Download MAB111 Sample Final Exam

Final Exam MAB 111
Name___________________________________
SHORT ANSWER. Show all work necessary to complete each problem.
Factor out the GCF from the polynomial.
1) 32x - 8
1)
Factor the polynomial completely. If the polynomial cannot be factored, write prime.
2) x2 + 5x - 36
2)
3) 5x2 - 35x + 50
3)
4) 6y2 + 27y - 15
4)
5) 81 - 4x2
5)
Find the domain of the rational expression.
3x
6) f(x) = -2 + x
6)
Simplify the rational expression.
15x3
7)
5x
8)
7)
3x - 6
14 - 7x
8)
D‐1
Multiply. Simplify if possible.
4
z3
· 9)
28z 2z 2
9)
Divide. Simplify if possible.
x5
10x2
÷ 10)
x2 - 1 (x + 1)2
10)
Perform the indicated operation. Simplify if possible.
6x
30
11)
- x - 5 x - 5
12) - 13)
11)
5
6
- 18 3x
12)
3
x
+ 5x - 25 x2 - 25
13)
Solve the equation.
x x
14) - = 8
5 6
14)
Solve the proportion.
r + 6 r + 8
15)
= 5
7
15)
Find the square root. Assume that all variables represent positive real numbers.
16) - 16
D‐2
16)
Use a calculator to approximate the square root to 3 decimal places. Check to see that the approximation is reasonable.
17) 51
17)
Find the cube root.
3
18) 343x6
18)
Use radical notation to write the expression.
19) -321/5
19)
Write with positive exponents. Simplify if possible.
20) 27-4/3
20)
Use the product rule to multiply. Assume all variables represent positive real numbers.
21) 18 · 2
21)
Use the quotient rule to divide and simplify.
3
22)
49
22)
Simplify the radical expression. Assume that all variables represent positive real numbers.
23) 27x2 y
23)
Solve.
24)
x - 5 = 6
24)
25)
12x - 12 = x + 2
25)
D‐3
26)
3x - 10 = x + 11
26)
Solve the equation.
27) 49x2 + 24 = -98x
27)
28) x2 + 12x + 22 = 0
28)
29) x2 + 5x - 5 = 0
29)
30) 2x2 + 8x = - 1
30)
31) 4x2 + 24x = - 14
31)
Sketch the graph of the quadratic function. Give the vertex and axis of symmetry.
32) f(x) = (x - 1)2
y
10
5
-10
-5
5
10
x
-5
-10
D‐4
32)
33) f(x) = (x - 3)2 - 5
33)
y
10
5
-10
-5
5
10
x
-5
-10
Solve the problem.
34) A window washer accidentally drops a bucket from the top of a 400-foot building. The
height h of the bucket after t seconds is given by h = -16t2 + 400. When will the bucket hit
34)
the ground?
35) The area of a square is 49 square miles. Find the length of a side of the square.
Solve the equation.
36) 5 (10 - 3x) = 625
35)
36)
Write as a logarithmic equation.
1
37) 5 -3 = 125
37)
Write as an exponential equation.
1
38) log
= -3
4 64
38)
D‐5
Solve the equation. Give an approximate solution to four decimal places.
39) 3 x + 8 = 7
39)
Solve the equation.
40) log (5 + x) - log (x - 4) = log 4
40)
D‐6
Answer Key
Testname: FINAL 111 1)
2)
3)
4)
5)
6)
8(4x - 1)
(x + 9)(x - 4)
5(x - 2)(x - 5)
3(2y - 1)(y + 5)
(9 + 2x)(9 - 2x)
{x|x is a real number and x ≠ 2}
7) 3x2
3
8) 7
9)
10)
1
14
10(x + 1)
x3 (x - 1)
11) 6
-5x - 36
12)
18x
13)
8x + 15
5(x + 5)(x - 5)
14) 240
15) r = -1
16) -4
17) 7.141
18) 7x2
19) -2
1
20)
81
21) 6
22)
3
7
23) 3x 3y
24) 41
25) 4
21
26)
2
2
12
27) x = - , x = - 7
7
28) -6 - 14, -6 + 14
-5 - 3 5 -5 + 3 5
29)
, 2
2
30)
-4 - 14 -4 + 14
, 2
2
31)
-6 - 22 -6 + 22
, 2
2
D‐7
Answer Key
Testname: FINAL 111 REVISED
32) vertex (1, 0); axis x = 1
y
10
5
-10
-5
5
10
x
10
x
-5
-10
33) vertex (3, -5); axis x = 3
y
10
5
-10
-5
5
-5
-10
34) 5 sec
35) 7 mi
36) 2
37) log
1
= -3
5 125
38) 4 -3 = 1
64
39) -6.2288
40) 7
D‐8