A Tale of Three Calculators: Problem Solving with Graphing Calculators on the
UIL Mathematics Exam
By
JAMES STEVEN DAUBNEY
July 2008
A Project Submitted
In Partial Fulfillment of
The Requirements for Degree of
MASTER OF SCIENCE
The Graduate Mathematics Program
Curriculum Content Option
Department of Mathematics and Statistics
Texas A&M University-Corpus Christi
APPROVED:
Dr. George Tintera _____________________________________
Committee Chair
Dr. Elaine Young
____________________________________
Committee Member
Dr. Nadina Duran-Hutchings _____________________________
Committee Member
Dr. Blair Sterba-Boatwright ______________________________
Chair, Department of Mathematics and Statistics
Date _____________________
Style: APA
ABSTRACT
The Texas University Interscholastic League (UIL) Mathematics
Examination is given every March to secondary students. It includes topics from
algebra I and II, geometry, trigonometry, math analysis, analytic geometry, precalculus and elementary calculus. Contestants are allowed the use of any
commercially available silent hand-held calculator. The most common high
school calculator is the TI-83/84, and to date it is also the most popular on the
exam. However, a growing number of participants have been using the TI-89
CAS calculators. The even newer TI-Nspire CAS calculators will be available for
the 2009 examinations. Yet many students and educators are unfamiliar with
these CAS calculators and their capabilities. Accordingly, this project purports to
familiarize the education community with all three of these calculators (the TI-84
Plus, the TI-89 Titanium, and the TI-Nspire CAS), all of which are being actively
marketed, by juxtaposing their utilization on the 2008 District II UIL Mathematics
Examination. The author has produced a series of PowerPoint lessons which
demonstrate how to solve the problems presented on the examination using the
Texas Instrument graphing calculators which are currently marketed for
education. Side-by-side comparisons of algorithms, entries, announcements,
menus, graphs and tables will enhance a reader’s capacity to use a variety of
calculators in this context. It is the author’s hope that this will result in both a
greater understanding of the calculators’ broad capabilities and improvement of
students’ mathematical problem-solving abilities.
ii
TABLE OF CONTENTS
Introduction .........................................................................................................1
Literature Review ................................................................................................3
Methodology ........................................................................................................9
Results ...............................................................................................................10
Summary ...........................................................................................................13
References ........................................................................................................14
Appendix A: 2008 District II UIL Mathematics Examination and Key ................16
Appendix B: Question 45 with Calculator Solutions ..........................................26
Appendix C: Calculator Lessons .......................................................................42
Appendix D: Calculator Topical Index and Page C............................................47
iii
INTRODUCTION
The University Interscholastic League (UIL) is the state-wide organization
for public elementary and secondary interschool competition in Texas. The UIL
Mathematics Examination was first introduced in 1991 and presently consists of
60 questions with a 40-minute time limit (Texas Competitive Mathematics, 2008).
It is currently based on the secondary mathematics Texas Essential Knowledge
and Skills (TEKS), including concepts from algebra I and II, geometry,
trigonometry, math analysis, analytic geometry, pre-calculus and elementary
calculus. The district examinations are given annually in the spring, however,
many invitational meets occur throughout the year. There are two releases
annually of UIL exams prepared for invitational meets, plus several more
annually from the Texas Math and Science Coaches Association (TMSCA).
Contestants are allowed the use of any unmodified commercially available silent
hand-held calculators that do not require auxiliary electric power. They are
allowed to maintain any equations or programs that they may have stored in their
calculator’s memory, and they are allowed to bring a spare calculator. Small,
hand-held computers are not permitted (UIL, 2007). The most popular calculator
used is the TI-84 Plus, although increasingly more contestants are using the TI89 Titanium. A new graphing calculator, the TI-Nspire CAS, will also be eligible
for the examination.
By focusing on problem solving in the UIL Mathematics Examination and
by juxtaposing strategies on these three calculators, the author has produced
educational materials which will help students achieve greater competency with
1
graphing calculators (including the newer CAS models) and problem-solving
techniques.
This project has produced classroom lessons and activities for use with
secondary educators and students involved in UIL Mathematics, as well as
advanced secondary mathematics students who use graphing calculators in their
studies. These lessons and activities will meaningfully engage educators and
students in problem solving and graphing calculator usage, which may extend
beyond the UIL Mathematics examination and into life-long problem-solving
strategies. This project is based on the following guiding principles:
•
•
•
•
Multiple representations offered by graphing calculators
enhance student understanding of mathematical principles
and aid in problem solving.
The UIL Mathematics Examination offers a wide variety of
problems suitable for teaching mathematics problem solving
at the secondary level.
Juxtaposing different calculator strategies for the same
problem is an efficient method of teaching calculator logic
and usage.
Computer algebra system (CAS) graphing calculators can
increase mathematical understanding.
Calculators may be classified as four-function, scientific, graphing, and computer
algebra system (CAS). The four-function calculator adds, subtracts, multiplies
and divides. The scientific calculators employ scientific notation, floating point
arithmetic, logarithmic functions, trigonometric functions, exponents and roots,
and constants such as pi (π) and e. Deluxe scientific calculators also include
hexadecimal and binary calculations, complex numbers, fractions, and statistical
2
and probability calculations. Graphing calculators have all of the above functions,
plus they are capable of plotting graphs, solving systems of equations, and are
often programmable. CAS calculators are graphing calculators which store and
display values symbolically rather than floating-point numbers. They feature
automated symbolic manipulation, as well as various algebraic and calculus
based functions, including symbolic limits, derivatives, and integrals.
Virtually all calculators now employ liquid crystal displays (LCD), but some
can be further differentiated by larger QWERTY keyboards, similar to typewriters.
Another differentiating factor is input, which may be either reverse Polish notation
(RPN) or algebraic. Algebraic input follows mathematical expressions from left to
right. However, RPN inputs require that operands are entered immediately
preceding their operators. Presently, only Hewlett-Packard mass markets
calculators with predominantly RPN input.
LITERATURE REVIEW
Battery-powered pocket calculators were commercially introduced
circa 1970 and the first scientific pocket calculator, the HP-35, appeared in 1972
at a cost of $395. During the 1970’s, as calculator prices fell, calculator sales
grew, while sales of slide rules and math tables plummeted. The NCTM
advocated broad student access to scientific calculators (Kennedy, 2002), and
the College Board acquiesced, by allowing, but not requiring, scientific
calculators for the first time on the 1983 AP calculus examinations. The
3
experiment lasted only two years, as the results were poor and the construct
validity of the examination was called into question (Kennedy, 2002).
It is often said that assessment drives the curriculum, and in 1989 the
National Council of Teachers of Mathematics (NCTM, 1989) reiterated this
position in the Curriculum and Evaluation Standards for School Mathematics by
pointing out that appropriate calculators should be available to all students at all
times, and calculators should be fully integrated into the teaching and the testing
of mathematics.
The mass marketing of graphing calculators in 1988 renewed this debate,
and by 1993 scientific calculators were required on the AP examinations.
Beginning in 1995, graphing calculators which could graph a function, solve an
equation, compute a numerical derivative at a point, and compute a definite
integral numerically were required. However, a portion of the multiple-choice test
was kept calculator-free. When CAS calculators became widely available and
were approved for testing in 1999, the College Board made a portion of the freeresponse section calculator-free as well (Kennedy, 2002).
Calculators have been allowed, but not required, for the Scholastic
Aptitude Test (now the SAT) since 1994. This policy allows any type of
calculator, from basic four-function calculators to graphing calculators with
symbolic algebra capabilities (Dion, Harvey, Jackson, Klag, Liu & Wright, 2002).
The UIL added the Mathematics Examination for Texas secondary students in
1991 and recently changed its rules to allow any commercially available silent
4
hand-held calculator that does not require auxiliary electric power (Texas
Competitive Mathematics, 2008).
The advent of the CAS graphing calculator has renewed the technology
controversy in mathematics instruction and assessment (Zbiek & Schoaff, 2002).
Although it is a commonly held belief that the use of CAS in secondary school
mathematics causes atrophy of paper and pencil symbolic manipulations skills, a
survey of numerous studies points to the contrary (Heid, Blume, Hollebrands, &
Piez, 2002). In fact, students who have utilized CAS based instruction have
surpassed their counterparts even in paper and pencil skills. CAS gives students
greater flexibility in problem solving by offering them a greater range of strategies
while developing deeper understanding of the concepts of function, variable, and
parameter (Heid, et al., 2002). Mathematics is really about reasoning and
problem solving. The calculations, numerical or algebraic, are only a means to an
end.
CAS allows students to learn precalculus and calculus even though they
may not have mastered algebra (Mahoney, 2002). CAS calculators solve
equations symbolically, and have the potential to cause a major paradigm shift in
teaching mathematics, just as scientific and graphing calculators have done
before.
When using CAS and most graphing calculators, students can seamlessly
transition between symbolic, numeric and graphical representations (Pierce &
Stacey, 2002). “Student’s engagement with, and ownership of, abstract
mathematical ideas can be fostered through technology. Technology enriches
5
the range and quality of investigations by providing a means of viewing
mathematical ideas from multiple perspectives” (NCTM, 2000, 24).
Calculators can change the way we teach. Bert K. Waits reports ten
fundamental activities done with hand-held visualization technology in the
classroom work of students in the Calculator and Computer Precalculus project
(involving more than 1,000 schools in the USA). These activities are:
1) Approach problems numerically.
2) Use analytic algebraic manipulations to solve equations and
inequalities and then support using visual methods.
3) Use visual methods to solve equations and inequalities and then
confirm using analytic algebraic methods.
4) Model, simulate and solve problem situations.
5) Use computer generated visual scenarios to illustrate
mathematical concepts.
6) Use visual methods to solve equations and inequalities which
can not be solved or are impractical using analytic algebraic
methods.
7) Conduct mathematical experiments, and make and test
conjectures.
8) Study and classify the behavior of different classes of functions.
9) Foreshadow concepts of calculus.
10) Investigate and explore various connections among different
representations of a problem situation.
(Carvalho, 1996, citing Waits, 23).
The National Council of Teachers of Mathematics advocates introducing,
teaching, and assessing mathematics through problem-solving (NCTM, 2000).
The Texas UIL Mathematics Examination provides a wealth of problems on a 60question examination designed to test knowledge and understanding in the areas
of algebra I and II, geometry, trigonometry, math analysis, analytic geometry,
pre-calculus and elementary calculus. These are aligned with Texas Essential
Knowledge and Skills (TEKS) for secondary students (Texas Education Agency,
6
2007). A total of seven tests are generated per year and are released to the
public (Texas Competitive Mathematics, 2008). The rules allow almost any handheld calculator. Accordingly they constitute an excellent problem bank for
teaching problem solving with technology.
The world calculator market has four major manufacturers: Casio, Texas
Instruments, Hewlett-Packard and Sharp. However, the North American
educational market is virtually monopolized by Texas Instruments, so this project
will utilize the three TI models which are actively marketed to the secondary and
college market (Texas Instruments, 2008):
1. The TI-84 Plus (released in 1999 as the TI-83 and re-released in
2004 as the TI-84 Plus), which is by far the most common graphing
calculator found in American secondary and post-secondary
education today;
2. The TI-89 Titanium (released in 1998 as the TI-89 and rereleased in 2004 as the TI-89 Titanium), which is the most widely
used CAS calculator in North America, and which is used in many
secondary and university advanced mathematics classes; and
3. The TI-Nspire CAS, (preliminary release in 2007, mass release in
2008, also released in a non-CAS version), which is heralded as the
next generation calculator of the future. It is also equipped with
dynamic geometry and spread sheet capabilities (Woerner, 2007).
Calculator techniques will be learned by solving problems. Problems
taken from the 2008 UIL Mathematics Examination will be solved simultaneously
7
utilizing all three calculators, juxtaposing multiple representations, so as to build
upon the schemas of most educators and students with respect to the TI-84,
while introducing new methods and algorithms characteristic of the newer CAS
calculators. A copy of the 2008 District II UIL Mathematics examination is
attached as Appendix A.
Vygotsky’s zone of proximal development represents the difference
between what a person can do with and without help; that is, just beyond the
learner’s current competence. Activities such as associations, imitations and
manipulations are a necessary part of concept formation and can bridge the gap
between mathematical activities and the formation of mathematical concepts,
thereby complementing and building upon existing abilities (Berger, 2005).
Students and educators who may already have a working knowledge of the TI83/84 can build upon that knowledge while learning analogous strategies on the
TI-89 and Nspire CAS calculators.
Skemp and others have posited that mathematical understanding can be
bifurcated into instrumental understanding and relational understanding (Skemp,
1987). The former involves the mere mechanical application of rules and
formulas which students may not be able to apply outside the narrow context in
which they were learned; the latter necessitates deeper understanding of
mathematics principles, and while harder to learn it is easier to remember and
apply to other situations. Many would argue that teaching problem solving with
calculators would be a quintessential case of instrumental teaching, but the
author takes the contrary position. Problem solving with graphing calculators,
8
particularly CAS graphing calculators, necessitates a fundamental understanding
of basic mathematic principles, and with practice this knowledge is organic; that
is, it nurtures its own growth and development. Problem solving with calculators
promotes relational understanding, transcending multiple representations of
problems.
METHODOLOGY
This project began with a detailed study of the Texas Instrument
Calculator Manuals and the 2008 UIL District II Mathematics Examination. The
author also attended several TI-Nspire training sessions conducted by Teachers
Teaching with Technology - T3, a training division of Texas Instruments.
Independent problem-solving strategies were developed for each of the three
calculators for each of the thirty odd-numbered problems. These strategies have
been implemented and documented with step-by-step calculator screen captures
and accompanying explanations. These materials have been developed for
educators and students who have access to at least one of these three graphing
calculators, and preferably more than one. Partial results were presented to UIL
coaches and secondary mathematics teachers at the Coastal Council of
Teachers of Mathematics annual mathematics conference, (ME)2 by the Sea, at
Texas A & M University-Corpus Christi in June of 2008. This project is intended
to be used as training for UIL contestants and secondary mathematics students
in Algebra II and above.
9
RESULTS
This project demonstrates strategies to utilize three Texas Instrument
calculators, the TI-84 Plus, TI-89 Titanium and the TI-Nspire CAS, to solve
questions on the 2008 UIL Mathematics Examination. The model examination is
the 2008 District II version, and the thirty odd-numbered questions are examined.
A complete copy of this examination, as well as the answer key, is attached as
Appendix A. A complete solution for each problem is demonstrated on each
calculator, including an overall strategy, step-by-step screen captures, and
accompanying text explanations and menu instructions. It is presented in an
interactive PowerPoint format appropriate for group presentations or individual
use. It is intended to assist UIL contestants, their coaches, as well as secondary
and college-level mathematics students, to gain a greater understanding of
mathematics problem solving and a greater mastery of the most advanced Texas
Instrument calculators.
A review of the questions and their three calculator solutions reveals that
the problems logically fall into one of three categories. The first category is where
the strategies and tactics for a particular question are the same for all three
calculators, as is the case in question 29. This is a right triangle trigonometry
problem and the strategy is to use the trigonometric ratio sine of theta equals the
ratio of the opposite over the hypotenuse, where theta and the hypotenuse are
known. The tactic for all three calculators is to use the solve command to find the
unknown opposite side. A second category is where strategies are the same for
each calculator, but tactics differ among the calculators due to differences in their
10
menus and programming, as is the case in question 45. All three strategies
involve solving a system of equations, but the calculator tactics very
considerably. The TI-84 solution involves creating a two-by-three matrix
representing the equations and then converting it to reduced row echelon form.
The TI-89 tactic is simpler. It involves using an application called Simultaneous
Equation Solver, inputting the coefficients, and pressing Solve for the solution.
The TI-Nspire tactic is perhaps the simplest of all, providing us the solution after
we input the two equations exactly as they are written using a system of
equations template with the solve command. A third category of question from
the examination is where both strategies and tactics vary among the calculators,
as is the case with question 43. This is due to the differing capabilities of the
calculators. The strategy for the TI-84 involves first manually calculating the area
of numerous individual rectangles and triangles and then adding them together to
find the net area of the pentadecagon. The strategy for the TI-89 involves using
Pick’s theorem, which may be stored in the calculator earlier, as a user-defined
function, and inputting the number of perimeter grid points and interior grid points
as arguments to find the area of the polygon. The TI-84 does not offer the option
of user-defined functions. Yet another strategy is possible with the TI-Nspire.
Using the Graphs & Geometry screen and the grid option, we can actually
reproduce the irregular pentadecagon using the polygon construction tool and let
the area function calculate the area. This method is not possible on the other two
calculators. The various problems solved in the project demonstrate many of the
11
more powerful problem-solving applications available on the newer CAS
calculators.
The user has four avenues available to view the materials. First, she may
simply review the problems in numerical order, which reproduces their sequence
in the examination. Second, she may use the UIL Questions and Solutions index,
which has a hyperlink directly to each problem, to select individual problems of
interest. As an example one of the thirty problems and its calculator solutions are
reproduced in Appendix B. She may also review the problems grouped into six
Calculator Lessons of five problems each, arranged by level of difficulty, with
hyperlinks to the respective problems. Copies of the calculator lessons slides are
attached as Appendix C. Finally, the user will have the option of selecting specific
topics from the Calculator Topic Index, which lists topics alphabetically. A
representative slide from the Index is attached as Appendix D. In any case, with
over 1000 slides to view, it is the author’s hope that this endeavor will promote
greater mathematical understanding, and more efficient use of calculator
technology, in the State of Texas.
Student results might include increased interest in calculator-assisted
problem solving, and enhanced performance on UIL Mathematics examinations
and other examinations permitting the use of CAS and non-CAS graphing
calculators, such as the TAKS, SAT, ACT, and AP exams. It is hoped that this
may also enhance students’ success in college-level courses permitting CAS
graphing calculators.
12
SUMMARY
This project has produced a series of lessons to enable mathematics
coaches and students to more effectively utilize graphing calculators in problemsolving situations. The thirty model problems are taken from the 2008 District II
UIL Mathematics Examination. The lessons include strategies, tactics, and stepby-step instructions for each the three TI graphing calculators: the TI-84 Plus,
The TI-89 Titanium, and the TI-Nspire CAS. Each step is further documented
with calculator screen captures.
It is expected that the use of these materials may result in enhanced
problem-solving abilities and more effective calculator utilization. The author will
employ these materials extensively in his capacity as a UIL Mathematics coach,
and on an ad hoc basis with his upper-level secondary mathematics courses,
and lower-division college-level mathematics courses.
13
REFERENCES
Berger, M. (2005). Vygotsky’s theory of concept formation and mathematics
education. In H.L. Chick & J.L. Vincent (Eds.), Proceedings of the 29th
Conference of the International Group for the Psychology of Mathematics
Education, Vol. 2, (pp. 153-160). Melbourne: PME. Retrieved April 25,
2008, from http://www.emis.de/proceedings/PME29/PME29RRPapers
/PME29Vol2Berger.pdf
Carvalho, J. (1996). Are graphing calculator the catalyzers for a real change in
mathematics education? In Gomez & Waits (Ed.), Roles of calculators in
the classroom, (pp. 21-30). Retrieved March 19, 2008, from
http://ued.uniandes.edu.co/servidor/em/recinf/tg18/ArchivosPDF
/Carvalho.pdf
Dion, G., Harvey, A., Jackson, C., Klag, P., Liu, H., & Wright C. (2002). A survey
of calculator usage in high schools. International Journal of Mathematics
Education Science Technology, 33 (1), 15-36. Retrieved from Wilson Web
database.
Heid, M. K., Blume, G. W., Hollebrands, K. & Piez, C. (2002). Computer algebra
systems in mathematics instruction: Implications from research.
Mathematics Teacher, 95 (8), 586-591.
Kennedy, D. (2002). AP calculus and technology: A retrospective. Mathematics
Teacher, 95 (8), 576-581.
Mahoney, J. F. (2002). Computer algebra systems in our schools: Some axioms
and some examples. Mathematics Teacher, 95 (8), 598-605.
National Council of Teachers of Mathematics. (1989). Curriculum and Evaluation
Standards for School Mathematics. Reston, VA: National Council of
Teachers of Mathematics.
National Council of Teachers of Mathematics. (2000). Principles and Standards
for School Mathematics. Reston, VA: National Council of Teachers of
Mathematics.
Pierce, R. U. & Stacey, K. C. (2002). Algebraic insight: The algebra needed to
use computer algebra systems. Mathematics Teacher, 95 (8), 622-627.
Skemp, R. (1987). The psychology of learning mathematics. Hillsdale, NJ:
L. Earlbaum Associates.
Texas Competitive Mathematics. (2008). Texas Math & Science Community
Articles. Retrieved March 19, 2008, from http://texasmath.org/
14
Texas Education Agency. (2007). Texas essential knowledge and skills (TEKS).
Retrieved March 19, 2008 from http://www.tea.state.tx.us/teks/index.html
Texas Instruments (2008). Education technology. Retrieved April 10, 2008 from
http://education.ti.com/educationportal/sites/US/homePage/index.html
UIL Constitution Sec. 942 Mathematics. (2007). Policy & administration.
Retrieved March 19, 2008, from
http://www.uil.utexas.edu/policy/constitution/index.html
Woerner, J. (2007). Datamath Calculator Museum. Retrieved April 14, 2008, from
http://www.datamath.org/Graphing/NSpire_CAS.htm
Zbiek, R. M. & Schoaff, E. (2002). Welcome to our focus issue on computer
algebra systems. Mathematics Teacher, 95 (8), 561.
15
APPENDIX A
16
2008 UIL District II Mathematics Examination and Key
17
18
19
20
21
22
23
24
25
APPENDIX B
26
UIL Questions and Solutions Index
UIL QUESTIONS & SOLUTIONS
(click on any question to hyperlink)
•
•
•
•
•
•
•
•
•
•
Question 1
Question 3
Question 5
Question 7
Question 9
Question 11
Question 13
Question 15
Question 17
Question 19
Question 21
Question 23
Question 25
Question 27
Question 29
Question 31
Question 33
Question 35
Question 37
Question 39
Question 41
Question 43
Question 45
Question 47
Question 49
Question 51
Question 53
Question 55
Question 57
Question 59
Return to the table of contents
27
Question 45 with Calculator Solutions
No. 45
TI-84 STRATEGY
Enter the system of equations as a 2 x 3
augmented matrix and find the reduced row
echelon form to see the solution in the last
column.
28
Press 2ND MATRIX to see
the Matrix menu. Select
EDIT and 1:[A].
Type 2 x 3 to establish
the dimensions of matrix
A and then input the
values for each cell
according to the system
of equations.
29
Press 2nd QUIT and then
press 2ND MATRIX again
and select MATH and
B:rref( to find the reduced
row echelon form of
augmented matrix A.
Press 2ND MATRIX to see
the Matrix menu. Select
NAMES and 1:[A].
30
Press 2ND MATRIX to see
the Matrix menu. Select
NAMES and 1:[A].
ENTER.
Press 2ND MATRIX to see
the Matrix menu. Select
NAMES and 1:[A].
ENTER for the solution
matrix.
31
Press MATH and select
1:Frac to change the
decimal answer to
fraction format.
Press MATH and select
1:Frac to change the
decimal answer to
fraction format.
32
TI-89 STRATEGY
Enter the simultaneous equations as a 2 x
3 augmented matrix and use the calculator
Simultaneous Equation Solver.
Press APPS and select
Simultaneous Equation
Solver.
33
Select 3:New
Input 2 equations and 2
unknowns. ENTER to
see the augmented
matrix template.
34
Input 2 equations and 2
unknowns. ENTER to
see the augmented
matrix template.
Type the corresponding
values in each cell. The
1st equation goes in the
first row.
35
Select F5 Solve.
TI-NSPIRE STRATEGY
Use the solver and the simultaneous
equation template to solve for x and y.
36
Press APPS and select
1:Calculator.
Press CATALOG.
37
Select 5:Templates and
the two simultaneous
equations template.
ENTER.
Select 5:Templates and
the two simultaneous
equations template.
ENTER.
38
Move the cursor to the
left of the template and
press MENU and select
4:Algebra and 1:Solve.
ENTER.
Move the cursor to the
left of the template and
press MENU and select
4:Algebra and 1:Solve.
ENTER.
39
ENTER for the solution.
23
(E) 25
40
No. 45
•
•
•
•
Table of Contents
Calculator Lessons
UIL Questions & Solutions
Calculator Topical Index
41
APPENDIX C
42
Calculator Lessons
CALCULATOR LESSONS
(click on any lesson to hyperlink)
•
•
•
•
•
•
Lesson A: Basics I
Lesson B: Basics II
Lesson C: Intermediate I
Lesson D: Intermediate II
Lesson E: Advanced I
Lesson F: Advanced II
Return to the table of contents
Lesson A: Basics I
(click on any question to hyperlink)
• Question 1
• Question 7
order of operations, factorial, menus,
clear screen
data editor, plot, window, zoom,
coordinates, polygon, area
text, notes, folios
• Question 11
graphing, equation editor, inequalities
• Question 35
probability, percentage, fraction part
• Question 5
Return to the calculator lessons home page
43
Lesson B: Basics II
(click on any question to hyperlink)
• Question 13
interest, roots, percentages
• Question 17
exponents, graphing,
intersections, non-linear system
• Question 29
right triangle trigonometry, sin
• Question 39
nets, edges, cube
• Question 57
absolute value, graph, solve,
one-variable equation
Return to the calculator lessons home page
Lesson C: Intermediate I
(click on any question to hyperlink)
• Question 19
• Question 31
• Question 43
• Question 45
• Question 59
regression, sets, data editor,
lists, delta list
matrices, determinants, inverse
polygon, area, geometry, grid,
Pick’s theorem, library, draw
system of equations, matrix
simultaneous equations,
reduced row echelon form
system of equations, matrix
simultaneous equations,
reduced row echelon form
Return to the calculator lessons home page
44
Lesson D: Intermediate II
(click on any question to hyperlink)
• Question 3
system of equations, matrices
• Question 25
ellipses, graph, intersect, slope
• Question 41
system of equations, rate of
change, equation solver
probability, combinations,
library, user-defined functions
• Question 53
• Question 55
zeros, non-linear system,
numeric solver, copy and past
Return to the calculator lessons home page
Lesson E: Advanced I
(click on any question to hyperlink)
• Question 9
• Question 23
bearing, mode, parametric
graph, unit circle, arc
vectors, proportions, solver
• Question 27
complex numbers, roots
• Question 37
number theory, programming,
abundant and happy numbers
• Question 47
trigonometry, solver, graph,
domain restrictions, intersect
Return to the calculator lessons home page
45
Lesson F: Advanced II
(click on any question to hyperlink)
• Question 15
• Question 21
• Question 33
• Question 49
• Question 51
angle of rotation, conic, ellipse,
trigonometry
rational expressions, mixed
number, symbolic manipulation
numeric integration, constant of
integration, antiderivative
rational expression, polynomial
division, slant asymptote,
expansions
symbolic integration, calculus
Return to the calculator lessons home page
46
APPENDIX D
47
Calculator Topical Index and Page C
Calculator Topical Index
(click on any letter to hyperlink)
•
•
•
•
•
•
•
A
E
I
M
Q
U
Y
B
F
J
N
R
V
Z
C
G
K
O
S
W
D
H
L
P
T
X
Return to the table of contents
C
•
•
•
•
•
•
•
•
•
•
•
Calculus
Chain rule
Clear screen
Combinations
Complex numbers
Conics
Constant of integration
Construction
Coordinates
Copy and paste
Cosine
33
33
1
53
27
15
33
5
5
55
47
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48
51
25
43