MAT 110 Arizona State University Algebra Math Multiple Choice Questions

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
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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)
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MAT 110, Pr. Shibalovich