Transcript Math 154B Final Review

Math 154B Final Review
Exponents
and
Polynomials
Factoring
and
Applications
Rationals
and
Applications
Roots
and
Radicals
Quadratic
Equations
10
10
10
10
10
20
20
20
20
20
30
30
30
30
30
40
40
40
40
40
50
50
50
50
50
Exponents and Polynomials 10 points
Evaluate:
5 5
0
Answer:
26

25
2
Exponents and Polynomials 20 points
Simplify:
 4x y z

2
3
 5 x yz
3
4
2



Answer:
3 15 3
125 x y z
64
3
Exponents and Polynomials 30 points
Subtract:
5x
3
 

 3x  6 x  4 x  3x  3x  5
2
3
2
Answer:
x  6 x  3x  5
3
2
Exponents and Polynomials 40 points
Multiply:
2 x3 x  4 
2
Answer:
18 x  48 x  32 x
3
2
Exponents and Polynomials 50 points
Divide using long division.
3x
5

 7 x  4 x  2 x  8  x  2
3
2
Answer:
52
3x  6 x  5 x  14 x  30 
x2
4
3
2
Factoring and Applications 10points
Factor:
16
x 
25
2
Answer:
4 
4

 x   x  
5 
5

Factoring and Applications 20points
Factor:
x  2 x  24
2
Answer:
x  6x  4
Factoring and Applications 30points
Factor:
 6 x  20 x y  6 xy
3
2
Answer:
 2xx  3 y 3x  y 
2
Factoring and Applications 40points
Solve for k.
k  7 
2
 k  k  1
2
Answer:
k  12, k  4
2
Factoring and Applications 50points
Solve for x by using the Pythagorean
2
2
2
Theorem, a  b  c
and then factoring.
10
x
x-2
Answer:
x  8, x  2  6
Rationals and Applications 10 points
Divide:
k  7k  12 k  2k  8

2
2
k 9
k k 6
2
2
Answer:
k4
k 4
Rationals and Applications 20 points
Subtract:
2
1

2
x  2x  1 x  1
Answer:
 x 1
2
x  1
Rationals and Applications 30 points
Solve for x.
2x
1
6

 2
x 3 x 3 x 9
Answer:
1
x
2
Rationals and Applications 40 points
Together, you and your friend
can do a job in 3 hours. Alone,
your friend do a job in 4 hours.
How long would it take you to do
the job alone?
Answer:
x  12 hours
Rationals and Applications 50 points
On steady ground you can walk 5 feet per second.
Walking on a moving sidewalk, you can travel 28 feet in
the same amount of time it takes to walk 12 feet in the
opposite direction. How fast is the moving sidewalk?
Distance
W/ sidewalk
28 feet
A/ sidewalk
12 feet
Answer:
Rate
5 r
5r
28
12

5 r 5r
r  2 feet per second
Time=
Distance
Rate
28
5r
12
5r
Roots and Radicals 10 points
Simplify:
12a b  3b
3 4
Answer:
6ab
5
a
6
Roots and Radicals 20 points
Simplify:
18  50  8
Answer:
6 2
m
2
7
Roots and Radicals 30 points
Simplify:
2
4
6c d
2 7
30c d
Answer:
5d
2
5d
Roots and Radicals 40 points
Rationalize the denominator:
2 x
3 2 x
Answer:
6 2x  2x
18  x
Roots and Radicals 50 points
Solve for k.
3k  1  3  k
Answer:
k 8
Quadratic Equations 10 points
Solve for k using the square root
property.
(k  2)  36
2
Answer:
k  4, k  8
Quadratic Equations 20 points
Solve for x by completing the
square.
x  8x  9
2
Answer:
x  9, x  1
Quadratic Equations 30 points
Solve for x by using the
quadratic formula.
3x  8 x  7  0
2
Answer:
no real solution
Quadratic Equations 40 points
The product of two
consecutive integers is 240.
What are the integers?
Answer:
x  15, x  1  16
OR
x  16, x  1  15
Quadratic Equations 50 points
Solve for x by using the
quadratic formula.
2 2 3
x  x 1  0
5
5
Answer:
5
x  , x  1
2