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Mathematics Articles

by Stan Brown, Oak Road Systems

Contents: General  |  Student Success  |  Algebra/Precalc  |  Probability  |  Trig  |  Statistics  |  Calculus

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General Mathematics

Math Sites and Software (revised 7 Jan 2011)
Help desks, FAQs, Web-based software, and more

TI-83/84 Troubleshooting (revised 13 Jun 2014) calculator procedure
Got a screen full of lines? the “INVALID DIM” message? Lost a list?

What’s Different between TI-83 and TI-84? (revised 4 Nov 2013) calculator procedure

Student Success

How to Succeed in Math (revised 11 Aug 2013)

Why is Math so Hard? (revised 2 Jul 2013)

How to Work a Math Problem (revised 6 Dec 2011)

Show Your Work! (revised 12 Apr 2013)

How to Study Math (revised 15 Aug 2006)

How to Take a Math Test or Quiz (revised Feb 7)

How to Read a Math Book (revised 22 Sep 2014)

Math Students’ FAQ (revised 26 Dec 2012)

Algebra / Precalculus

How to Convert Units of Measurement (revised 17 Feb 2009)

Combining Operations (Distributive Laws) (revised 10 Jun 2010)

Factoring the Sum of Squares (revised 22 Apr 2011)

Solving Polynomial Equations (revised 3 Jan 2013)

It’s the Law — the Laws of Exponents (revised 7 Mar 2011)

It’s the Law Too — the Laws of Logarithms (revised 3 Jul 2013)

Loan or Investment Formulas (revised 17 Aug 2013)

Quadratic Equations on TI-83/84 (revised 30 Nov 2009)
with TI-83/84 program QUADRAT for download calculator procedure

Evaluating Functions with TI-83/84 (revised 5 Aug 2007) calculator procedure

Graphing Functions on TI-83/84 (revised 5 Aug 2007) calculator procedure
It’s easy to do, harder to do well.

Graphing Piecewise Functions on TI-83/84 (revised 4 Oct 2008) calculator procedure

Inverse Functions on TI-83/84 (revised 15 Feb 2009) calculator procedure

Complex Numbers on TI-83/84 (revised 26 Jan 2011) or on the TI-89 calculator procedure
computations in polar form or rectangular form (a+bi)

Adding Vectors Graphically on TI-83/84 (revised 7 Aug 2007)
with TI-83/84 program VECADD for download calculator procedure

Multiplying Vectors on TI-83/84 (revised 31 Dec 2013)
with TI-83/84 program VECPRODS for download calculator procedure to compute scalar product (dot product) and vector product (cross product)


MATH200A Program — Statistics Utilities for TI-83/84 (revised May 16) includes some utilities for probability
with TI-83/84 program MATH200A for download calculator procedure

Probability of Shared Birthdays (revised 25 May 2003)
In a group of N people, how likely is it that two or more share a birthday? How big a group do you need before it’s more likely than not?

Medical False Positives and False Negatives (revised 3 Feb 2013)

Binomial Probability Distribution on TI-89 (revised 17 Sep 2011) or on the TI-83/84 calculator procedure


Trig without Tears (revised 10 Aug 2014)
You don’t need to memorize those identities!
(also available in a printer-friendly version)

10-Minute Trig (revised 28 Mar 2006)
for those who just want a fast review

Solving Trigonometric Equations (revised 6 Jul 2010)

Statistics — Free Textbook

Stats without Tears is a full textbook, roughly 100,000 words, with practice exerises and full solutions.

Statistics, Descriptive

Sample Statistics on TI-83/84 (revised 31 Dec 2010) calculator procedure
mean, median, standard deviation, five-number summary, and more

MATH200A Program — Statistics Utilities for TI-83/84 (revised May 16)
histograms, frequency polygons, box-whisker diagrams, binomial probability, check for normality, and more
with TI-83/84 program MATH200A for download calculator procedure

Box-Whisker Plots on TI-89 (revised Feb 2) or on the TI-83/84 (revised 18 Dec 2012) calculator procedure

MATH200B Program — Extra Statistics Utilities for TI-83/84 (revised 2 Aug 2012)
skewness and kurtosis, time-series graphs, and more
with TI-83/84 program MATH200B for download calculator procedure

Measures of Shape: Skewness and Kurtosis (revised Feb 22)

Least Squares — the Gory Details (revised 9 Aug 2007)
what we mean by the “line of best fit”, and how we find it—surprisingly, no calculus is required

Scatterplot, Correlation, and Regression on TI-89 (revised Jan 3) calculator procedure

Finding ŷ from a Regression on TI-89 (revised 9 Jun 2013) calculator procedure

Normality Check and Finding Outliers in Excel (revised Feb 22)

Normality Check on TI-83/84 (revised Feb 22) calculator procedure

Normality Check on TI-89 (revised Feb 22) calculator procedure

Statistics, Inferential

Normal Calculations on TI-83/84 or TI-89 (revised 23 Oct 2012) calculator procedure
in a normal population or a sampling distribution, finding probability or inverse probability

Inferential Statistics Cases (revised 29 Dec 2014)
a summary of inferential statistics from a first course in stats

Triage: Which Inferential Stats Case Should I Use? (revised 27 Jul 2013)

How Big a Sample Do I Need? (revised 24 Aug 2013)

Top 10 Mistakes of Hypothesis Tests (revised 18 Dec 2010)

MATH200A Program — Statistics Utilities for TI-83/84 (revised May 16) calculator procedure
estimate sample size; χ² goodness of fit
with TI-83/84 program MATH200A for download calculator procedure

MATH200B Program — Extra Statistics Utilities for TI-83/84 (revised 2 Aug 2012) calculator procedure
confidence intervals and hypothesis tests for standard deviation, correlation, and regression; critical t and chi-squared
with TI-83/84 program MATH200B for download calculator procedure

Inferences about One Population Standard Deviation (revised 8 Jul 2012)

List Operations for Paired t Test on TI-83/84 (revised 23 Dec 2011) calculator procedure
the calculator’s list operations make this a snap

Inferences about Linear Correlation (revised 25 Dec 2009) explains how to tell whether there is correlation in the population, and how strong it is

Inferences about Linear Regression (revised 20 Dec 2010) to do hypothesis tests and confidence intervals on slope of the regression line and on y responses to particular x values

Testing Goodness of Fit on TI-83/84 (revised 31 Jul 2013) calculator procedure

Testing Goodness of Fit on TI-89 (revised 25 Apr 2013) calculator procedure

Confidence Intervals for Goodness of Fit (revised 11 Jun 2011)

One-Way ANOVA (revised May 10)


Derivatives on TI-83/84 (revised 5 Jan 2014) calculator procedure

Optimization (revised 1 Jan 2014)
maximum profit, minimum cost, and so forth

Newton’s Method on TI-83/84 or TI-89 (revised 19 Jul 2012)
with TI-83/84 program NEWTON for download calculator procedure to find solutions of an equation numerically

Area by Upper and Lower Sums (revised 24 Jul 2012)
introduction to integration

Definite Integrals on the TI-83/84 (revised 22 Dec 2009) calculator procedure

u-Substitution — Changing Variables in Integrals (revised 15 Aug 2009)

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