Midterm ExamMAT

110

03 & 04

Shibalovich

2022

March 17

1 hr. 30 min.

X

X

X

Use a scientific calculator.

This test is a take-home test. Please take it by yourself without help

from anyone else. Please be honest.

Midterm Exam

College Algebra, MAT 110

Name _________________________

This exam is worth 100 points. Solve each problem below on a separate sheet of paper and then transfer your answers to

enclosed bubble sheet. Please use a blue or black pen on the bubble sheet.

Write the quadratic function in the form y = a(x – h)2 + k.

1) y = x2 – 16x + 70

A) y = (x + 8)2 + 6

B) y = (x – 8)2 + 6

D) y = (x + 8)2 – 6

C) y = (x – 8)2 – 6

Find the domain and range.

2) f(x) =

x2 – 49

A) D: (-«, -7] U [7, «) , R: [0, «)

B) D: (-«, -7] U [7, «) , R: (-«, «)

C) D: (-«, «) , R: [0, «)

D) D: [-7, 7] , R: [0, «)

Solve.

3)

4)

2

-2

1

+

=

x+5 x+3

x2 + 8x + 15

3

A) 0

B) 3

3x + 4 = -3

31

A)

3

B) –

C) -5

31

3

C)

D) No Solution

23

3

D) -31

Write the formula expressed by the variation.

5) y varies jointly as x and the square of w: y = 118.9728, when x = 2.4 and w = 5.4.

A) y = 9.18xw

B) y = 9.18xw2

C) y = 3.825x2w

D) y = 1.7xw2

Find the inverse of the function.

6) f(x) = (x – 9)2 + 1 , x ≥ 9

A) f -1(x) = x + 1 – 9

B) f -1(x) = x – 1 + 9

D) f -1(x) = 1×2 + 9

C) f -1(x) = x + 9 – 1

Determine whether the pair of lines is parallel, perpendicular, or neither.

7) 3x – 4y = 6

8x + 6y = 6

A) Perpendicular

B) Neither

Page 1

C) Parallel

MAT 110, Pr. Shibalovich

Solve the problem.

8) Compute the average rate of change of f(x) = 6×2 + 2 from x = 2 to x = 5. Round your

1

2

answer to two decimal places.

A) 42.00

B) 42.91

C) 43.34

D) 39.29

Identify the vertex of the parabola.

9) f(x) = -5×2 + 30x – 47

A) (-3, -2)

B) (2, -3)

C) (-3, 2)

D) (3, -2)

C) y = -2×2 – 5

D) y = 2×2 – 5

Write equation of the graph below.

10)

y

-5

x

5

-5

-10

-15

A) y = -x2 – 5

B) y = x2 – 5

Determine what symmetry given equation has: with respect to the x-axis, the y-axis, or the origin.

11) y = 2×2 – 4

A) x-axis only

C) x-axis, y-axis, origin

B) Origin only

D) y-axis only

Write an equation in standard form using only integers for the line described.

12) The line perpendicular to x = 1 and containing (5, 8)

A) x = 5

B) y = 8

C) 8x + 5y = 0

D) 5x + 8y = 0

Find x-intercepts for the given function.

13) f(x) = x2 – 14x + 40

A) (10, 0) and ( 4 , 0)

C) (36, 0) and (4, 0)

B) ( 40, 0) and ( -40, 0)

D) (-10, 0) and (-4 , 0)

Find the product.

14) (-2×2 + 10y)(2×2 + 9y)

A) -4×4 + 2x2y + 90y4

B) -4×4 + 2x2y + 90y2

D) -4×4 + 2x2y2 + 90y2

C) -4×2 + 2xy + 90y2

Page 2

MAT 110, Pr. Shibalovich

Divide.

15)

-10×3 – 18×2 + 9x – 1

-5x + 1

A) x2 + 4x – 1

B) x2 – 4x + 1

C) 2×2 + 4x – 1

D) 2×2 – 1

For the given function, find all asymptotes of the type indicated (if there are any).

16) f(x) =

x2 + 5x – 8

, oblique

x-4

A) y = x + 1

B) None

C) x = y + 9

D) y = x + 9

Find the requested composition of functions.

17) Given f(x) = x + 5 and g(x) = 8x – 9, find (f † g)(x).

A) 8 x + 5 – 9

B) 2 2x + 1

C) 2 2x – 1

D) 8 x – 4

Use the rational zero theorem to find all possible rational zeros for the polynomial function.

18) P(x) = -2×4 + 4×3 + 6×2 + 18

1

A) ±1, ± , ±2, ±3, ±6, ±9, ±18

2

B) ±1, ±

C) ±1, ±2, ±3, ±6, ±9, ±18

1

3

9

, ±2, ±3, ± , ±6, ±9, ± , ±18

2

2

2

D) ±1, ±2, ±

1

1

1

1

1

,± ,± ,± ,±

2

3

6

9

18

Find all of the real and imaginary zeros for the polynomial function.

19) f(x) = 3×4 – 10×3 + 20×2 – 40x + 32

4

4

B) , 2, -i, i

A) , 2, -2i, 2i

3

3

C)

2

, 2, -4i, 4i

3

D) –

4

, -2, -2i, 2i

3

Solve the problem.

20) The area of a square is 81 square centimeters. If the same amount is added to one

dimension and removed from the other, the resulting rectangle has an area 9 square

centimeters less than the area of the square. How much is added and subtracted?

A) 9 cm

B) 4 cm

C) 12 cm

D) 3 cm

Write the quotient in the form a + bi.

21)

8 + 4i

6 – 7i

A) –

76 16

+

i

13 13

B) –

4

16

+

i

13 13

C)

4

16

+

i

17 17

D)

76 32

+

i

17 17

C)

4

22

; 0,

5

5

1

5

D) 1 ; 0,

4

22

Find the slope and the y-intercept of the equation.

22) 4x + 5y = 22

4

22

A) – ; 0,

5

5

1

5

B) -1 ; 0,

4

22

Page 3

MAT 110, Pr. Shibalovich

Simplify given radical expression.

23)

4

729 x4

A) 27|x|

B) 27

4

x4

C) 3|x|

4

9

D) 3

4

9×4

Match the graph to the correct inequality.

24)

10

5

-10

-5

5

10

-5

-10

A) 2x + y ≥ -3

B) -2x + y ≥ -3

C) 2x + y ≤ -3

D) -2x + y ≤ -3

C) [-15,3]

D) M

Solve the inequality. Write the solution set in interval notation.

25) |h + 6| + 1 ≤ 10

A) [-15,10]

B) (-15,3)

Page 4

MAT 110, Pr. Shibalovich

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