MATH 002
Intermediate Mathematics
Lesson 1. Numerical Mathematics and the Graphing Calculator
Chapter 1 of your text introduces the use of the graphing calculator, the properties of the real number system, and the basic rules for performing arithmetic operations on signed numbers. Number line relationships of inequality and distance are explored through interval notation and absolute value. You will evaluate algebraic expressions for given values of the variable(s) using mental, paper and pencil, and graphing calculator computational methods. Linear equations and inequalities in one variable will be solved. In particular, be sure to carefully study Examples 4 and 5 in Section 1.4. The chapter concludes with a discussion of problem solving applications through the use of several different strategies. The variety of approaches support Polya's four-step process: understand the problem, devise a plan, carry out the plan, and look back.
Objectives
After completing the writing assignment, you should be able to:
- Classify numbers according
to the subsets of the real numbers.
- Use interval notation to
describe inequality relationships between real numbers.
- Evaluate expressions using
the order of operations.
- Translate a written statement
to an algebraic statement.
- Identify and apply the properties
of real numbers.
- Use the notation of absolute
value and inequalities.
- Perform the four arithmetic
operations with signed numbers.
- Evaluate algebraic expressions
for given values of the variable(s).
- Solve linear equations and
inequalities in one variable by algebraic methods.
- Use various strategies to set up problem situations and solve algebraically.
Calculator Skills
- Turn the calculator on/off.
- Adjust the screen darkness.
- Use the graphing utility
as a calculator. Practice entering expressions.
exponents
parentheses
order of operations
square root
correct typing errors
insert with the use of the arrow keys
delete
absolute value
negative (-) vs. -
- Divide numerator by denominator
to determine whether a rational number is a repeating or terminating
decimal.
- Use a grapher to evaluate algebraic expressions (see page 29 in your text).
Problem Assignment
Reminder: Do not submit the problem assignments for grading. Work the exercises as preparation for the writing assignment. Check the solutions to the odd-numbered problems in your text.
The "eoo" in parenthesis means "every other odd."
Section
1.1 pg. 12-15 1-15 (eoo), 19, 21, 23, 25-45 (eoo), 47-71 (eoo), 73-81 (odd)
1.2 pg. 23-25 1-57 (eoo), 59-79 (odd)
1.3 pg. 31-34 1-51 (odd)
1.4 pg. 42-44 1-7 (odd), 23-59 (eoo), 33, 37, 67-81 (odd)
1.5 pg. 53-56 1, 3, 5, 7, 10, 11, 13, 15
1.6 pg. 63-66 1-21 (eoo), 23, 25, 31, 33, 35, 37
Lesson I: Flashcards
| 1) "a is less than or equal to b" is written | 1) a 
b |
| 2) The interval [-1, 4) drawn on the number line is | 2)
 |
| 3) Which of the following are rational numbers? a. 2/1; b. 5; c. 3/4; d. all of these, |
3) d. all of these |
| 4) Which of the following are irrational numbers? a. 13; b. 1/2; c. √2; d. all of these |
4) c) √2 |
5) The graph of the interval [-4,  )
on the number line is |
5)  |
| 6) bn | 6) b·b·b ... b (n factors) |
| 7) 43 | 7) 4·4·4 |
8) The absolute value of a signed number b, denoted
|b|, is: a. b, if b 
0; -b, if b < 0; b. b's distance from 0 on the number line;
c. both of these |
8) c. both of these |
| 9) |-3| = | 9) 3 |
| 10) The sign of the product or quotient of two numbers with the same sign is | 10) positive |
| 11) The sign of the product or quotient of two numbers with different signs is | 11) negative |
12) 
= |
12) 8 |
| 13) (-9)(7) = | 13) -63 |
| 14) What percent of 5 is 5? | 14) 100% |
| 15) In the expression 5 - 6x, x reserves a place for a single number and is called a | 15) variable |
| 16) The expression 2x - 4y + 3z has ________ terms. | 16) three |
| 17) A statement that two mathematical statements are equal is called | 17) an equation |
| 18) The _________ of an equation is the statements are equal is called collection of all numbers that make the equation true. | 18) solution |
| 19) Give an algebraic equation for the phrase "length L is 15 more than width W." | 19) L = W + 15 |
| 20) Give an algebraic expression for the phrase "8% of a number x." | 20) 0.08x |
| 21) Give an algebraic expression for the phrase "50 less than a number z." | 21) z - 50 |
| 22) Wholesale price + markup = | 22) retail price |
| 23) When evaluating an expression, the innermost parentheses should be evaluated __________. | 23) first |
| 24) When evaluating the expression 5(2 · 42 - 3 · 2), the first calculation is | 24) 42 |
| 25) -32 = | 25) -9 |
| 26) (-3)2 = | 26) 9 |
Writing Assignment I
Answer all of the following questions on Independent Study lesson paper. Each problem is worth 3 points. Partial credit will be awarded for worked solutions with careless errors. All work must be shown in order to receive credit for the problem. Simplify all answers to receive full credit. Be sure to include an Independent Study cover sheet when you submit your completed assignment.
Show all work. Simplify answers. Work must justify answers!
1. Identify each number as a member of as many of these sets as apply: natural number, whole number, integer, rational number, and irrational number.
- 18
- -2
- _ 40
43
2. Graph each of the following intervals on a number line.
- [-3, 5)
- (-,
2]
- (1, )
3. Evaluate with paper and
pencil. Check your answer with a grapher.
17 + 33 X 2
- 5 + 24 ÷ 6
4. Compute the following. Show
your thinking with paper and pencil. Check your answer with a grapher.
| -27.7 - (-16.2)
| - | -44.3 |
5. Translate each of the following statements, using symbols.
- four times the quantity x plus seven
- the absolute value of the sum of a number and -4.3
- three less than twice a number is twelve
6. State which property is used to show that the following are true statements.
- 5(x + 2) = (x + 2)5
- 4(25b) = (4 · 25)b
- 7(y - 3) = 7y - 21
7. Evaluate the given expression if x = 2.6, y
= -1.2, and z = -1.1. Round your answer
to the nearest hundredth.
7x2 -
3y + 2z2
8. Solve the following inequality
algebraically. Write the answer in interval notation.
4x - 9
15
9. Solve the following equation
algebraically. Write a short paragraph describing the solution process
and justification for each step taken. Be sure to use complete sentences
and correct mathematical vocabulary.
7(2 - x) + 3x =
11x - 8
10. A baseball is thrown straight up into the air with an initial velocity
of 96 ft/sec. It is h feet above the ground t
seconds later. The algebraic representation for height in terms of time
is
h = -16t2
+ 96t
Use the Make a Table strategy to find the maximum
height for this ball's trajectory and the time in seconds it takes to reach
this maximum height.
11. Josh has 36 feet of fencing
to enclose all four sides of a rectangular garden. Complete the following
table to show what the width and area would be for each of the given
lengths.
length width area
6 ______ ______
8 ______ ______
x______ ______
12. Kim made a single investment into a savings account that pays 10% per year. At the end of one year, Kim had $89,924.96 in the account. How much was her original investment? Round the answer to the nearest dollar.