Math 10007 Test 01 & Math 10023 Midterm Examination STUDY ...

Math 10007 Test 01 & Math 10023 Midterm Examination STUDY GUIDE Spring 2011

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The use of a calculator is permitted on this exam. Duration of the test is 100 minutes and will have less number of questions than this study guide. This study guide does not necessarily contain questions from every possible topic covered by the final exam. Any topic covered in the course may be represented in the final. It is recommended that students study all topics of the course. We also recommend studying chapter tests and chapter exercises. All questions are the property of Math Department at Kent - Trumbull.

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

Find the value of the expression for the given replacement value.

1)

x2 - 10x + 5 x2 + 2x - 1

;

x = 7

A) -

8 31

B) 2

C)

-

1 4

1)

D)

8 31

Evaluate the rational function for the given replacement value.

2)

f(x)=

x2 - 10x + 5 x2 + 2x - 1

;

f( 7).

A) Undefined

B)

-

8 31

C) 2

2)

D)

8 31

Evaluate the rational expression.

3)

f(a)=

1

a2 - a2

;

Find f(-9).

A) -

80 81

B)

81 82

C)

-

81 80

3)

D)

81 80

Simplify the expression.

4)

3x + 2 12x2 + 17x +

6

A)

1 4x +

3

B)

3x + 4 4x + 17

4)

C)

3x + 2 12x2 + 17x +

6

D)

3x 4x + 3

5)

y2 + y2 +

10y + 13y +

25 40

A)

10y + 13y +

25 40

B)

-

y2 y2

+ +

10y + 13y +

25 40

C)

y + y +

5 8

5)

D)

10y + 5 13y + 8

6)

6x2 + 18x3 5x + 15x2

A)

6x 5

B)

6 5

C)

6 + 18x3 5x + 15

6)

D)

6x2 + 18x3 5x + 15x2

1

7)

a2 - ab + 11a a + 11

- 11b

A) a - 2b + 1

C) a - b

7)

B)

1 a + 11

D)

a2 -

ab + 11a a + 11

11b

Find the product and simplify.

8)

x2 + 7x + 12 x2 + 10x + 21

?

x2 + 9x + 14 x2 + 6x + 8

8)

A)

x x

+ +

7 2

B)

x + x +

4 7

C)

1 x +

2

D) 1

9)

x2 + x2 +

7x + 8x +

10 12

?

x2 + 6x x2 + 2x - 15

A)

x

x -

3

B)

1 x -

3

9)

C)

x2 +

x 8x

+ 12

D)

x(x + 6) x - 3

Find the quotient and simplify.

10)

x 5

+ 6 - x

?

x2 - 9x + 18 x2 - 11x + 30

A) -

x x -

6 3

B)

-

(x

+ 6)(x (x - 5)2

6)

C)

-

x x

+ -

6 3

10)

D)

x x

- 6 - 3

11)

(x

(x + 5) + 5)(9x +

5)

?

9 9x +

5

A) 9

B) 1

11)

C)

1 9

D)

9 (9x +

5)2

Multiply or divide as indicated.

12)

(x + 4)2 x - 4

?

x2 4x -

16 16

A)

(x (x

+ -

4)2 4)2

B)

8(x2 + 16) x2 - 16

C)

(x + 4)3 4(x - 4)

12)

D)

4(x + 4) x - 4

Perform the indicated operation. Simplify if possible.

13)

x2

+

x 3x

-

40

-

x2

+

5 3x

-

40

A)

1 2(x +

8)

B) x - 5

C)

1 x +

8

13) D) x + 8

2

14)

3x - 6 x2 + 7x -

8

-

2x - 5 x2 + 7x -

8

A)

x2

x +

+ 1 7x -

8

B)

x2

1 + 7x - 8

C)

1 x +

8

14)

D)

x

1 - 1

Find the LCD for the list of rational expressions.

15)

x2 +

8 5x +

4

,

x2

8 + 8x +

16

15)

A) (x - 1)(x - 4)(x + 4) C) (x + 1)(x + 4)(x + 4)

B) (x + 4)(x + 4) D) (x + 1)(x + 4)

Rewrite the rational expression as an equivalent rational expression with the given denominator.

16)

x

x + 5

=

2x

+ 10

16)

A)

2 2x +

10

B)

5x 2x + 10

C)

x 2x +

10

D)

2x 2x + 10

17)

15 3 - y

=

y - 3

A)

15 y - 3

B)

-

15(y - 3) y - 3

C)

-

15 y - 3

17)

D)

-

1 y - 3

Perform the indicated operation. Simplify if possible.

18)

9 4x -

16

+

x x2 -

16

A)

4(x

x + 9 + 4)(x

-

4)

B)

13x + 36 4(x + 4)(x -

4)

C)

10x + 36 (x + 4)(x - 4)

18)

D)

13x (x + 4)(x - 4)

19)

11 x - 8

+

13 8 - x

A) -

2 x -

8

B)

-

24 x - 8

C)

24 x - 8

19)

D)

x

2 - 8

20)

8 x9

-

11x

A)

8

- 11x10 x9

B)

8 - 11x8 x9

C)

11x10 x9

8

20)

D)

8

- 11x x9

Solve the equation.

21)

6 y+ 2

-

4 y -

2

=

4 y2 -

4

A) -12

B) 12

C) 24

21) D) 24

3

22)

x 2x +

2

=

-2x 4x + 4

+

2x - 3 x + 1

A) 3

B)

3 2

C) -3

22) D) no solution

Solve.

23)

w

1 + 10

=

3 5w

A) w = 15

B) w = 3

C) w = 5

23)

D)

w

=

15 4

Solve.

24) The ratio of the weight of an object on Earth to the weight of the same object on Pluto is 100 to 3. If a 24)

buffalo weighs 3612 pounds on Earth, find the buffalo's weight on Pluto. (Round to the nearest

pound.)

A) 10,836 lb

B) 8 lb

C) 108 lb

D) 1,083,600 lb

25) The ratio of a quarterback's completed passes to attempted passes is 7 to 8. If he attempted

25)

16 passes, find how many passes he completed. Round to the nearest whole number if necessary.

A) 14 passes

B) 18 passes

C) 2 passes

D) 8 passes

26) The scale on a map states that 1 centimeter corresponds to 30 kilometers. On the map, two cities are 26)

11 cm apart. Find the actual distance.

A) 33 km

B) 330 km

C) 33,000 km

D) 3300 km

27) A punch recipe calls for mixing 3 parts of orange juice with 7 parts of strawberry juice. Find how

27)

much orange juice should be mixed with 63 ounces of strawberry juice.

A) 21 oz

B) 27 oz

C) 9 oz

D) 147 oz

Given that the pair of triangles is similar, find the missing length.

28)

28)

39

5

13

36 A) x = 20

12 B) x = 5

C) x = 15

D) x = 9

29) 6 2 4

A) x = 4

9 3

B) x = 12

C) x = 11

29) D) x = 16

4

30)

30)

6 16 A) x = 9.6

x

25.6 B) x = 96

C) x = 3.75

D) x = 0.375

Solve.

31) Two times the reciprocal of a number equals 36 times the reciprocal of 45. Find the number.

31)

A) 90

B)

5 2

C) 11

D)

8 5

32) Five divided by the sum of a number and 6, minus the quotient of 3 and the difference of the

32)

number and 6 is equal to 6 times the reciprocal of the difference of the number squared and 36.

What is the number?

A) -21

B)

-

21 4

C) 9

D) 27

33) A painter can finish painting a house in 5 hours. Her assistant takes 7 hours to finish the same job. 33)

How long would it take for them to complete the job if they were working together?

A)

12 35

hours

B)

2

11 12

hours

C) 4 hours

D) 6 hours

34) Mark and Rachel both work for Smith Landscaping Company. Mark can finish a planting job in 2 34)

hours, while it takes Rachel 5 hours to finish the same job. If Mark and Rachel will work together

on the job, and the cost of labor is $35 per hour, what should the labor estimate be? (Round to the

nearest cent, if necessary.)

A) $122.50

B) $100.00

C) $50.00

D) $24.50

35) One pump can drain a pool in 4 minutes. When a second pump is also used, the pool only takes 3 35)

minutes to drain. How long would it take the second pump to drain the pool if it were the only

pump in use?

A) 11 minutes

B)

1 12

minutes

C) 12 minutes

D)

1

5 7

minutes

36) A car travels 400 miles on level terrain in the same amount of time it travels 160 miles on

36)

mountainous terrain. If the rate of the car is 30 miles per hour less in the mountains than on level

ground, find its rate in the mountains.

A) 50 mph

B) 40 mph

C) 80 mph

D) 20 mph

37) Jim can run 5 miles per hour on level ground on a still day. One windy day, he runs 11 miles with 37)

the wind, and in the same amount of time runs 6 miles against the wind. What is the rate of the

wind?

A) 5 mph

B)

1

8 17

mph

C)

2

1 2

mph

D) 17 mph

5

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