MAT 1033
LCCC Final Exam Review - Part 1
Multiple Choice - Select the best response and bubble in the answer on the scantron answer sheet provided. Be sure to put your test version on the scantron answer sheet. Solve the inequality. Write the solution set in interval notation and graph the solution set. 1)
1) 8x - 2 > 7x - 8
A) (-6, ∞)
-13 -12 -11 -10 -9
-8
-7
-6
-5
-4
-3
-2
-1
0
1
B) [-6, ∞)
-13 -12 -11 -10 -9
-8
-7
-6
-5
-4
-3
-2
-1
0
1
C) (-10, ∞)
-17 -16 -15 -14 -13 -12 -11 -10 -9
-8
-7
-6
-5
-4
-3
D) (-∞, -6]
-13 -12 -11 -10 -9
-4
-3
-2
-1
0
1
-8
-7
-6
-5
Solve. 2) |7x + 8| + 8 = 17 17 1 , - A) 8 8
2) 1 17 B) , - 7 7
1 17 C) - , 7 7
D) ∅
Simplify. 3)
4x-2 y2 3 12x-4 y-1 A)
x6 y9 27
3) B)
x6 y9 3
C)
x8 y6 9
D)
x2 y3 3
Find the slope of the line containing the pair of points. 4) (2, -1) and (16, -6) 14 A) - 5
4) 5 B) - 14
5 C) 14
7 D) - 18
Find the x-intercept and y-intercept. 5) 4x + 3y = 24
5)
A) x-int: (0, 6); y-int: (8, 0)
B) x-int: (4, 0); y-int: (0, 3)
C) x-int: (6, 0); y-int: (0, 8)
D) x-int: (0, 4); y-int: (3, 0)
Find the specified slope. 6) Find the slope of a line parallel to the line -6x + 8y = -9. 4 3 A) - B) C) -9 3 4
1
6) D) Undefined
7) Find the slope of a line perpendicular to the line -5x - 3y = -7. 3 3 C) - A) -7 B) 5 5
7) D) Undefined
Use the slope-intercept form of the linear equation to write the equation of the line with the given slope and y -intercept. 2 8) 8) Slope ; y-intercept (0, 3) 3 2 A) y = - x - 3 3
2 B) y = x - 3 3
2 C) y = - x + 3 3
2 D) y = x + 3 3
Write an equation of the line with the given slope and containing the given point. Write the equation in the slope-intercept form y = mx + b. 7 9) Slope - ; through (2, 2) 9) 8 15 7 A) y = x - 4 8
7 15 B) y = x + 8 4
7 15 C) y = - x - 8 4
7 15 D) y = - x + 8 4
Find an equation of the line. Write the equation in standard form. 10) Undefined slope; through (2, 8) A) x = 8
10)
B) x = 2
C) y = 2
D) y = 8
Set up the system of two equations that can be used to solve the problem. 11) A vendor sells hot dogs and bags of potato chips. A customer buys 4 hot dogs and 5 bags of potato chips for $7.75. Another customer buys 5 hot dogs and 2 bags of potato chips for $6.50. Find the cost of each item. Let h = cost of the hotdogs and c = cost of the chips A) 4h - 5c = 7.75 5h - 2c = 6.50
B) 4h + 5c = 7.75 5h + 2c = 6.50
C) h + c= 7.75 h - 2c = 6.50
D) 5h + 4c = 7.75 2h + 5c = 6.50
12) You invested $10000 between two bank accounts. One pays 6% interest and the other pays 5%. If you earned $535 in combined interest from the accounts after 1 year, how much did you invest in each? A) x - y = 1000 5x + 6y = 535
B) x + y = 535 5x + 6y = 1000
C) x + y = 1000 0.05x + 0.06y = 535
D) x + y = 1000 5x + 6y = 535
13) A chemist needs 70 milliliters of a 62% solution but has only 52% and 66% solutions available. Find how many milliliters of each that should be mixed to get the desired solution. A) x + y = 70 0.52x = 0.63y
B) x + y = 70 0.52x + 0.66y = 62
C) x - y = 70 0.52x - 0.66y = 43.4
D) x + y = 70 0.52x + 0.66y = 43.4
2
11)
12)
13)
Graph the inequality. 14) -3x - 4y ≥ -12
14)
A)
B) y
-10
y
10
10
5
5
-5
5
10
x
-10
-5
-5
-5
-10
-10
C)
5
10
x
5
10
x
D) y
-10
y
10
10
5
5
-5
5
10
x
-10
-5
-5
-5
-10
-10
Factor. 15) 343x3 + 1
15)
A) (7x + 1)(49x2 - 7x - 1)
B) (7x + 1)(49x2 + 7x + 1)
C) (7x + 1)(49x2 + 1)
D) (7x + 1)(49x2 - 7x + 1)
16) 3x2 - 75
16)
A) 3(x - 5)2
B) 3(x + 5)(x - 5)
C) 3(x + 5)2
D) prime polynomial
Perform the indicated operation. Simplify if possible. x - 5 x + 3 17) - x - 8 x + 8 A)
8x + 16 (x - 8)(x + 8)
B)
17)
8x - 16 (x - 8)(x + 8)
C) -
3
8 16
D) 0
Simplify the rational expression. 8x2 - 22x + 12 18) x - 2 A)
1 x - 2
18) B) 8x - 6
C)
8x2 - 22x + 12 x - 2
D) 8x2 - 28
Divide and simplify. x2 + 9x + 18 x2 + 6x 19) ÷ x2 + 12x + 27 x2 + 16x + 63 A)
x + 7 x2 + 9x
19)
B) x + 7
C)
x + 7 x
D)
x x2 + 12x + 27
Multiply and simplify. 9x2 + 21x + 10 8x - 12x2 · 20) 9x2 - 4 9x2 + 30x + 25 A)
4x(2 - 3x) 3x + 5)(3x - 2)
20)
B) 1
C)
4x 3x + 5
D) -
4x 3x + 5
Simplify. Assume that all variables represent positive real numbers. 21)
68
21)
A) 34
B) 4 17
C)
68
D) 2 17
Use radical notation to write the expression. Simplify if possible. 22) 274/3
22)
A) 81
B) 2187
C) 243
D) 729
Simplify. Assume that all variables represent positive real numbers. 3 23) 64x4 y5 A) 4xy
3
xy
B) 2xy
3
xy2
C) 4xy xy2
23) D) 4xy
3
xy2
Add or subtract. Assume all variables represent positive real numbers. 24)
2a + 3 32a + 4 72a A) 37 106a
24) B) 7 106a
C) 7 2a
D) 37 2a
Find the square root. Assume that all variables represent nonnegative real numbers. 169 25) 100 A)
7 5
B)
13 11
C)
4
13 10
25) D)
42 25
Rationalize the denominator and simplify. Assume that all variables represent positive real numbers. 5 26) 2 A)
5
B)
10 2
C)
10
D)
26)
10 4
Solve. 27) A painter can finish painting a house in 5 hours. Her assistant takes 7 hours to finish the same job. How long would it take for them to complete the job if they were working together? 11 12 hr B) 4 hr C) 2 hr D) 6 hr A) 12 35
27)
Use the square root property to solve the equation. 28) (x + 6)2 = 14
28)
A) {-6 - 14, -6 + 14}
B) {6 - 14, 6 + 14}
C) {8}
D) {- 14, 14}
29) x2 + 36 = 0 A) {-6, 6}
29) B) {1296}
C) {6}
D) {-6i, 6i}
Add the proper constant to the binomial so that the resulting trinomial is a perfect square trinomial. Then factor the trinomial. 30) x2 + 8x
30)
A) x2 + 8x + 64 = (x + 8)2
B) x2 + 8x + 4 = (x + 16)2
C) x2 + 8x + 16 = (x + 4)2
D) x2 + 8x + 8 = (x + 64)2
Use the quadratic formula to solve the equation. 31) x2 + 14x + 85 = 0
31)
A) {-13, -1}
B) {-7 - 36i, -7 + 36i}
C) {-7 + 6i}
D) {-7 - 6i, -7 + 6i}
Perform the indicated operation. Write the result in the form a + bi. 32) (7 + 9i) - (-9 + i) A) 16 + 8i
32) B) -16 - 8i
C) 16 - 8i
D) -2 + 10i
33) (5 -2i)(3 + i) A) 17
34)
33) B) 13 - i
C) 17 - i
D) 8 - i
9 + 4i 3 - 6i A) -
34) 1 22 + i 27 27
B)
1 22 + i 15 15
C) -
5
17 22 + i 9 27
D)
17 14 + i 5 5
Find the function value. 35) Find f(4) when f(x) = 5x2 + 4x. A) 36
35)
B) 64
C) 96
D) 56
Determine which of the following graphs is not a function. 36)
36) B)
A) y
y
5
5
-5
5
x
-5
-5
5
x
5
x
-5
C)
D) y
y
5
-5
5
5
x
-5
-5
-5
Given the following function, find the indicated values. 37) Find h(-1), h(0), and h(-3) when h(x) = x2 + 4x + 3. A) 8, 0, 18
37)
B) 0, 3, -6
C) 0, 3, 0
D) 8, 3, 24
Find the domain and range. 38) {(29, -3), (4, -2), (4, 0), (8, 2), (20, 4)}
38)
A) domain: {29, 8, 4, 20}; range: {-3, -2, 0, 2, 4} B) domain: {-3, -2, 0, 2, 4}; range: {29, 8, 4, 20} C) domain: {29, 8, 4, 20}; range: {-3, -2, 2, 4} D) domain: {-3, -2, 2, 4}; range: {29, 8, 4, 20}
6
Decide whether the relation is a function. 39) {(-4, -3), (-2, 7), (1, -4), (1, 4)}
39)
A) not a function
B) function
Use the vertical line test to determine whether or not the graph is a graph of a function. 40)
40) y
x
A) function
B) not a function 41)
41) y
x
A) not a function
B) function
Use factoring to solve the polynomial equation. 42) x3 + 4x2 - x - 4 = 0 A) {1, -4, 4}
42) B) {-1, 1, -4}
C) {-4, 4}
D) {16}
Answer the question. 43) Given the cost function, C(x), and the revenue function, R(x), write the profit function from producing and selling x units of the product. C(x) = 0.4x + 770 R(x) = 1.1x A) P(x) = -0.7x + 770
B) P(x) = -0.7x - 770
C) P(x) = 0.7x + 770
D) P(x) = 0.7x - 770
7
43)
Use the graph to find the indicated function value. 44) y = f(x). Find f(4)
44) 5
y
4 3 2 1 -5
-4
-3
-2
-1
1
2
3
4
5 x
-1 -2 -3 -4 -5
A) -0.9
B) 3.8
C) 0.9
D) -3.8
Find the indicated function value. 45) f(x) = x - 1, g(x) = x - 6 Find (f + g)(-3). A) -1
45) C) -13
B) 1
8
D) -11
Answer Key Testname: MAT 1033.FINALREVIEW.PART1.F07
1) A 2) B 3) A 4) B 5) C 6) B 7) B 8) D 9) D 10) B 11) B 12) C 13) D 14) A 15) D 16) B 17) B 18) B 19) C 20) D 21) D 22) A 23) D 24) D 25) C 26) B 27) C 28) A 29) D 30) C 31) D 32) A 33) C 34) B 35) C 36) C 37) C 38) A 39) A 40) B 41) B 42) B 43) D 44) B 45) C
9
