TLM
Module A02
Formatting for
TLM - Part II
Copyright
This publication © The Northern
Alberta Institute of Technology
2002. All Rights Reserved.
LAST REVISED Oct., 2008
Formatting for TLM - Part II
Statement of Prerequisite Skills
Complete Formatting for TLM – Part 1 before beginning this module.
Required Supporting Materials
Access to the World Wide Web.
Internet Explorer 5.5 or greater.
Rationale
Why is it important for you to learn this material?
The math course you are about to take requires you to enter data into a computer.
Computers are only as accurate as the code that has been programmed into them. It
is not possible to include every possible version of an answer in the computer and for
this reason a TLM formatting technique must be followed. If you do not follow this
technique TLM may mark answers wrong that would normally be considered correct.
Be sure to follow the TLM formatting guidelines set out in this module to reduce the
frustration of data entry in the computer.
Learning Outcome
When you complete this module you will be able to…
Enter answers into TLM.
Learning Objectives
1.
2.
3.
4.
5.
6.
7.
8.
Apply TLM formatting to terms with a coefficient of one.
Apply TLM formatting to descending powers.
Apply TLM formatting to questions that refer to lists.
Apply TLM formatting to scientific notation.
Apply TLM formatting to factors.
Apply TLM formatting to products.
Apply TLM formatting to square root and cube root.
Apply TLM formatting to yes and no answers.
Connection Activity
Have you ever approached an instructor or a teacher to discuss the way they marked a
problem on an exam? They may have been looking for a particular procedure or way
of answering a question. Upon discussing the problem you may have been awarded
part marks or possibly walked away with no more marks but a better understanding
of what was being asked. Imagine having this conversation with your computer!
TLM is much less forgiving when marking and for this reason you need a thorough
understanding of exactly how to enter answers into the computer.
1
Module A02 − Formatting 2
OBJECTIVE ONE
When you complete this objective you will be able to…
Apply TLM formatting to terms with a coefficient of one.
Exploration Activity
If a term has a numerical coefficient of one, do not enter the one.
EXAMPLES
Algebraic expression
TLM Format
1x2
x^2
1x2 + 1y2 + 2xy
x^2+2xy+y^2
2
Module A02 − Formatting 2
OBJECTIVE TWO
When you complete this objective you will be able to…
Apply TLM formatting to descending powers.
Exploration Activity
When entering an algebraic expression with the same base raised to different powers,
always put terms in order of descending powers.
Also remember that alphabetical order supercedes descending powers.
Algebraic expression
2
3
TLM Format
1.
3x + 7x +5x
7x^3+3x^2+5x
2.
x5 +3a +7b
3a+7b+x^5
3.
− 1b 2 − 4ac
-sqr(-4ac+i^2)
4.
5v2 +7ir +6ab
6ab+7ir+5v^2
3
Module A02 − Formatting 2
OBJECTIVE THREE
When you complete this objective you will be able to…
Apply TLM formatting to questions that refer to lists.
Exploration Activity
Often, a number of solutions for TLM are presented on lists. This method is used for
graphing and for solving equations.
EXAMPLE
You will be asked to plot the graph of a linear equation y = 2x + 1.
Then you will refer to a list and identify the graph that is the same as the one you
sketched.
The number of the graph will be the correct answer.
4
Module A02 − Formatting 2
OBJECTIVE FOUR
When you complete this objective you will be able to…
Apply TLM formatting to scientific notation.
Exploration Activity
For some answers, you will be asked to express the results in scientific notation.
Note below: "answer" is abbreviated "ans".
EXAMPLE
1. Express 457.25 in scientific notation.
Answer = 4.5725 ×102
When entering this result, you will use the following procedure:
a) ans 1 is a number between 1 and 10.
b) ans 2 is the appropriate power of 10.
Therefore: 457.25 = 4.5725 × 102
TLM Format
ans 1 = 4.5725
ans 2 = 2
Note: We already know that scientific notation uses 10 as the base, therefore we
do not need to include this in the answer.
2. Express 0.025 in scientific notation.
0.025 = 2.5 × 10-2
TLM Format
ans 1 = 2.5
ans 2 = −2
5
Module A02 − Formatting 2
OBJECTIVE FIVE
When you complete this objective you will be able to…
Apply TLM formatting to factors.
Exploration Activity
EXAMPLES
Factor the following completely:
Algebraic Expression
TLM Format
1.
x2 + 2x + 1 = (x+1)(x+1)
(x+l)(x+l) or (x+l)^2
2.
x2y + xy = xy(x + 1)
xy(x + 1)
3.
x2 + x − 2 = (x + 2)(x − 1)
(x+2)(x−1) or (x−1)(x+2)
4.
x3 +3x2y + 3xy2 + y3 = (x+y)(x+y)(x+y)=(x+y)3
(x+y)^3
5.
x3 + x2y = x2(x + y)
x^2(x+y)
6
Module A02 − Formatting 2
OBJECTIVE SIX
When you complete this objective you will be able to…
Apply TLM formatting to products.
Exploration Activity
Products follow the rules of Objective 2: alphabetic order with descending powers.
EXAMPLES
Write the product of each of the following:
Algebraic Expression
TLM Format
1.
(x+y)2 = x2+2xy+y2
x^2+2xy+y^2
2.
(x+y+z)2=x2+2xy+2xz+y2+2yz+z2
x^2+2xy+2xz+y^2+2yz+z^2
7
Module A02 − Formatting 2
OBJECTIVE SEVEN
When you complete this objective you will be able to…
Apply TLM formatting to square root and cube root.
Exploration Activity
If the result requires a square root sign use sqr( ) and if the result is a cube root,
use cbr( )
EXAMPLES
Algebraic Expression
1.
TLM Format
x
sqr(x)
2.
3
y
cbr(y)
3.
4 b
4sqr(b)
4.
a3 b 2
acbr(b^2)
8
Module A02 − Formatting 2
OBJECTIVE EIGHT
When you complete this objective you will be able to…
Apply TLM formatting to yes and no answers.
Exploration Activity
For some questions you will be asked to respond yes or no.
For a yes response type 1, and for a no response type 0.
EXAMPLES
TLM Format.
Is 5 greater than 10 (yes or no)?
ans = no
TLM ans = 0
2. 100 is greater than 10 (yes or no)?
ans = yes
TLM ans = 1
NOTE: If you have any questions concerning TLM Format, see your instructor.
Practical Application Activity
Complete the formatting – part 2 module assignment in TLM.
Summary
This module introduced the student to advanced formatting issues in TLM.
9
Module A02 − Formatting 2
Appendix
Examples of Computer Coding Using a Minimum of Parenthesis
ALGEBRA
COMPUTER
REASONING
2 − 3x
3x + 2a +x2
4x − 1x2 +3ax
(4x−3x3+7)(2y+x)2x
(x+2y)(1−2x)
16
−3x+2
2a+x^2+3x
3ax−x^2+4x
2x(x+2y)(−3x^3+4x+7)
(x+2y)(−2x+1)
sqr(16)
Polynomial, descending order
Alphabetic first
Alphabetic first, coefficient 1 is omitted
Shorter factors ahead of longer factors
Alphabetic, Polynomial order
Special function, need the brackets
8
cbr(8)
Special function, need the brackets
5 + 3x
sqr(3x+5)
Special function, note the brackets, order
1 − 2x
cbr(−2x+1)
Special function, note the brackets, order
A +2B2 − 5AB
a−5ab+2b^2
Lower case letters, alphabetic order
ay − ax + 2b
−ax+ay+2b^2
(x+5y)/a
(−3x+2y)/(−a+4x)
Alphabetic order, note symbol for power
Brackets if 2 or more terms, forward slash for
division.
Brackets if 2 or more terms
2xy/(−b+4x)
Brackets if 2 or more terms in the denominator
xy/(wz)
(4x−y^2)/x^3
Brackets if 2 or more factors in the denominator.
Note: no brackets in numerator.
Brackets if 2 or more terms in the numerator.
(sqr(3x)+7)/(−2x^2+3)
Brackets if 2 or more terms, polynomial order
a^(2b)+x^2
3a^2b^2
(sqr(−4ac+b^2)−b)/(2a)
Alphabetic, note the exponent in brackets.
Alphabetic, coefficient in front
Brackets if 2 or more terms in the numerator and
brackets if 2 or more factors in the denominator.
5ax^2/y^2
No brackets since the numerator is 1 term and the
denominator is 1 factor.
(x−3y^2)/(−3x^2+y)
Brackets if 2 or more terms, alphabetic order
(x+3)^(1/2)(3x−4)^−2/
((x+3)^(−1/3) +1)
Brackets if 2 or more terms, exponents with more
than 1 factor in brackets.
3
3
2
x + 5y
a
2 y − 3x
4x − a
2 xy
4x − b
xy
wz
4x − y 2
x
3
7 + 3x
3 − 2x 2
x 2 + a 2b
3× b × a
2
2
− b + b 2 − 4ac
2a
5ax 2
y2
x − 3y 2
y − 3x
2
( x + 3)1 2 (3x − 4) −2
1 + ( x + 3)
−1 3