MathPro Tutoring

05/21/2017

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02/02/2017

Young women! Embrace math and science. Our future depends on your unique perspective.

Maryam Mirzakhani, an Iranian mathematician, just became the first woman ever to win the prestigious Fields Medal.

08/21/2015

SAT Question of the Day from the College Board on 8/8, but do it MY WAY!

For every 10 dollars Ken earns mowing lawns, he gives 3 dollars to his younger brother, Tim, who helps him. Which of the following gives the relationship between d, the number of dollars Ken earns, and t, the number of dollars he gives to Tim?

https://sat.collegeboard.org/practice/sat-question-of-the-day?questionId=20150808&oq=1

The explanation there is surprisingly simple, but I have something even better...

Just choose convenient numbers for d and t. The easiest ones are d=10 and t=3, meaning Ken earns 10 dollars and gives 3 to Tim. The only choice that is true with these values for d and t is:

(B) d = 10t/3 ...... 10 = 30/3

If more than one choice is true, try different numbers in the same ratio, like d-20 and t=6.

Can you answer today's SAT question? Tease your brain with real SAT questions and SAT preparation materials from the test maker.

08/18/2015

Please 'like' if you see this post, so that I know you're there. Thanks!

Another one... It's SAT season again! From the College Board, the SAT Official Question of the Day from 8/11:

If Kelly buys t pens priced at 2 dollars each and u pens priced at 4 dollars each, which of the following expresses, in terms of t and u, the average (arithmetic mean) price, in dollars, of these pens?

Look at the choices: https://sat.collegeboard.org/practice/sat-question-of-the-day?questionId=20150811&oq=1, and choose one to see a complicated yet correct explanation. Then Do IT MY WAY!

Put in some convenient numbers for t and u. I'm choosing t=7 and u=3. Now, the question becomes:

If Kelly buys 7 pens priced at 2 dollars each and 3 pens priced at 4 dollars each, which (blah blah blah) is the average (arithmetic mean) price, in dollars, of these pens?

We need to find the average price of 10 pens. Find the total price and divide by the number of pens.

The first 7 cost $2 each. 7x2 = $14
The other 3 cost $4 each. 3x4 = $12
$14 + $12 = $26 total.
7 + 3 = 10 pens

The average price is $26/10 = $2.60, or 2.6 dollars.

Find the choice that equals 2.6 when t=7 and u=3 (the numbers we chose earlier):

A) (3*7+3*3)/(7+3) = 30/10 = 3. Wrong.
B) (3*7+3*3)/(7*3) = 30/21 = 1.42... Wrong.
C) (3*7*3)/(7+3) = 63/10 = 6.3. Wrong.
D) (2*7+4*3)/(7+3) = 26/10 = 2.6. Right!.. but just to be sure it wasn't a coincidence due to the numbers we chose, try the rest to see that only one is equal to 2.6 ...
E) (2*7+4*3)/(7*3) = 26/21 = 1.23... Wrong.

To save time, only consider the choices with a denominator of 10, since we divided by 10 in the calculation above. That would eliminate B and E right away.

Please 'like' if you see this post, so that I know you're there. Thanks!

12/03/2014

SAT Official Question of the Day: "On the last day of a one-week sale, customers numbered 149 through 201 were waited on. How many customers were waited on that day?"

See the explanation here: http://sat.collegeboard.org/practice/sat-question-of-the-day?questionId=20141203&tq=1 It's exactly the explanation I would have given.

The answer is 53. Why? 201 - 149 = 52, right? So, why isn't it 52? I'll get to that, but first let's see why you should NOT choose 52, even if you don't know what the right answer is. Because it's TOO EASY! This test, the SAT, is a test you take to get into COLLEGE, not 3rd grade! Do you really think there would be a question on the SAT for which you just had to subtract the two numbers? No. So, in this case, the best strategy is to eliminate the answer that is 'too easy'.

So then, why do we add 1 to obtain 53? Consider that this question is really: 'How many integers are there from 149 to 201?' You don't really want to count them all, and you know that 201 - 149 is 'too easy'. Let's make this into a simpler question, so we can find a rule:

How many integers are there from 3 to 6? Count them: {3, 4, 5, 6}. There are four integers. Yes, 6 - 3 = 3, but this only counts the spaces between the numbers. You also need to count either the first or last number, which has not yet been included. That's the reason for the 'plus one'.

Now, generalize. For integers a and b, there are are (b - a + 1) integers from a to b, inclusive.

Apply it to the current problem, and your answer is 201 - 149 + 1 = 53.

And NOW, you will get *every* problem like this one correct from now on.

Can you answer today's SAT question? Tease your brain with real SAT questions and SAT preparation materials from the test maker.

11/30/2014

When the 'like' count on this page hits 300, I'm going to give away a free lesson to one lucky fan right HERE! (You don't even have to be local - I do online tutoring, too.) So, share me with your friends! www.facebook.com/mathprotutoring.

(Find lots more information here: www.mathprotutoring.com)

Click 'share' at the bottom of this or any post. Add your own comment to let your friends know to (first) *go to the page*, then 'like' the page! Thank you!

Math tutoring by Linda Sinclair: Algebra through Calculus, SAT, ACT, TI-84 Plus Training, and much more!

11/26/2014

SAT Official Question of the Day for 11/24, but once again, do it MY WAY!
http://sat.collegeboard.org/practice/sat-question-of-the-day?questionId=20141124&oq=1 The solution given on the SAT site (look at it, please) requires you to remember what absolute value inequalities really mean, and how to create one backwards from the solution. What if you don't remember?? DO IT MY WAY!!!!!!

Choose a value for d. d is between 6 and 10 (including 6 and 10). The correct answer is just another inequality that is equivalent to the one given in the question. So, any value between and including 6 and 10 will make the correct answer also true.

One possible value for d is 6. Plug d=6 into all the choices and cross out the ones that are not true.

When d=6,

(A) becomes 0

11/23/2014

Do this SAT Question of the Day MY WAY! http://sat.collegeboard.org/practice/sat-question-of-the-day?questionId=20141121&oq=1 The explanation given on the SAT site (look please!) is a good one, but ONLY if you would have thought of it! That's the way your Algebra teacher wants you to do the problem. But DON'T SKIP IT! Do it MY WAY!

Q: A woman drove to work at an average speed of 40 miles per hour and returned along the same route at 30 miles per hour. If her total traveling time was 1 hour, what was the total number of miles in the round trip?

There's always a way to get rid of a choice or two. Let's look...

(A) 30
(B) 30 1/7
(C) 34 2/7
(D) 35
(E) 40

Is it 30? No. Driving a distance of 30 miles in a total of 1 hour would give an overall average speed of 30 miles per hour. 30 mi/hr is the average speed for the second part of the trip, but the speed for the first part is 40 mi/hr. So, the overall average speed would be somewhere between 30 and 40, and therefore the number of miles would be between 30 and 40. (We're talking about 1 hour, so the speeds and the distances will be the same numbers.) Cross out choice (A). Also cross out choice (E) for the same reason.

You're down to three choices. At this point if you just guessed, you stand to gain more than you would lose. But you can do even better.

The (wrong) answer they want you to fall for is (D). It's too easy. It's not just the average of 30 and 40, since the times spent at 30 vs 40 miles per hour are different. Cross out choice (D).

Two choices left. You were convinced above that 30 was the wrong answer. 30 1/7 is too close to 30 to make that big of a difference. The extra 1/7 of a mile wouldn't be enough to raise the average speed to 40 for the first part of the trip. Cross out choice (B).

Done. The answer is C.

11/21/2014

SAT Official Question of the Day for 11/18, but do it MY WAY! http://sat.collegeboard.org/practice/sat-question-of-the-day?questionId=20141118&oq=1 The solution given on the SAT site (look at it, please) is soooo much harder than doing THIS! Go get your graphing calculator and read on...

Look at the choices:
a) -8
b) -4
c) 4
d) 8
e) 10

Try one. How about -8? So, we assume b = -8. Press 'Y=' on your TI-84 Plus (top left). Type into Y1: -2x^2-8x+5. That's the function you get if you substitute -8 for b. Now press GRAPH (top right). (Do 'ZOOM-6' if you need a better picture.) What is the x-value of the highest point? It looks like about -2. The question says it should be 2. So, it's not choice (a).

Try the next one: -4. Change Y1 (just type 4 over the 8), and press GRAPH again. This time it looks like the highest point is at x=-1. Still not right. It's not choice (b).

Try 8. Change Y1 (just type +8 over the -4), and press GRAPH again. This time it looks like the highest point is at x=2. Choice (d) is correct.

And *THIS* is why I tell all of you to get the TI-84 Plus Graphing Calculator! Get one now: http://amzn.to/1tXyOTH

11/18/2014

Students taking the SAT or ACT: Use my TI-84 Plus program DISTANCE for these problems from your prep books:
http://wp.me/p54iav-5T

11/07/2014

This week's topic is: Distance, Midpoint, and Slope.

Q: The slope of the line passing through (-1,-3) and (7,y) is -1/2. What is the value of y?