MAT 080 STUDY GUIDE & ASSIGNMENTS
Transcript of MAT 080 STUDY GUIDE & ASSIGNMENTS
MATH 070 STUDY GUIDE & ASSIGNMENTS (Revised: Summer 2012)
CERTIFY mode is where you will complete your Hawkes assignments.
You may use the PRACTICE mode in a lesson before attempting to certify in the lesson.
Most lessons require 80 - 85% of the assignment to be correct to certify.
After you have certified in a lesson, a certificate will appear on the monitor, indicating that you
have successfully certified in that lesson.
If you do not receive a certificate, you should practice more problems and then attempt to certify
the lesson again.
Your homework is not complete until you have submitted your certificate electronically on or
before the lesson’s due date.
Hawkes certificates are automatically submitted if you are connected to the internet. If you are not
connected to the internet, save your certification on a portable storage device and go to
http://www.hawkeslearning.com/ROCKINGHAMCOMBO to submit your assignments at a later
date when you have access to the internet.
Some assignments are to be completed using paper and pencil. These are located in the textbook
or in the RCC Moodle site for this course.
STUDENT NAME: ______________________________________________________
HAWKES COURSE ID: ROCKINGHAMCOMBO
MY HAWKES ACCESS CODE IS: _________________________________________
UNIT 0: Prerequisite Unit
Lesson Section Topic Homework Assignments
1 WS Order of Operations with Whole
Numbers Worksheet A, #1-10.
2 Text &
WS Operations with Fractions
2nd Ed: Page 70, #3, 5, 6, 8,
15, 16, 17, 21, 23, 24.
Worksheet A, #11-23.
3 WS Operations with Decimals Worksheet A: #24-32.
UNIT 2: Introduction to Algebra
Lesson Section Topics Homework Assignments
1 2.1c Evaluating algebraic expressions Hawkes 2.1c
Worksheet A, # 1-7
2 2.1a
Variables and Algebraic
Expressions, Terms and Coefficients Hawkes 2.1a and 2.1b
Worksheet A, #8-13 2.1b Simplifying Expressions
3 Distributive Property Hawkes – Ch. 2 Review
Worksheet A, #14-23
4 2.2 Translation of Verbal Expressions
Hawkes 2.2
2nd
Ed., Page 114, Translate and
simplify if possible # 21, 24, 25, 29, 30,
33, 35, 36.
Worksheet A, #24-28
Review
UNIT 2 TEST
UNIT 1: Real Numbers
Lesson Section Topic Homework Assignments
1 1.1a Introduction to Real Numbers Hawkes 1.1a and 1.1b
Worksheet A: #1,2, 3 1.1b Absolute Value
2 1.2 Addition of Real Numbers Hawkes 1.2
Worksheet A: #4-13
3 1.3 Subtraction of Real Numbers Hawkes1.3
Worksheet A: #14-20
4 1.4 Multiplication & Division of Real Numbers Hawkes 1.4
Worksheet A: #21-28
5 1.8 Order of Operations Hawkes 1.8
Worksheet A: #29-34
Review
UNIT 1 TEST
UNIT 3: Linear Equations
Lesson Section Topics Homework Assignments
1
2.3a Solutions to Equations, Linear
Equations of Form Ax+B=C
Hawkes 2.3a, 2.3b, 2.4
Worksheet A, #1-5 2.3b
2.4
2 2.5
Linear Equations involving
Parentheses and of Form
Ax+B=Cx+D
Hawkes 2.5
3 WS A Equations with Fractions Worksheet A, #6-15
4 Text - 3.1 Literal Equations 2
nd Ed. Page 186, #29, 31, 33, 36, 37, 38, 40,
41, 43, 46, 47, 49, 54, 55, 56, 57, 58, 59, 60.
5 3.4 Linear Inequalities & Graphs Hawkes 3.4
6 2.6a Applications – Direct
Translation Hawkes 2.6a
7 WS B Applications - Geometry Worksheet B, #1-10
Review
UNIT 3 TEST
UNIT 4: Graphing Linear Equations
Lesson Section Topics Homework Assignments
1 4.1 Cartesian Coordinate
System
Hawkes 4.1
2nd
Ed: Page 264, #3,5,6.
2 4.2 Graphing Lines
Hawkes 4.2
2nd
Ed: Page 279,
Graph by making a table of values: #7, 11, 15, 16,
18, 27, 31, 33, 35, 36, 38, 43, 45, 47.
Worksheet A, #1 - 6.
3 Text - 4.3 Slope and Slope-Intercept
Form
2nd
Ed: Page 290, #1-8
Worksheet A, #7-18.
4 4.4a Equations of Lines Hawkes 4.4a
5 4.6 Linear Inequalities Hawkes 4.6
2nd
Ed: Page 332, #9, 11, 13, 17, 19, 23.
6 Using Linear Graphs LAB 4
Review
UNIT 4 TEST
UNIT 5: Exponents and Scientific Notation
Lesson Section Topics Homework Assignments
1 WS A Definition of Exponents Worksheet A, #1-20.
2 Rules of Exponents – Non-negative
exponents Hawkes, Chapter 5 Review
3 WS B Definition of Negative Exponent Worksheet B, #1-25.
4 5.1, 5.2a Rules of Exponents – Integer exponents Hawkes, 5.1, 5.2a
5 5.2b, WS C Scientific Notation Hawkes, 5.2b
Worksheet C, #1-10.
6 Unit Analysis LAB 5
Review
UNIT 5 TEST
UNIT 6: Polynomials
Lesson Section Topics Homework Assignments
1 5.3, 5.4 Identifying Polynomials; Addition and
Subtraction of Polynomials Hawkes 5.3 and 5.4
2 5.5, 5.6a,
5.7a
Multiplication of Polynomials, FOIL,
Division by Monomials Hawkes 5.5, 5.6a and 5.7a
3 WS A Order of Operations with Polynomials Worksheet A, #1-12.
4 6.1b Greatest Common Factor Hawkes 6.1b
5 6.2 Trial & Error – Leading Coefficient 1 Hawkes 6.2
6 6.3a, 6.4a Trial & Error, Difference of Squares Hawkes 6.3a and 6.4a
Review
UNIT 6 TEST
MATH 070 UNIT 0 WORKSHEET A Evaluate each expression.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
Perform the indicated operations.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
ANSWERS:
MATH 070 UNIT 1 WORKSHEET A
1. Find the opposite of each number:
2. Simplify.
3. Evaluate:
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
33.
34.
L
E
S
S
O
N
1
L
E
S
S
O
N
2
L
E
S
S
O
N
3
L
E
S
S
O
N
4 L
E
S
S
O
N
5
MATH 070 UNIT 1 WORKSHEET A
ANSWERS:
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
33.
34.
L
E
S
S
O
N
1
LESSON 2
LESSON 3
LESSON 4
LESSON 5
MATH 070 UNIT 2 WORKSHEET A
Evaluate each expression using the indicated values.
1.
2.
6.
7.
;
3.
4.
5.
Simplify each expression.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
Translate and simplify if possible.
24.
25.
26.
27.
28.
Answers:
MATH 070 UNIT 3 WORKSHEET A Determine whether the given number is a solution to the equation.
1.
2.
3.
4.
5.
It is often easier to solve an equation involving fractional coefficients if the fractional coefficients are eliminated. This can be done by multiplying each side of the equation by the common denominator of the fractions. NOTE: Eliminating fractions can be used only when solving equations and inequalities.
Example:
Exercises: Eliminate fractions before solving each of the equations below.
6. x
3 = -2 7.
2
3x
5
2 =
-1
2 8. x
2
3 =
-1
4 9.
x
5 2 = 3
10. x
2 + 4 =
1
3x 1 11.
1
2x 7 =
3
5x + 4 12.
3
2x + x + 2x – 4 = 7
13. 2
1(x + 3) =
4
x 14.
2
1x –
10
1
5
x x = 3 15.
3
x + 2 =
4
3x – 3
ANSWERS: 6) x = -6 8) x = 5
12 10) x = -30 12) x = 3 14) x =
2
15
Multiply both sides of the
equation by the common
denominator of 12.
Subtract 9x from both sides.
Add 72 to both sides.
Divide both sides by negative 3.
11
MATH 070 UNIT 3 WORK SHEET B
The perimeter of a geometric figure is a measure of the distance around the figure. When the sides of a geometric figure are line segments, the perimeter of the figure can be found by adding the lengths of the sides.
Triangle a b c Perimeter = a + b + c EXAMPLE 1: The perimeter of a rectangle is 26 ft. The length of the rectangle is 1 ft. more than twice the width. Find the length and width of the rectangle. SOLUTION: Draw a picture of your figure. 1. Name and represent the unknowns with variables. 2x + 1 Name Representation x x Width: x Length: 2x + 1 2x + 1 2. Add the lengths of the sides of the rectangle and set the sum equal to the perimeter. (x) + (2x + 1) + (x) + (2x + 1) = 26 (x + 2x + x + 2x) + (1 + 1) = 26 6x + 2 = 26 6x = 24 x = 4
3. To find the length & width, substitute the value of x, which is 4, into the representation of the length and width.
Length: 2 x + 1 Width: x = 2(4) + 1 = 4 = 9 ANSWER: The length is 9 ft. and the width is 4 ft.
12
In a triangle, the sum of the measures of all three angles is 180O. B
) A C (
A + B + C = 180o
Two special triangles are show below.
A right triangle has one right angle (90O
). The other two angles are acute (less than 90O
). An isosceles triangle has two equal angles and two equal sides. Two equal sides and two equal angles
90o ) ( Right triangle Isosceles triangle
EXAMPLE 2: In a certain right triangle, the measure of one of the acute angles is twice the measure of the smallest angle. Find the measure of the other two angles.
SOLUTION: Draw your picture. x
1. Name and represent the angles:
smallest = x second = 2x 90o
right = 90o 2x
2. Substitute the values into the angles of a triangle formula and solve the equation.
A + B + C = 180 x + 2x + 90 = 180 3x + 90 = 180 3x = 90
x = 30o
3. To find the other two angles, substitute the value of x, which is 30o, into their representatives.
smallest: x second: 2x
= 30o = 2(30) = 60
o
ANSWER: The measures of the other two angles are 30o and 60
o.
13
Exercises: 1. In an isosceles triangle, two sides are equal. The length of one of the equal sides is 3 times the
length of the third side. The perimeter is 21 m. Find the length of each side. 2. The perimeter of a rectangle is 42 m. The length of the rectangle is 3 m less than twice the
width. Find the length and width of the rectangle. 3. The perimeter of a triangle is 110 cm. One side is twice the second side. The third side is 30
cm more than the second side. Find the length of each side. 4. The perimeter of a rectangle is 48 m. The width of the rectangle is 8 m less than the length.
Find the length and width of the rectangle.
5. In an isosceles triangle, the measure of one angle is 5 less than three times the measure of one of the equal angles. Find the measure of each angle.
6. The measure of the first angle of a triangle is twice the measure of the second angle. The
measure of the third angle is 10 less than the measure of the first angle. Find the measure of each angle.
7. The measure of the first angle of a triangle is three times the measure of the second angle. The
measure of the third angle is 33 more than the measure of the first angle. Find the measure of each angle.
8. In an isosceles triangle, the measure of one angle is 12 more than twice the measure of one of the equal angles. Find the measure of each angle.
9. The measure of one angle of a right triangle is 3 less than twice the measure of the smallest angle. Find the measure of each angle.
10. In a triangle, the measure of one angle is 5 more than the measure of the second angle. The
measure of the third angle is 10 more than the measure of the second angle. Find the measure of each angle.
ANSWERS:
1) 9m, 9m, 3m 3) 20 cm, 40 cm, 50 cm 5) 37, 37, 106
7) 63, 21, 96 9) 31, 59, 90
14
MATH 070 UNIT 4 WORK SHEET A
PART I: Graphing Lines
Graph each line. Give a table of values.
PART II: DETERMINING SLOPE FROM THE GRAPH
The slope of a line can be determined from its graph. The slope formula requires two points, whose
coordinates can be read from the graph. These coordinates are substituted into the slope formula,
m =
12
12
xx
yy
.
Example 1: Find the slope of the line graphed.
Let P1 = (-1, -3) and
P2 = (2, 1)
m =
12
12
xx
yy
=
)1(2
)3(1
=
3
4
Exercises: Find the slope of each line. 7. 8. 9..
15
10. 11. 12.
ANSWERS: 7. 4
5 9.
2
1 11. –1
PART II DETERMINING SLOPE FROM THE EQUATION OF THE LINE
The slope of a line can also be found directly from its equation. Once any two points on the line have
been determined, the slope formula, m =
12
12
xx
yy
, is used.
Example 1: Find the slope of the line 3x – 2y = 8 by finding two points.
Solve for y. 3x 2y = 8
-2y = -3x + 8
2
y2
=
2
8x3
y = 2
3x 4
Find two points. x y
0 -4 Let P1 = (0, -4) and
2 -1 P2 = (2, -1).
Use the slope formula. m =
12
12
xx
yy
=
02
)4(1
=
2
3
Observe that in Example 1, the slope is
Furthermore, when we solve for y = mx + b, the coefficient of x is
16
Any time an equation can be written in the form y = mx + b, the slope of the line is
m, the coefficient of x.
Example 2: Find the slope of the line 7x 3y = 10 by solving for y.
Solve for y. 7x 3y = 10.
3y = 7x + 10
3
y3
=
3
10x7
y = 3
x7
3
10
The slope is
, the coefficient of x.
Exercises: Find the slope of each line using the method in example 2.
13. 17.
14. 18.
15.
16.
ANSWERS: 13. –2 15. 5
7 17.
17
MATH 070 LAB 4: USING LINEAR GRAPHS
PART I: While surfing the Internet, you find a site that claims to sell DVD’s at cheap prices with a monthly membership fee of $8. Unfortunately, the site does not tell you how much they charge for each DVD, but it does give you the following information:
Number of DVD’s Ordered 1 2 3
Total Cost (Includes S & H, Excludes membership fee)
$15 $24 $33
a. Let x = the number of DVDs ordered in one month and y = the monthly cost.
Complete the table of values for x = 1, 2, and 3
b. Plot the points from the table on the graph below and connect the points.
c. Note that the points form a straight line. Therefore,
the rate of change is constant. Find the slope of the line.
d. Find the equation of the line using the point-slope form for the equation of a line.
X Y
1
2
3
50 45 40 35 30 25 20 15 10
5 1
2 3 4 5
18
e. Use the simplified equation from part d to find the cost if 9 DVDs are ordered.
PART II: An educator wants to see how student performance on the MAT 070 final exam affects the student’s performance in the next math course. The following data was collected for fifteen of her MAT 070 students after they completed their next math course.
MAT 070 Final Exam Grade
Next Math Course Final Average
61 80
76 84
100 96
70 85
65 70
40 70
97 90
85 89
43 62
88 85
73 76
56 70
85 79
76 80
88 80
19
1. Plot the data points using the x-axis for the MAT 070 final exam grade and the y–axis for the grade in the next math course.
2. Draw the line which best fits the data points. (Note: The line will not pass
through all of the points.)3. Find the equation of the line as follows:
a) Find the coordinates of two points on the line.
b) Calculate the slope of the line using the points from part a.
100 95 90 85 80 75 70 65 60 55 50 45 40 35 30 25 20 15 10
5 5
10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100
20
c) Determine the equation of the line using the point-slope form of a line and parts a & b.
Use the equation from part 3c to answer Questions 4 and 5. 4. If a student scores an 82 on the MAT 070 Final Exam, predict the final grade the student will receive in the next math course. 5. If the student received a grade of 90 in the next math course, determine what score the
student was likely to have earned on the MAT 070 Final Exam.
21
MATH 070 UNIT 5 WORK SHEET A The meaning of exponents can be used to simplify expressions involving products, quotients, and powers of variable expressions raised to positive integer exponents. Recall that in an exponential expression such as x3, x is the base, and 3 is the exponent which indicates how many times the base is used as a factor. That is,
x3 = x x x
3 factors To expand an exponential expression, write the expression in factored form.
Example 1: Expand (-5x4)(2x2) Solution: (-5x4)(2x2) = (-5 2)(xxxx xx) Example 2: Expand (-3a2b)3 Solution: (-3a2b)3 = (-3a2b)(-3a2b)(-3a2b)
= (-3)(-3)(-3)(aa aa aa)(b b b)
Example 3: Expand y12x
4xy2
4
Solution: y12x
4xy2
4
=
x x y12
x y y y y4
To simplify an exponential expression, write the expression in factored form. Then write the result in exponential form.
Example 1: Simplify (-5x4)(2x2) Solution: (-5x4)(2x2) = (-5 2)(xxxx xx)
=
Example 2: Simplify (-3a2b)3 Solution: (-3a2b)3 = (-3a2b)(-3a2b)(-3a2b)
= (-3)(-3)(-3)(aa aa aa)(b b b)
=
Example 3: Simplify y12x
4xy2
4
Solution: y12x
4xy2
4
=
x x y12
x y y y y4 =
22
EXERCISES: Simplify each expression.
1. (8m2)(5m) 8. (-2nt3)2 15. 3m22
m11
2. (-7w2)(-3w4) 9. (-a3b)2 16.
4
32
a
a
3. (-3a3)(-3a3) 10. (cd)3(cd3) 17.
2
32
ab
abba
4. (xy2)(x4y2) 11. (4k2)(-3k)2 18.
3
2
6
32
x
xx
5. (2bc)(-b5c) 12. 2
4
3
6
x
x 19.
4
2
y2
y4
6. (pq2r)(p2q)(r3q2) 13. 3
5
5
15
n
n
20.
2
4
p4p2
p6
7. (z4)2 14. 5
4
z
z
ANSWERS:
1. 40m3 11. 36k4
3. 9a6 13. -3n2
5. -2b6c2 15. 2m2
1
7. z8 17. a2b2
9. a6b2 19.
2y
8
23
MATH 070 UNIT 5 WORKSHEET B
RULES OF EXPONENTS: Let x and y denote rational numbers and let a and b denote
integers.
1. xa x
b = x
a + b 5.
a
y
x
=
a
a
y
x y 0
2. xa x
b = x
a-b x 0 6.
x
0 = 1
3. (xa)
b = x
ab 7. x
-a =
ax
1
4. (x y)a = x
a y
a
EXAMPLES:
Simplify the following:
a) (-2)-4
b) 2
4
3 c) (x
5) (x
-4) d)
4
5
x
x
e) (x-5
)4 f) (x
2 y)
-3 g)
3
y
x h) (2x)
3
Solutions:
a) (-2)-4
= 42)(
1
=
16
1
b) 2
4
3 =
2
2
4
3
= 2
2
3
4 =
9
16
c) x5 x
-4 = x
5 + 4 = x
1 = x
d) 4
5
x
x
= x –5 4
= x-9
= 9
1
x
e) (x-5
)4 = x
-5 4 = x
-20 =
20
1
x
f) (x2 y)
-3 = (x
2)
-3 y
-3 = x
-6 y
-3 =
6
1
x
3
1
y =
36
1
yx
g)
3
y
x =
3
y
x 3
= 3
3
x
y
h) (2x)3 = 2
3 x
3 = 8x
3
(OVER)
24
EXERCISES:
1. 6-2
2. 2
4
3 3.
6
2
1 4.
3-2
1
5. x8 x
11 6.
11
8
x
x 7. (x
8)
11 8.
3
y
x
9. (a-8
) (a3) 10.
3
8
a
a
11. 8
3
a
a 12.
42
x
13. (x-3
)2 14. (a
-8)
-2 15. (3a
-1)
2 16. (3a
-1)
-2
17. (2x3 y) (3x
4 y
-2) 18.
3
42
7
14
yx
yx 19. (3p
-2) (p
8)
20. 63
32
ba
ba
21.
4
b
a 22. 4x
0 (2y)
0
23. x-8
x-12
24. (2x)3 (4x)
2 25.
432
5
x
x
ANSWERS:
1. 36
1 3.
64
1 5. x
19 7. x
88
9. 5
1
a 11. a
11 13.
6
1
x 15.
2
9
a
17. y
x 76 19. 3p
6 21.
4
4
a
b 23. x
4
25. 3
40
x
25
MATH 070 UNIT 5 WORKSHEET C
28.63 x 10
-8 is in neither scientific notation nor decimal notation. The following illustrates
one method of converting to scientific notation.
Example - Convert to scientific notation.
EXERCISES:
Convert to scientific notation:
1. 286. 3 x 105 2. 26.34 x 10
-12
3. 0.412 x 10-6
4. 0.81 x 1011
Perform the operation and write the answer in scientific notation:
5. (8.6 x 10-8
) (4.3 x 103) 6. (4.78 x 10
4) (–1.3 x 10
18)
7. 8
15
105
108.4
x
x 8.
3
2
101.8
104.6
x
x
9. (0.38 x 102) (–1.7 x 10
9) 10.
4
5
100.3
103.6
x
x
ANSWERS:
1. 2.863 x 107 3. 4.12 x 10
-7
5. 3.698 x 10-4
7. 1.68 x 107
9. –6.46 x 1010
26
MAT 070 LAB 5 UNIT ANALYSIS
The metric system is a measurement system used by most of the world. All of the conversions
use the same place values that are used in the base-ten numeration system. The purposes of this
lab are to teach
the metric prefixes
unit analysis.
The base unit of length in the metric system is the meter (m) which is just a little longer than a
yard. All multiple and submultiple units are based on powers of ten. Greek prefixes (kilo,
hecto, and deka) are used for multiple units and Latin prefixes (deci, centi, and milli) are used
for submultiple units. The following table shows the metric prefixes, their meanings, and their
symbols.
PREFIX MEANING SYMBOL kilo 1000 k
hecto 100 h deka 10 da
deci 0.1 d
centi 0.01 c milli 0.001 m
Combining the prefixes with the base unit of meter, one
obtains
Most people prefer not to work with decimals. The decimals can be cleared in the
submultiple units as follows.
1 dm = 0.1 m 1 cm = 0.01 m
10(1 dm) = 10 (0.1 m) 100(1 cm) = 100 (0.01 m)
10 dm = 1 m 100 cm = 1 m
Similarly, 1000 mm = 1 m.
The conversions now read
Unit analysis is used to convert among the units. Setting up a unit analysis conversion is
much like reading a road map. The following diagram shows a possible arrangement for the
metric units of length along with routes connecting them.
1 km = 1000 m 10 dm = 1 m
1 hm = 100 m 100 cm = 1 m
1 dam = 10 m 1000 mm = 1m
1 km = 1000 m 1 dm = 0.1 m
1 hm = 100 m 1 cm = 0.01 m
1 dam = 10 m 1 mm = 0.001 m.
27
1.234 hm
Note that a conversion fact enables a route. One can go
from any prefix to the base unit and from the base to any
prefix unit.
The following are the steps used to perform unit analysis.
1. Use the diagram to write “travel” directions.
2. List the appropriate conversions.
3. Form a chain of multiplication to cancel unwanted units and be left with the desired unit.
4. Perform the multiplication or division to get the answer.
Example: Convert 1234 dm to hectometers.
Step 1. dm m hm
km hm
mm m dam
cm dm
Step 2. 10 dm = 1 m and 1 hm = 100 m
Step 3. Note that the quantity is being multiplied by 1 each time!
Step 4. hm1000
1234 =
Metric conversions cannot involve more than two moves (given prefix to base and base to
desired prefix). When either the given unit or the desired unit is the base, there is only one
move.
Example: 0.84 km = ______ m
Step 1 km m (one move)
Step 2 1 km = 1000 m
1234 1 1
1 10 100
dm m hmx x
dm m
28
Step 3 0.84 1000
1 1
km mx
km
Step 4
EXERCISE SET 1: Use unit analysis to perform the following conversions. Be sure to
show and label all steps.
1. 58 m = _____dam 2. Convert 1.23 hm to meters
3. Convert 0.7 m to decimeters 4. 78.54 m = _____km
5. 0.3 cm = _____mm 6. 34.98 mm = ____ dam
7. 84.5 km = ____ dam 8. 0.008 dm = _____ mm
ANSWERS TO ODD PROBLEMS:
1. 5.8 dam 3. 7 dm 5. 3 mm
7. 8450 dam
One of the big advantages of the metric system is that the conversions for length, mass, and
capacity work the same way. In other words, the same prefixes are used with all base metric
units. The purposes of this lab are to
introduce the base metric units for mass and capacity
review unit analysis as a tool to perform metric to metric conversions
demonstrate the power of unit analysis in U.S. to metric and metric to U.S.
conversions.
The base metric unit of mass is the gram (g). A nickel has mass of approximately 5 grams.
The base metric unit for capacity is the liter (L), which is just a little more than a quart. The
conversion charts for mass and capacity are identical to the chart for length, except that meter
is replaced with gram or liter.
840 m
29
MASS
1 kg = 1000 g
1 hg = 100 g
1 dag = 10 g
10 dg = 1 g
100 cg = 1 g
1000 mg = 1 g
CAPACITY
1 kL = 1000 L
1 hL = 100 L
1 daL = 10 L
10 dL = 1 L
100 cL = 1 L
1000 mL = 1 L
As with length, one uses unit analysis to do conversions.
Example: Convert 0.025 kg to grams
Step 1 kg g
Step 2 1 kg = 1000 g
Step 3 0.025 1000
1 1
kg gx
kg
Step 4
Example: Convert 24.7 dL to milliliters.
Step 1 dL L mL
Step 2 10 dL = 1 L and 1000 mL = 1 L
Step 3 24.7 1 1000
1 10 1
dL L mLx x
dL L
Step 4
There are no exact conversions between the common U.S. units and the metric units;
however, one can use the following bridges to get approximate answers.
QUANTITY
BRIDGE
Length 1 in = 2.54 cm
Capacity 1 L = 1.06 qt
Mass/Weight 1 kg = 2.2 lbs
25 g
2470 mL
30
Example: Michael is 4 ft 7 in tall. Express his height in centimeters.
1 ft = 12 inches; therefore 4 ft. = 48 inches and 4 ft 7 in = 55 in. Now use unit analysis to
convert to centimeters.
Step 1 in cm
Step 2 1 in = 2.54 cm
Step 3 55 2.54
1 1
in cmx
in
Step 4
Example: Joanne bought a Mini-Cooper that has a gas tank capacity of 37 liters. To the
nearest tenth, how many gallons of gas will the tank hold?
One needs to know that a gallon is four quarts.
Step 1 L qt gal
Step 2 1 L = 1.06 qt and 4 qt = 1 gal
Step 3 37 1.06 1
1 1 4
L qt galx x
L qt
Step 4
Example: Mrs. Hurley has a holiday recipe that calls for 12 ounces of jasmine tea. Her
internet source sells only by the gram. How many grams of the tea should she order?
The 12 ounces must be converted to grams. The English to metric bridge given earlier is 1
kg = 2.2 lb. One must recall that 1 lb = 16 oz. Now, unit analysis can be used to perform
the conversion.
Step 1 oz lb kg g
Step 2 1 lb = 16 oz, 1 kg = 2.2 lbs, and 1 kg = 1000 g
139.7 cm
9.8 gal
One must get to the bridge unit, cross the bridge, and then go to the desired unit.
31
Step 3 12 1 1 1000
1 16 2.2 1
oz lb kg gx x x
oz lb kg
Step 4
EXERCISE SET 2 (problems 1-16): Use unit analysis to perform the indicated conversions.
1. 5000g = ______kg 2. 14.6 kg =_____g 3. 18 mg = _____g
4. 493 L = _____Kl 5. 5.1 kg = _____cg 6. 800.37 mL = ____hL
7. 47.1 dL = _____daL 8. 0.0034 hL = ___ cL 9. 8 in = ______cm
10. 0.4 lb = _____g
11. The standard width of a bowling lane is 41 in. Express this width in centimeters.
12. Your chemistry professor mixes the contents of two beakers containing 2.5 L and 700
mL of a liquid. What is the combined amount in liters?
13. A prehistoric bird had a wingspan of 8 m. Express this wingspan in feet.
14. In 1989, an oil tanker in Alaska spilled 10 000 000 gal of oil in Prudhoe Bay. What
is the quantity of this spillage expressed in kiloliters?
15. A passenger car is generally considered small if the distance between its front and
back wheels is less than 95 inches. What is this distance expressed in meters?
16. One of the heaviest babies ever born was an Italian boy who weighed 360 oz. at birth.
What was the baby’s mass in kilograms?
ANSWERS:
1. 5 kg 3. 0.018 g 5. 510,000 cg
7. 0.471 daL 9. 20.32 cm 11. 104.14 cm
13. 26.25 ft 15. 2.41 m
341 g
32
MATH 070 UNIT 6 WORKSHEET A
ORDER OF OPERATIONS To simplify polynomial expressions, one follows the rule for the order of operations. Example: Simplify (2x – 1)(x – 3) – 2(x – 1)2 + 3x2 – 2(x + 4)
1. Work inside symbols of inclusion
(2x –1)(x – 3) – 2(x – 1)2 + 3x2 – 2x - 8 2. Raise to powers (2x – 1)(x – 3) – 2(x2 – 2x + 1) + 3x2 – 2x - 8
3. Multiply
(2x2 – 7x + 3) – (2x2 - 4x + 2) + 3x2 – 2x - 8 4. Add and subtract
(2x2 – 7x + 3) + (-2x2 + 4x – 2) + 3x2 – 2x - 8
ANSWER: 3x2 – 5x – 7 Exercises: Simplify: 1. 2(x – 3) – 4(2x – 1) 7. (2x +3)(x – 2) – (x + 1) (2x – 3) 2. x(2x + 3) + 2x(x – 1) 8. (x + 2)2 – x(2x – 1) 3. x2(2x – 3) – x(x2 – 3x + 4) 9. (x + 2)2 – (x – 1)2 4. 5x3(x – 1) – 2x2(x2 + 3x – 2) 10. x(x – 4) – (x – 2)2 5. 3x(x – 1) + 5x(2x – 3) 11. 4x – (2x – 3)2 + 8x2 6. (x – 1)(x + 1) + (x + 2)(x – 2) 12. 3x – (4x – 5)(x – 2) + x(3x – 1) Answers: 1. –6x – 2 7. –3 3. x3 – 4x 9. 6x + 3 5. 13x2 – 18x 11. 4x2 + 16x – 9 REVISED August 30, 2011