Mid Term-0312-Ch:2-7
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Factor the trinomial completely.
1) 4x3 + 12x2y - 40xy2
1)
A) (4x2 + 8xy)(x - 5y)
C) 4x(x + 2y)(x - 5y)
B) (x - 2y)(4x2 + 20xy)
D) 4x(x - 2y)(x + 5y)
Suppose that segment PQ has the given coordinates for one endpoint P and for its midpoint M. Find the
coordinates of the other endpoint Q.
1
2) P(1, 8) and M - , 1
2)
2
A) Q -3, -14
3
C) Q - , - 7
2
B) Q -1, 2
Find the midpoint of the segment with the given endpoints.
3) (-4, -3) and (3, 3)
1
7
A) - , 0
B) - , - 3
C) -1, 0
2
2
D) Q(-2, -6)
3)
D) -7, -6
Decide whether the ordered pair is a solution of the given system.
4) x + y = 1
x - y = 9 ; (-5, -4)
A) Yes
B) No
4)
Divide.
5)
18x7 - 30x5
-6x7
A) 18x7 + 5)
5
x2
B) -3 - 30x5
C) -3 + 5x2
D) -3 + 5
x2
Write the rational expression in lowest terms.
m2 - 16m
6)
16 - m
A) -m
6)
B) m + 4
C) m
D) -(m + 4)
Find an equation of the line satisfying the conditions. Write the equation in slope-intercept form.
7) Through (-6, 7); parallel to 3x + 7y = 3
3
31
7
7
3
31
3
3
A) y = x - B) y = - x + C) y = - x + D) y = x + 7
7
3
3
7
7
7
7
Graph the line described.
1
7)
8) Undefined slope; through (-1, 9)
8)
y
10
5
-10
-5
5
10
x
-5
-10
A)
B)
y
-10
y
10
10
5
5
-5
5
10
x
-10
-5
5
-5
-5
-10
-10
C)
10
x
D)
y
y
10
10
5
-10
10
x
-10
-5
5
10
x
-5
-10
-10
Find the slope of the line through the pair of points.
9) (7, -9) and (-4, -9)
A) 0
B) -11
9)
C) 11
2
D) Undefined
Add or subtract as indicated. Write the answer in lowest terms.
2ab
b
10)
- + 4
a2 - b2 a - b
A)
4a + 5b
a + b
B)
4a + 5b
a2 - b2
C)
(a - b)(5a + 5b)
a2 - b2
D)
2ab - b + 4
a + b + 1
Solve the equation.
11) 3m + 5 = 7
2
A) - , 4
3
12)
10)
11)
2
B) , - 4
3
C) ∅
2 12
D) , - 5
5
6
8
= 1 + x - 6
x + 6
A) {-10, 12}
12)
C) ∅
B) {-8, 12}
D) {10, -12}
Solve the system by elimination. If the system is inconsistent or has dependent equations, say so.
13) x + 4y = 13
2x + 3y = 6
A) {(3, 5)}
B) {(-3, 4)}
C) {(-4, 5)}
D) ∅; inconsistent system
Express the rational expression in lowest terms.
y2 + 2y - 24
14)
y2 + 3y - 28
A)
2y - 6
3y - 7
B) - 13)
14)
y2 + 2y - 24
y2 + 3y - 28
C)
2y - 24
3y - 28
D)
y + 6
y + 7
Find the product.
15) (9m + 5)2
A) 9m2 + 90m + 25
15)
B) 81m2 + 25
D) 9m2 + 25
C) 81m2 + 90m + 25
16) (4p - 1)(16p2 + 4p + 1)
A) 64p3 + 1
16)
B) 64p3 + 20p2 - 1
C) 64p3 - 1
D) 16p3 - 1
Factor the polynomial completely.
17) 48a4 - 27b2
17)
B) 3(4a2 + 3b)2
D) 3(4a2 + 3b)(4a2 - 3b)
A) (12a2 + 9b)(4a2 - 3b)
C) 3(4a2 - 3b)2
Name the quadrant, if any, in which the point is located.
18) (15, -15)
A) III
B) IV
18)
C) I
3
D) II
Graph the linear inequality in two variables.
19) 5x + y ≤ -2
19)
y
10
5
-10
-5
5
10
x
-5
-10
A)
B)
y
-10
y
10
10
5
5
-5
5
10
x
-10
-5
-5
-5
-10
-10
C)
5
10
5
10
x
D)
y
-10
y
10
10
5
5
-5
5
10
x
-10
-5
-5
-5
-10
-10
Find the requested value.
20) If f(x) = x2 + 5x + 2 and g(x) = 3x - 1, find (fg)(5).
A) 749
20)
B) 118
C) 728
D) 28
Find all numbers not in the domain of the function.
3
21) f(x) = x + 9
A) None
x
21)
B) 0
C) 9
4
D) -9
Express the area of the figure as a polynomial in descending powers of the variable x.
22)
4x - 3
22)
x + 5
A) 4x2 + 17x - 15
B) 3x2 - 23x + 15
C) 4x2 + 23x - 10
D) -4x2 + 16x + 15
Find the slope and the y-intercept of the line.
23) 4x - 5y = 5
23)
A) Slope 1; y-intercept (0, 1)
4
B) Slope - ; y-intercept (0, 1)
5
C) Slope -1; y-intercept (0, -1)
4
D) Slope ; y-intercept (0, -1)
5
Perform the indicated operation and express in lowest terms.
k2 + 9k + 18
k2 + 5k
24)
· k2 + 11k + 30 k2 + 11k + 24
A)
k
2
k + 11k + 30
B)
k
k + 8
C)
24)
k2 + 5k
k + 8
D)
1
k + 8
Solve the formula for the specified variable.
1
25) A = h(B + b) for B
2
A) B = A - bh
h
B) B = 25)
2A + bh
h
C) B = 2A - bh
h
D) B = 2A - bh
Solve the problem.
26) Company A rents copiers for a monthly charge of $300 plus 12 cents per copy. Company B
rents copiers for a monthly charge of $600 plus 6 cents per copy. What is the number of copies
above which Company Aʹs charges are the higher of the two?
A) 5100 copies
B) 5000 copies
C) 10,000 copies
D) 2500 copies
27) Find f(-3) when f(x) = 5x2 - 3x + 5.
A) 59
B) 23
26)
27)
C) 41
Find all solutions by factoring.
28) -6b2 + 54 = 0
D) 49
28)
A) {-6, 3}
C) No real solution
B) {0, 3}
D) {-3, 3}
5
Simplify the complex fraction.
1
+ 1
a
29)
1
- 1
a
A)
29)
1 + a
1 - a
C) 1 - a2
B) 1
D)
a
1 - a2
Write an inequality statement involving the letter x that describes the given graph or interval notation.
30)
30)
-7 -6 -5 -4 -3 -2 -1 0
1
A) 3 < x ≤ 7
2
3
4
5
6
7
C) 3 ≤ x < 7
B) 3 < x < 7
Decide whether the pair of lines is parallel, perpendicular, or neither.
31) 3x - 8y = -12 and 32x + 12y = -11
A) Parallel
B) Perpendicular
D) 3 ≤ x ≤ 7
31)
C) Neither
Solve the inequality. Give the solution set in both interval and graph forms.
32) -6(4y - 13) < -30y + 54
A) (-∞, -4)
-11 -10 -9
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
B) (-30, ∞)
-37 -36 -35 -34 -33 -32 -31 -30 -29 -28 -27 -26 -25 -24 -23
C) (-∞, -30)
-37 -36 -35 -34 -33 -32 -31 -30 -29 -28 -27 -26 -25 -24 -23
D) (-4, ∞)
-11 -10 -9
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
6
3
32)
Answer Key
Testname: MT‐0312
1) D
2) D
3) A
4) B
5) D
6) A
7) C
8) D
9) A
10) A
11) B
12) D
13) B
14) D
15) C
16) C
17) D
18) B
19) D
20) C
21) D
22) A
23) D
24) B
25) C
26) B
27) A
28) D
29) A
30) B
31) B
32) A
7