x - 3) B) y = 2x C) y - 3 = -2(x - 5) D) y - 3 = x - 5

17) Passing through (5, 2) and parallel to the line whose equation is 4x + y - 8 = 0;slope-intercept form

17)

A) y = - 4x - 22 B) y = - 4x + 22 C) y = 4x - 22 D) y = - 14 x -

112

18) Passing through (3, 3) and perpendicular to the line whose equation is y = 3x + 7;point-slope form

18)

A) y - 3 =13

(x + 3) B) y - 3 = - 13 (x - 3)

C) y - 3 =13

(x - 3) D) y = - 3x - 12

Add or subtract as indicated and write the result in standard form.19) 5i - (-5 - i) 19)

A) 5 + 6i B) -5 - 6i C) -5 + 4i D) 5 - 4i

20) -3 - (6 + 10i) - (5 - 6i) 20)A) -14 - 4i B) -14 + 4i C) -11 - 4i D) -11 + 4i

Perform the indicated operations and write the answer in the form a + bi, where a and b are real numbers.21) (9 + 9i)(2 - 9i) 21)

A) -63 + 99i B) -81i2 - 63i + 18 C) 99 - 63i D) 99 + 63i

22) (8 + 7i)(8 - 7i) 22)A) 64 - 49i B) 15 C) 64 - 49i2 D) 113

Divide and express the result in the form a + bi, where a and b are real numbers.

23) 5i2 + i

23)

A) 1 + 2i B) 1 + 5i C) 1 - 2i D) -1 + 2i

3

24) 4 - 5i5 + 4i

24)

A) -1 B) i C) -i D) 1

25) 89 - i

25)

A) 3641

- 441 i B) 36

41+

441 i C) 9

10-

110 i D) 9

10+

110 i

Solve the quadratic equation by any method.26) x2 + 9x - 36 = 0 26)

A) {-12, 1} B) {12, -3} C) {-12, 3} D) {12, 3}

27) 2x2 + 6x + 2 = 0 27)

A) -3 - 52

, -3 + 52

B) -3 - 132

, -3 + 132

C) -6 - 52

, -6 + 52

D) -3 - 54

, -3 + 54

28) 6x2 + 19x + 10 = 0 28)

A) 52

, - 23

B) -56

, - 15

C) -52

, - 23

D) 52

, 23

29) x2 = x + 72 29)A) {1, 72} B) {8, 9} C) {-8, 9} D) {-8, -9}

30) 10x2 - 8x = 0 30)

A) 0, 45

B) 45

, - 45

C) -45

, 0 D) {0}

31) (5x - 12)2 = 20 31)

A) -12 - 2 55

, -12 + 2 55

B) 12 - 2 55

, 12 + 2 55

C) {-2 5, 2 5} D) - 85 , 32

5

32) (2x + 3)2 = 25 32)A) {1, 4} B) {-4, 1} C) {0, 1} D) {-14, 14}

33) 16x2 + 1 = 7x 33)

A) -7 ± 1532

B) 7 ± i 1532

C) -7 ± i 1532

D) 7 ± 1532

4

Use completing the square to find the constant that should be added to the binomial to create a perfect square trinomial.34) x2 - 8x+_____ 34)

A) 16 B) 4 C) 64 D) -16

35) x2 -27

x+___ 35)

A) 249

; x2 -27

x + 249

= x - 17

2B) 4

49; x2 -

27

x + 449

= x - 27

2

C) 149

; x2 -27

x + 149

= x - 17

2D) 1

49; x2 -

27

x + 149

= x + 17

2

36) x2 - 5x+_____ 36)

A) -254

; x2 - 5x - 254

= x - 52

2B) 25; x2 - 5x + 25 = (x - 5)2

C) 52

; x2 - 5x + 52

= x - 52

2D) 25

4; x2 - 5x + 25

4= x - 5

22

Solve the equation, and check all proposed solutions.37) x - 3x - 2 = 4 37)

A) {1, 2} B) {9} C) {2, 9} D) {-1}

38) x3/2 = 343 38)

A)3

7 B) {2401 7} C) {49} D) {7}

The graph of a quadratic function is given. Determine the function's equation.39) 39)

A) h(x) = (x - 1)2 + 1 B) j(x) = (x - 1)2 - 1C) g(x) = (x + 1)2 - 1 D) f(x) = (x + 1)2 + 1

5

40) 40)

A) f(x) = (x + 2)2 + 2 B) g(x) = (x + 2)2 - 2C) j(x) = (x - 2)2 - 2 D) h(x) = (x - 2)2 + 2

41) 41)

A) h(x) = (x - 3)2 + 3 B) f(x) = (x + 3)2 + 3C) g(x) = (x + 3)2 - 3 D) j(x) = (x - 3)2 - 3

Find the coordinates of the vertex for the parabola defined by the given quadratic function.42) f(x) = (x - 5)2 - 5 42)

A) (-5, 0) B) (0, -5) C) (5, -5) D) (5, 5)

Find the axis of symmetry of the parabola defined by the given quadratic function.43) f(x) = 5 - (x + 4)2 43)

A) x = 4 B) x = 5 C) x = -4 D) x = -5

44) f(x) = 11(x - 2)2 + 5 44)A) x = 5 B) x = -2 C) x = 2 D) x = 11

Find the coordinates of the vertex for the parabola defined by the given quadratic function.45) f(x) = 5 - (x + 3)2 45)

A) (5, 3) B) (-3, 5) C) (5, -3) D) (3, 5)

46) f(x) = 6x2 + 12x - 8 46)A) (-1, -14) B) (-2, 4) C) (2, 40) D) (1, 10)

6

Find the domain and range of the quadratic function whose graph is described.47) The vertex is (1, 11) and the graph opens down. 47)

A) Domain: (- , )Range: (- , 11]

B) Domain: (- , )Range: [11, )

C) Domain: (- , 1]Range: (- , 11]

D) Domain: (- , )Range: (- , 1]

Find the range of the quadratic function.48) y + 4 = (x - 2)2 48)

A) (- , - 2] B) [- 4, ) C) [4, ) D) (- , 4]

49) f(x) = x2 + 12x + 2 49)A) [6, ) B) (- , -34] C) (- , -106] D) [-34, )

Determine whether the given quadratic function has a minimum value or maximum value. Then find the coordinates ofthe minimum or maximum point.

50) f(x) = 2x2 + 2x - 1 50)

A) maximum; -12

, - 32 B) maximum; -

32 , - 1

2

C) minimum; - 32 , - 1

2 D) minimum; -12

, - 32

Find the distance between the pair of points.51) (-4, 3) and (-8, 0) 51)

A) 6 B) 25 C) 10 D) 5

52) (-5 2, -3) and (-3 2, -2) 52)

A) 3 B) 2 C) 92

D) 9

53) (0, -6) and (-5, -6) 53)A) 25 B) 5 C) 61 D) 6

Find the midpoint of the line segment whose end points are given.54) (9, 8) and (6, -8) 54)

A) (15, 0) B) (152 , 0) C) (

32 , 8) D) (3, 16)

55) (- 35

, 14 ) and (- 1,

12 ) 55)

A) (- 85

, 34 ) B) (-

15 , 1

8) C) ( 1

5, -

18 ) D) (- 4

5,

38 )

7

Write the standard form of the equation of the circle with the given center and radius.56) Center at (-3, -5); radius of 9 56)

A) (x + 3)2 + (y + 5)2 = 81 B) (x - 5)2 + (y - 3)2 = 9C) (x - 3)2 + (y - 5)2 = 81 D) (x + 5)2 + (y + 3)2 = 9

57) (0, 3); 10 57)A) x2 + (y + 3)2 = 10 B) (x - 3)2 + y2 = 100C) (x + 3)2 + y2 = 100 D) x2 + (y - 3)2 = 10

58) (0, 0); 8 58)A) x2 - y2 = 8 B) x2 + y2 = 8 C) x2 + y2 = 16 D) x2 + y2 = 64

Complete the square and write the equation in standard form. Then give the center and radius of the circle.59) x2 - 2x + 1 + y2 + 10y + 25 = 4 59)

A) (x + 5)2 + (y - 1)2 = 4(5, -1), r = 4

B) (x + 5)2 + (y - 1)2 = 4(-5, 1), r = 2

C) (x - 1)2 + (y + 5)2 = 4(-1, 5), r = 4

D) (x - 1)2 + (y + 5)2 = 4(1, -5), r = 2

60) x2 + y2 - 14x + 10y = 7 60)A) (x - 7)2 + (y + 5)2 = 81

(-7, 5), r = 81B) (x + 5)2 + (y - 7)2 = 81

(5, -7), r = 81C) (x - 7)2 + (y + 5)2 = 81

(7, -5), r = 9D) (x + 5)2 + (y - 7)2 = 81

(-5, 7), r = 9

Solve the problem.61) Claire has received scores of 85, 88, 87, and 75 on her algebra tests. What score must she receive on

the fifth test to have an overall test score average of at least 83?61)

A) 79 or greater B) 81 or greater C) 78 or greater D) 80 or greater

62) The equation V = -3000t + 22,000 describes the value (V) in dollars of a certain model of car after it ist years old. What is the age of the car, if it is currently worth $10,000?

62)

A) 4 years B) 3 years C) 6 years D) 5 years

63) A square sheet of paper measures 43 centimeters on each side. Using the Pythagorean Theorem,determine the length of the diagonal of this paper.

63)

A) 43 2 cm B) 86 cm C) 43 cm D) 3698 cm

64) A car rental agency charges $175 per week plus $0.25 per mile to rent a car. The total cost, C, for therenting the car for one week and driving it x miles can be modeled by the formula C = 0.25x + 175.How many miles can you travel in one week for $275?

64)

A) 1100 miles B) 375 miles C) 243.75 miles D) 400 miles

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Answer KeyTestname: CAUNIT1PRACTICEEXAMF2014FINAL

1) A2) A3) D4) C5) A6) B7) A8) D9) A

10) C11) B12) B13) D14) B15) D16) C17) B18) B19) A20) A21) C22) D23) A24) C25) B26) C27) A28) C29) C30) A31) B32) B33) B34) A35) C36) D37) B38) C39) B40) B41) A42) C43) C44) C45) B46) A47) A48) B49) D50) D

9

Answer KeyTestname: CAUNIT1PRACTICEEXAMF2014FINAL

51) D52) A53) B54) B55) D56) A57) D58) D59) D60) C61) D62) A63) A64) D

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