Download Module 5 - pgcc.edu

DVM 0071 Elementary Algebra
Review of Module 5 Objectives:
Mastering Polynomials & Integer Exponents
1. Simplify the following expressions
a)
3a – 5(b – 2)
b)
(3k + 1) – (4 – k)
c)
-4x(3x – 7y2 + 4)
d)
-7.1(3r +7) + 3.5(10r + 10)
2. Evaluate algebraic expressions, given the values of the variables.
a)
5x2 -5x + 4y
for x = ¾ and y = -1.5
b)
(3x – 2)2 + 1
for x = -4
c)
1
h(b1 + b2)
2
when b1=2, b2=4, and h=8
3. Find square roots (exact, rounded using a calculator, and estimate without a
calculator).
a) Estimate the value of √
b) Find the value of √
c) Find the value of √
to one decimal place without a calculator
without a calculator.
rounded to thousandths.
4. Simplify.
x2 
 3
y 
a) 
c)
4
x 3y 4
z 5
b) (4x)3 (2x2)4
d)
x x2 x3


y y y2
Module 5 Objectives: DVM 0071 Mastering Polynomials & Integer Exponents
e)
(2x)0
f) (2x23y3)2
g) [(a)-6]-3
h) ( x)2
5. Apply the basic operations to polynomials (monomial division only).
a) Add: 6x 4 2x 3  7x 2  5 and 3x 4  2x 3  4x 2  11
b) Subtract: 3x 2  4x  7 from 2x 2  9x  7
c) Multiply: x 2  2x  3 by 4x 3  7x
d) Multiply, using FOIL:
7a  3b 5a  5b 
e) Expand the following: 3y  4z 
2
f) Multiply the binomials: 3p  4 3p  4 
g) Expand the following:  4a  b 
3
h) Divide and Simplify: (16x4 – 8x2 + 12x)/(-3x8y3z)
6.
Write the numbers in scientific notation or standard form.
a)
295,060,000
write in scientific notation
b)
-9.105×10-7
write in standard form
c)
(5×103)(2.3×10-7)
write in standard form
Review of Module 5 Objectives: DVM 0071
2
Module 5 Objectives: DVM 0071 Mastering Polynomials & Integer Exponents
7.
Use Scientific Notation to solve applied problems
a) Light travels 300,000,000 meters per second. A light year is the
distance that light travels in one year. Use scientific notation to
express the number of meters traveled in one light year.
b) If E= Energy emitted by an oscillation and V=frequency of
oscillation, then E=kV where k Plank’s constant is 6.626×10-24J. Find
E if V= 1.25 ×1015 in J (Joules).
Review of Module 5 Objectives: DVM 0071
3
Module 5 Objectives: DVM 0071 Mastering Polynomials & Integer Exponents
Key
6c
MODULE 5
7a
1a
1b
1c
1d
3a -5b + 10
4k – 3
-12x2 + 28xy – 16x
7b
2a
2b
2c
3a
3b
3c
4a
-6.9375
197
24
3.9
13
4.796
4b
1024x11
.00115
9.4608 X 1015 m
8.2825 X 10-9 Joules
13.7r – 14.7
4c
4d
4e
4f
4g
1
36x4 y6
a18
4h
5a
5b
5c
5d
5e
5f
5g
3x4 + 11x2 - 6
–x2 + 5x
4x5 + 8x4 -19x3 -14x2 +21x
35a2 – 50ab +15b2
9y2 + 24yz +16z2
9p2 - 16
64a3 +48a2 b +12ab2 +b3
5h
+
6a
2.9506 X 107
- .0000009105
6b
-
Review of Module 5 Objectives: DVM 0071
4