## Finite Math Tutoring

There are common questions that students have in finite mathematics.  We answer a couple here and are willing to answer others for you.  Click on the "Contact Us" tab above.

Lionel poses the question, "How do I decide if I should use the formula for the number of permutations or the number of combination?  For example, I had the following question in the homework:  On a test, a student is to answer 10 out of 13 questions.   How many ways can this be done?

Lionel, that is a very good question.  Simply stated, a permutation is an order, an arrangement.  A combination is a set of objects, a collection of objects, without regard to order.  "Order" becomes the operative word.

Thus, the number of permutations of 13 items taken 10 at a time means the number of orders of 10 items taken from 13 items.  And the number of combinations of 13 items taken 10 at a time means the number of collections of 13 items we can form from 13 items.

In your example, the question is, does it matter which order the 10 questions are selected?  If order does, we use the number of permutation.  If order does not matter, we use the number of combinations.  The example by itself is unclear if we are to determine the number of orders or the number of sets of 10 questions we are to determine.

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## Statistics Math Tutoring

There are common questions that students have in statistics.  We answer a couple here and are willing to answer others for you.  Click on the "Contact Us" tab above.  ?The list below has the topics for questions students ask:

Statistics Videos

Permutations or Combinations?

P-value

Hypothesis Testing

Hypothesis Testing (P-value Method)

Which Formula for Z-score

PERMUTATIONS OR COMBINATIONS?  WHICH IS IT?

Ian poses the question, "How do I decide if I should use the formula for the number of permutations or the number of combination?  For example, I had the following question in the homework:  On a test, a student is to answer 10 out of 13 questions.   How many ways can this be done?

Ian, that is a very good question.  Simply stated, a permutation is an order, an arrangement.  A combination is a set of objects, a collection of objects, without regard to order.  "Order" becomes the operative word.

Thus, the number of permutations of 13 items taken 10 at a time means the number of orders of 10 items taken from 13 items.  And the number of combinations of 13 items taken 10 at a time means the number of collections of 13 items we can form from 13 items.

In your example, the question is, does it matter which order the 10 questions are selected?  If order does, we use the number of permutation.  If order does not matter, we use the number of combinations.  The example by itself is unclear if we are to determine the number of orders or the number of sets of 10 questions we are to determine.

P-value

Anna wants to know, "My calculator keeps giving me P-value everytime I do a statistic test.  I do not know what that is.  Please help me."

Anna, The P-value is the probability of getting the test (sample) statistic or even a more extreme value as representing the sample data if the null hypothesis is true.  The statistic is in the direction of the alternate hypothesis if the null hypothesis is true.  On the normal curve, the P-value is the area beyond the test statistic.

WHICH Z-SCORE

Noah notes, "I have question deciding which Z-score formula to use."

Noah, that is a very common question.
The following formula is used to gain information about an individual data value from a population:

z = (x – μ) / (σ) This is the basic z-score formula.

The following formula is used to gain information about a sample mean, called a sampling distribution:

z = (x – μ) / (σ / √n) where the x used here is the sample mean.

HYPOTHESIS TESTING

Eric asks, "Just what is a hypothesis and what is hypothesis testing?  I am confused about what it is and why we do it."

Eric, thanks for asking.  First, a hypothesis is a claim about a population parameter: the population proportion, the population mean, or the population standard deviation.

Then, hypotheses testing is a decision-making process for testing the claim on the population.  The researcher defines the population, defines the hypotheses about the population, define the level of significance, select a sample from the population, conduct the test procedure. and make a conclusion.

HYPOTHESIS TESTING (P-VALUE METHOD)

Peter of Kalamazoo College says, "Can you simplify the procedure for hypothesis testing using the P-value method?"

Sure Peter.  Let us just go through these steps:

Step 1:State the null and alternate hypotheses and identify the claim you are making.

Step 2:Calculate your test value (Z-value).

Step 3:Determine the P-value corresponding to the Step 2 test value.

Step 4:Make decision to reject or not reject null hypothesis.

Step 5:Summarize the results in relation to the claim.

STATISTICS VIDEOS

Emma asks, "Are there good statistics videos?"

Emma, there are great statistics videos at Khan Academy.  Click on http://www.khanacademy.org/. Then scroll down the page to the following topics:

Statistics: Videos for a first course in statistics.

Probability: Probability examples you will meet in your statistics class.

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## Calculus Math Tutoring

There are common questions that students have in calculus.  We answer a couple here:

Calculus Videos

More Complicated Integrals

Basic Integral Tables

Help and More Practice

CALCULUS VIDEOS

Tyler asks, "I am visual.  How can I find great videos to help me understand calculus?"

That is a great question, Tyler.  Today, in my opinion, the best source is Khan Academy.  The website supplies a free online collection of lectures via video tutorials stored on YouTube.  Click on Khan Academy and click on "Subjects" at the top of the home page.  Highlight "Math" and click on your calculus at the right.  Almost every calculus topic is explained.  If you are looking for differential equations assistance, click on "Differential Equations".  Or you can type your topic in the search box at the right of "Subjects".  The videos are great and free!

CALCULUS INTEGRATION STRATEGY

Brittany asks, "How can I perform an integration when it is not one of the basic, familiar integral forms?"  Brittany, use one of the following options:

• Transform the integrand into one of the basic, familiar forms using substitution or other techniques.  You will need to know the forms in the table below.

• Look up an integral form in tables at the front or back of your calculus textbook or in a handbook such as The Handbook of Chemistry and Physics or CRC Standard Mathematical Tables and Formulae.

• Use a computer algebra systems (CAS) program such as Mathematica. Maple, or Derive.  Sometimes the CAS program cannot evaluate the integral or gives the result in an extremely complicated form.

• Use a computer algebra system (CAS) found on a graphing calculator such as the TI-89.

BASIC CALCULUS INTEGRATION FORMULAS

Sydney wants to know, "Which basic, fundamental integration formulas do I need to learn and why?"

Sydney, there are just a few.  When we have an integrand different from our basic form, then we use algebraic methods such as substitution to change our integrand to the basic form.  Thus, you need to know the basic forms so you can develop a strategy to obtain the basic form.

You ask, Do I need to learn all of the basic integration formulas in the table below.?  Sydney, the answer is "YES" if you want to master calculus and excel in your calculus class! CALCULUS HELP AND PRACTICE PROBLEMS

Aiden asks, “How can I get help with my calculus? And how can I have more calculus practice problems?”

Good question Aiden. A possibility is to go to https://www.ixl.com/math/calculus and then select your topic from the topics found on the page.

.

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## Pre Calculus Math Tutoring

There are common questions that students have in algebra.  We answer here a couple here on the following topics:

Factoring ax2 + bx + c

More Practice Problems

Precalculus Videos

More Practice Problems

I need more practice on problems. Where can I find more practice problems?

I have two suggestions.  The first is to go to http://www.kutasoftware.com/ and click on "Worksheets" at the top of the page.  Then scroll down the page and click on "Algebra 2 Worksheets".  Pick the topic you want and click on it.  Answers are included with the worksheets.  The second great suggestion is go to https://www.ixl.com/math/precalculus and click on the topic you want to practice.

Factoring ax2 + bx + c

My teacher taught us a method she called “guess and check” or “trial and error”. It is so confusing and I have trouble if the coefficients are big especially if the coefficient of the first term is other than 1. Do you know an easy way?

Yes, I do. We will use factoring by grouping sometimes called the“box method”.You will look at the factors of ac that add to b.Then factor by grouping or arrange the terms in a box and factor.It works ever time.

Let us look at an example:Factor 2x2 – 15x + 18.Notice a = 2, b = -15, and c = 18.

Step 1: Calculate ac = 36 where b = -15

Step 2:Find the factors of ac = 36.They are:

1 and 36
- 1 and - 36
2 and 18
- 2 and - 18
3 and 12
- 3 and - 12
4 and 9
- 4 and - 9

Step 3: The only pair that adds to – 15 is - 3 and – 12.Write the polynomial as 2x2 3x – 12x+ 18 .

Step 4: Factor by grouping: Put the first two terms in parentheses and the last two terms separated by a plus sign. ( 2x2 – 3x) + ( – 12x+ 18).

Factor a common factor out of the first grouping and a common factor from the last grouping:
x ( 2x – 3) + ( - 6) ( 2x - 3).(Notice we factored (- 6) from the last two terms.)

Do you want to try one?Factor 3x2 + 10x – 8 following the steps above.

Solution:The product of ac = -24 and the factors you should have selected were - 2 and 12.

The polynomial you will then factor by grouping is 3x2 – 2x + 12x – 8 .

Your solution after factoring by grouping is (3x – 2)(x + 4).

Precalculus Videos

Michael asks, "Are there good algebra review and pre calculus videos?"

Michael, there are great precalculus and algebra videos at Khan Academy.  Click on http://www.khanacademy.org/.  Click on "Subjects" at the top and highlight "Math" from the drop down menu.  Then highlight and click on one of the following topics at the right:

Precalculus: Videos of the more common precalculus topics students want help with.

Trigonometry: Includes videos of some basic trigonometric topics.

Algebra I: Sample problems worked from Algebra I.

Another option at Khan Academy is to type your topic in the Seach area to the right of the "Subjects" drop down button.

Michael, this is another great site: Go to www.ck12.org/  and click on "Trigonometry" or "Analysis" under Math.  There are great videos and great worked examples.

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## Trigonometry Math Tutoring

There are common questions that students have in algebra.  We answer here a couple here on the following topics:

Definition of Sine and Cosine Functions

Definition of Other Trigonometric Functions

Trigonometry Videos

DEFINITION OF SINE AND COSINE FUNCTIONS

Kendra asks, "I get so confused with the definitions of the trigonometric functions.  How are the trigonometry sine and cosine functions defined?"

Kendra, to answer the question, let us together do the following:

1. First make a coordinate plane by drawing a horizontal x-axis and then a vertical y-axis.  Let us name the origin point O (0,0)
2. Locate, that is plot, a point P (x,y) any place on the coordinate plane.  That can be in any quadrant.
3. Name the x-intercept point Q (x, 0).  That is, the point on the x-axis directly above or below point P (x,y) is Q (x, 0).
4. Now you have formed a right triangle OPQ with a right angle at point P.
5. Calculate the distance between point O and point P either by using the distance formula for the distance between point O and point P or using the Pythagorean Theorem.   Name that distance r where r is .
6. For  angle POQ, name the side PQ the opposite side, side OQ the adjacent side, and side OP the hypotenuse of the  right triangle.

Then we define the following:

sin POQ = y / r = length of the opposite side / hypotenuse.

cos POQ = x / r = length of the adjacent side / hypotenuse.

DEFINITION OF THE OTHER TRIGONOMETRIC EQUATIONS

Matt wants to know, "Is there an easy way to remember the definitions of the tangent, cotangent, secant and cosecants?"

My experience is first to learn the definitions of sine and cosine that I have above.  Then use the following definitions:

tan POQ = sin POQ / cos POQ  = y /x = length of the opposite side / length of the adjacent side

cot POQ = cos POQ / sin POQ = x /y = length of the adjacent side / length of the opposite side

sec POQ = 1 / cos POQ = r /x =  hypotenuse / length of the adjacent side

csc POQ = 1 / sin POQ = r /y =  hypotenuse / length of the opposite side

Trigonometry Videos

Cody asks, "Are there good algebra review and pre calculus videos?"

Cody, there are great precalculus and trigonometry videos at Khan Academy.  Click on http://www.khanacademy.org/. Then scroll down the page to the following topics:

Precalculus: Videos of the more common precalculus topics students want help with.

Algebra I Worked Examples: Sample problems worked from Algebra I.

Trigonometry: Includes videos of some basic trigonometric topics in your precalculus.

Linear Algebra: Includes great videos on matrices and vectors.

ck12.org Algebra I Examples:  Great review videos to make sure you understand Algebra I topics.

STILL NEED HELP?  Our tutors are here to help you.  Just contact us right now for help.  Either register and log in at the left or click on the Contact Tab at the top of the page!  BOOK YOUR FREE CONSULTATION RIGHT NOW!