Kirk's Tutoring Blog

First we need to ask ourselves, what are we trying to accomplish.

Ideally, if you have prepared well, the last 24-48 hours should be dedicated to adequate rest. However the world isn't quite a perfect sphere, and we do not always have the perfect situation. If you haven't fully study yet, the volume of material to cover in these last 24-48 hours may be too much, therefore we need a survey strategy. The following works best for computational subjects such as math, physics, chemistry or disciplines such as engineering.

If this is a college prep/standardized test, take the practice test again...

The summer months are all but gone, withered into a faded memory, like an old black and white photo. Lets hope that it was as enjoyable as it was productive. Its time to turn a new leaf in the chapter of life. New challenges, new faces, new subjects and more tests. So what did you do in the summer to keep motivated, or practice new habits?

Here are my suggestions to staying motivated throughout the summer.
* Read a new book/s.
* Volunteer.
* Apply the knowledge gained through the school year to a project that you wanted to do but never completed.
* Research something you were interested...

Proof techniques are fun. They are mathematical arguments of sufficiency. The feeling you get from arguing your point logically to completion is always exhilarating. Let us put our mathematical reasoning power to the test. Now since this is our first of many proof techniques. I will start with something elementary.

1. Prove the following:

(a) Given that the average of y and z is odd, then z is an odd integer when y is odd.

When doing proofs  it is best to do so in algebraic and generalized form. A way to represent all possible cases. Using only examples would be trivial, since we know...

Students often ask me how do Mathematicians come up with various formulas in Trigonometry, Algebra and Calculus? By method of Proofs and Derivation I would exclaim, which in my opinion is becoming a lost art. I found deriving formulas helped to seal the understanding of the concepts and theories in Math. I believe it is thus fitting as an end to our talk on polynomials, to derive the equation of the quadratic formula. We will do so by using the last method we discussed, "Completing the Square".

Remember the standard form for the quadratic equation reads:

f(x) = ax^2 + bx + c

To find the roots...

It has been a while since my last post, but as promised I am back. Recently a reader of one of my blogs commented on how helpful they were in helping her explain a concept to her HS Junior. I was indeed very glad to hear. It certainly is an encouragement to see parents, not only sign their child up for tutoring but also willing to follow through the covered material as well. Expanding on the purpose of the blog page, would be a forum board where students/parents can post short questions and have tutor respond and perhaps even have their answers rated on helpfulness. This I believe would make...

Vertical Shifts:

Let f be a function and c a positive real number.
* The graph of y = f (x) + c is the graph of y = f (x) shifted c units vertically upward.
* The graph of y = f (x) – c is the graph of y = f (x) shifted c units vertically downward.

Horizontal Shifts:
Let f be a function and c a positive real number.
* The graph of y = f (x + c) is the graph of y = f (x) shifted to the left c units.
* The graph of y = f (x - c) is the graph of y = f (x) shifted to the right c units.

Reflection about the x-Axis:
* The graph of y = - f (x) is the graph of y = f(x) reflected about the x-axis.

A student got 50% of the questions on an algebra test correct. If he answered 10 out of the first 12 questions asked correctly but missed 3/4 of the remaining questions, how many questions were on the test?

So algebraically we need to setup an equation here. The sum of the 10 correctly answered questions and the remaining questions that were answered correctly divided by the total number of questions is 0.5. Let y represent the number of remaining questions answered correctly. Let x represent the number of questions in total. Then;

10/x + y/x = 0.5
10 +...

Studying Strategy

We have reviewing the six pillars of a good study habits, skills and strategies. Now I will talk about basic study techniques in assimilating the material. There are many self help books on how to study but to be honest the approach could vary based on the individuals learning abilities, the subject content at hand as well as the intent of the study session. There is no one size fits all approach. Studying is a discipline and as such, do start early, make a commitment at the beginning of the semester/the school year. Don’t wait until it is too late and be overwhelmed with...

Tutor's Guide to Proper Study Skills, Habits and Strategies

Throughout the school year I have worked with several students from diverse economic and social backgrounds. In the sessions I had the chance to observe their study habits, their improvements and successes. From these observations I gathered some interesting and useful information that I believe will help others avoid the pitfalls of bad study habits, ill preparation and last minute cramming for tests/exams. These suggestions may be self evident but if followed will contribute to improvement in learning, retention, and finally the...

Today I was working with a student preparing him for the upcoming SAT in June. We came across an interesting question, which I will share with everyone here. Here is the question:

(Q) There is a number ‘WXYZ’, (where W,X,Y and Z are integers), such that

x = w + y + z [equation(1)]

w = y + 1 [equation(2)]

z = w – 5 [equation(3)]

Find this number ‘WXYZ’?

In order to solve a system of equations involving four unknowns, we need four equations (relationships). We are only given three relationships, "Houston we have a problem." Do not worry, we have another approach. Let us find x in terms of...