Test # 1 Review (Sec. 2.2 &2.4, Ch.6) Math 1324
Name___________________________________ Date:________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Find the slope of the line, if it is defined.
1) Through (-2, -6) and (-3, -4)
A) 2
B) -1
1)
C) Undefined
D) -2
2) Through (-7, -7) and (-7, 8)
A) 3
B) 5
2)
C) Undefined
D) 15
3) Through (-4, 4) and (1, 4)
A) 7
B) 0
C) 2
D) 1
B) Undefined
3
C) -1
8
3
D) 1
8
3)
4) Through (-5, -4) and (3, 7)
A) 1
4)
Find the slope and the y -intercept of the line.
5) 3x + 4y = 14
7
3
4
B) m = ; b = 14
A) m = ; b = 2
4
3
6) 2x - 4y = 18
9
1
A) m = ; b = - 2
2
5)
4
C) m = - ; b = 4
3
3
7
D) m = - ; b = 4
2
6)
1
B) m = - ; b = 18
2
9
C) m = 2; b = - 2
1
D) m = - 2; b = -4
Choose one of the four lines graphed which most closely resembles the graph of the given equation.
7) y = 3x - 5
A)
B)
8
-8
-6
-4
y
8
6
6
4
4
2
2
-2
2
4
6
8 x
-8
-6
-4
-2
-2
-2
-4
-4
-6
-6
-8
-8
C)
y
2
4
6
8 x
2
4
6
8 x
D)
8
-8
-6
-4
y
8
6
6
4
4
2
2
-2
2
4
6
8 x
-8
-6
-4
-2
-2
-2
-4
-4
-6
-6
-8
-8
2
y
7)
8) y = -4x + 5
A)
8)
B)
8
-8
-6
-4
y
8
6
6
4
4
2
2
-2
2
4
6
8 x
-8
-6
-4
-2
-2
-2
-4
-4
-6
-6
-8
-8
C)
y
2
4
6
8 x
2
4
6
8 x
D)
8
-8
-6
-4
y
8
6
6
4
4
2
2
-2
2
4
6
8 x
-8
-6
-4
-2
-2
-2
-4
-4
-6
-6
-8
-8
3
y
Find the x- and y-intercepts for the equation. Then graph the equation.
9) 5x - 15y = 30
9)
y
10
5
-10
-5
5
10
x
-5
-10
A) (0, -2), (6, 0)
B) (0, -2), (-6, 0)
y
-10
y
10
10
5
5
-5
5
10
x
-10
-5
5
-5
-5
-10
-10
Decide whether the pair of lines is parallel, perpendicular, or neither.
10) 3x - 8y = -5
32x + 12y = -20
A) Perpendicular
B) Neither
11) 9x + 3y = 12
18x + 6y = 27
A) Perpendicular
10
x
10)
C) Parallel
11)
B) Neither
C) Parallel
12) The line through (-20, 5) and (-4, 7) and the line through (-5, 5) and (7, 4)
A) Parallel
B) Perpendicular
C) Neither
Find an equation of the the line satisfying the given conditions.
2
13) Through (4, 2); m = - 3
A) 2x + 3y = -14
B) 3x + 2y = -14
C) 2x - 3y = 14
Write an equation in standard form for a line passing through the pair of points.
14) (-8, -6) and (0, -3)
A) 2x - 3y = -9
B) -2x + 3y = -9
C) -3x - 8y = 24
4
12)
13)
D) 2x + 3y = 14
14)
D) 3x - 8y = 24
Find an equation of the the line satisfying the given conditions.
15) Through (9, 2); perpendicular to 3x + 2y = 31
A) 2x - 3y = 12
B) 3x - 2y = 12
C) 2x + 3y = 12
16) Through (-3, -12); parallel to -6x - 7y = 53
A) -6x + 7y = 102
B) -6x - 7y = 102
15)
D) 2x - 3y = 1
16)
C) -3x - 7y = 53
D) -7x - 6y = -12
Solve and graph the inequality and graph the solution.
17) -9y + 8 ≥ -8y - 3
17)
A) [-11, ∞)
-18 -17 -16 -15 -14 -13 -12 -11 -10 -9
-8
-7
-6
-5
-4
-6
-5
-4
-3
-2
B) (-∞, -9]
-16 -15 -14 -13 -12 -11 -10 -9
-8
-7
C) (-∞, 11]
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18
D) (-9, ∞)
-16 -15 -14 -13 -12 -11 -10 -9
-8
-7
-6
-5
-4
-3
-2
18) -2(4x - 14) < -10x + 12
18)
A) (-∞, -10)
-17 -16 -15 -14 -13 -12 -11 -10 -9
-8
-7
-6
-5
-4
-3
B) (-8, ∞)
-15 -14 -13 -12 -11 -10 -9
-8
-7
-6
-5
-4
-3
-2
-1
-8
-7
-6
-5
-4
-3
-2
-1
-17 -16 -15 -14 -13 -12 -11 -10 -9
-8
-7
-6
-5
-4
-3
C) (-∞, -8)
-15 -14 -13 -12 -11 -10 -9
D) (-10, ∞)
Solve the problem.
19) In order for a chemical reaction to take place, the Fahrenheit temperature of the reagents must be
9
at least 117.82°F. Find the Celsius temperatures at which the reaction may occur. (F = C + 32)
5
A) C ≥ 244.08°
B) C < 244.08°
C) C ≤ 47.68°
5
D) C ≥ 47.68°
19)
Solve the inequality and graph the solution.
20) ∣8x - 4∣ ≥ 3
20)
A)
-8
-6
-4
-2
0
2
4
6
8
B)
-8
-6
-4
-2
0
2
4
6
8
C)
-8
-6
-4
-2
0
2
4
6
8
D)
-8
-6
-4
-2
0
2
4
6
8
21) ∣6x + 7∣ < 4
21)
A)
-8
-6
-4
-2
0
2
4
6
8
B)
-8
-6
-4
-2
0
2
4
6
8
C)
-8
-6
-4
-2
0
2
4
6
8
D)
-8
-6
-4
-2
0
2
4
6
8
Solve the inequality.
22) A salesperson has two job offers. Company A offers a weekly salary of $ 270 plus commission of
18% of sales. Company B offers a weekly salary of $ 540 plus commission of 9% of sales. What is
the amount of sales above which Company Aʹs offer is the better of the two?
A) $3000
B) $3100
C) $1500
D) $6000
Determine whether the given ordered set of numbers is a solution of the system of equations.
23) (-1, -5)
4x + y = 1
3x + 4y = 17
A) No
B) Yes
23)
24)
24) (-2, 2, 3)
-3x - 5y + z = -1
-2x
+ 4z = 16
x + 5y - 4z = -4
A) No
B) Yes
Solve the system of two equations in two variables.
25) x - 5y = 29
-3x - 6y = 18
A) (-4, -4)
B) (3, -4)
26) 4x - 2y = 7
8x - 4y = 35
A) (0, -3.5)
22)
25)
C) (4, -5)
D) No solution
26)
B) (1, 0)
C) No solution
6
D) (1, -1.5)
27) 2x + 5y = 3
8x + 20y = 12
3
A) , 0
2
27)
B) - 1, 1
5
3
C) - y + , y for any real number y
2
2
D) No solution
Solve the system of equations. If the system is dependent, express solutions in terms of the parameter z.
28) x + y + z = 3
x - y + 2z = 11
3x + y + z = 5
C) (1, -2, 4)
D) (4, 1, -2)
A) No solution
B) (4, -2, 1)
Solve the problem by writing and solving a suitable system of equations.
29) Best Rentals charges a daily fee plus a mileage fee for renting its cars. Barney was charged $ 132 for
3 days and 300 miles, while Mary was charged $ 235 for 5 days and 600 miles. What does Best
Rental charge per day and per mile?
A) $30 per day and 16 cents per mile
B) $15 per day and 29 cents per mile
C) $29 per day and 15 cents per mile
D) $28 per day and 16 cents per mile
30) If 50 pounds of tomatoes and 30 pounds of bananas cost $45 and 10 pounds of tomatoes and
20 pounds of bananas cost $16, what is the price per pound of tomatoes and bananas?
A) tomatoes: $0.70 per pound; bananas: $0.33 per pound
B) tomatoes: $0.50 per pound; bananas: $0.67 per pound
C) tomatoes: $0.60 per pound; bananas: $0.50 per pound
D) tomatoes: $0.70 per pound; bananas: $0.50 per pound
Perform the indicated operation.
31) Let A = 1 3 and B = 0 4 . Find 4A + B.
26
-1 6
A)
B)
4 28
4 16
4 48
7 30
28)
29)
30)
31)
C)
D)
4 16
1 12
Given the matrices A and B, find the matrix product AB.
32) A = -1 3 , B = -2 0 Find AB.
32
-1 2
A)
B)
2 -6
20
-2 1
-3 4
4 7
7 12
32)
C)
D)
-1 6
-8 4
7
6 -1
4 -8
33) A = 3 -2 1 , B = 5 0 Find AB.
0 4 -2
-2 3
A)
15 -10 5
-6 16 -8
33)
B) AB is not defined.
D)
C)
15 -6
-10 16
5 -8
15 0
0 12
Determine whether the two matrices are inverses of each other by computing their product.
34) 5 3 and 2 -3
32
-3 5
A) No
B) Yes
34)
1 1
2 4
35) -2 4 , 1 1
4 -4
2 4
35)
A) Yes
B) No
Find the inverse, if it exists, of the given matrix.
36) A = 4 4
-3 3
A)
B)
1 1
1 1
8 6
8 6
1 1
- 8 6
- 36)
C)
1 1
8 6
8
D)
1 1
- 8 6
1 1
- 6 6
1
8
1
8
1
6
1
8
Answer Key
Testname: TEST # 1 REVIEW MATH 1324 FALL 2010
1) D
2) C
3) B
4) D
5) D
6) A
7) C
8) B
9) A
10) A
11) C
12) C
13) D
14) D
15) A
16) B
17) C
18) C
19) D
20) A
21) A
22) A
23) A
24) B
25) C
26) C
27) C
28) C
29) C
30) C
31) B
32) C
33) B
34) B
35) B
36) C
9