Category Archives: TI-83 Plus

11.20.14
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How to use the TI-84 Plus on the SAT for graphing!

SAT Official Question of the Day for 11/18, but do it MY WAY!

2014-11-21_000219
See the question here: 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

 

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11.07.14
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Slope

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?

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Answer: -7

Algebraic solution by hand:

Use the slope formula:

 

2014-11-07_153414

Solution using my TI-84 Plus program DISTANCE:

Run DISTANCE.  How?

Use your multiple choice answer choices.  One of them is -7.  (If you don’t have choices, draw a picture.  Plot the point (-1,-3) and do a slope of -1/2 from there – down 1, right 2, down 1, right 2, … until you get to a point where x is 7.  Read the y-value of that point – it will be -7 and check it using this program.)

x1=-1

y1=-3

x2=7

y2=-7

Ignore the distance information – we don’t need it for this problem.  Press ENTER for the midpoint information, which we don’t need either.  Press ENTER once more to find that the slope is -1/2.

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11.06.14
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Distance

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

Q:  For what value(s) of x is the point (x,4) exactly 5 units away from the point (6,8)?

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Answer: 3 or 9

Solution by hand:

Use the distance formula:

distance

Solution using my TI-84 Plus program DISTANCE:

Draw a picture:

distgraph

Guess that x=2, maybe.  It’s probably an integer if this is an SAT problem.  Use the answer choices if available.

Run DISTANCE.  How?

x1=2

y1=4

x2=6

y2=8

The distance is 5.66.  It’s too big – you wanted it to be 5 – so move the point a little closer to the middle.

Maybe x=3:

x1=3

y1=4

x2=6

y2=8

The distance is exactly 5.  Perfect.  (There’s also another possible answer, x=9.  If you have multiple choice answers, you will see 3 and 9 as a choice, so try both and see that they both work.  For a grid-in SAT problem, you would only have to find one answer anyway.)           :

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10.27.14
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Ratios

Q:  The ratio of blue cars to non-blue cars in the parking lot is 2:7.  If there are 1260 cars in the parking lot, how many are blue?

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Answer: 280

Solution by hand:

Number of blue cars = 2x

Number of non-blue cars = 7x

2x + 7x = 1260

9x=1260

x = 140

There are 2x blue cars, so there are 280 blue cars.

 

Solution using my TI-84 Plus Program RATIO:

Run RATIO.  How?

Total number of items = 1260

Number of categories of items = 2  (blue and non-blue)

Ratio part for category 1 (blue) = 2

Ratio part for category 2 (non-blue) = 7

Distribution is: blue = 280 and non-blue = 980.

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10.26.14
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TI-84 Plus Programs

My TI-84 Plus programs are now available here.  Instructions and examples for each of the 40 programs are there so you can learn how and when to use them.  I’m in the process of cross-indexing them with the problems posted here.  Check back often and ask me questions!

You know that SAT book everyone has?  The blue one:  This one, or this one.  I’m about to start going through it page by page, pointing out the problems that can be solved using my programs.  Stay tuned!

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10.11.14
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Get a TI-84 Plus Calculator!!

The BEST thing you can do to improve your SAT or ACT Math score is to get the TI-84 Plus calculator… and load it up with my programs.

It’s only $108 today on Amazon, with free shipping! This is the best deal I’ve seen. By comparison, Walmart has it for $119.27. Get it now: http://amzn.to/1vUA1IP

The TI-84 Plus is a great help to anyone taking the SAT or ACT. I have dozens of programs that will solve many typical problems in mere seconds. I can transfer these programs to your TI-84 Plus if you come to my office. BUT very soon they will be available for download on my website, with instructions and examples, so stay tuned!

By the way, there is no need to get any of the other fancier versions of this calculator. They won’t help you any more than this one does. But if you do want a certain color, well here are the other options:  http://amzn.to/1yi4bKd

(Yes, the TI-83 Plus is compatible with the programs, too, so that’s another option as listed in the above link, but the USB cable must be purchased separately.)

If all you need is the USB cable, here it is:

USB cable for  TI-84 Plus: http://amzn.to/1xAchur

USB cable for TI-83 Plus: http://amzn.to/1qAmCRx (Don’t buy the one above if you have the 83!!)

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09.12.14
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ACT, Geometry – diagonal of a rectangular prism

Q: What is the (straight-line) distance between points A and B on the figure below?

rectangularprism2

Answer:  7

Explanation:  We are finding the length of the green segment below:

 

rectangularprism2wline

This requires the three-dimensional version of the distance formula:

  2014-09-12_225150

There is another way to do this, using a progression of two right triangles, with the green segment being the hypotenuse of the second triangle, but I find the above formula much simpler.  It is just an extension of the ‘usual’ (2-dimensional) distance formula we are so familiar with from Algebra and Geometry.

BUT if you want an even easier way, and I know you do, use my TI-84 Plus program ‘DIST3D’.

 

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09.10.14
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Algebra 1 – Find the equation of a line

Q: If the slope of the line through (-3,6) and (1,y) is 1/2, what is the value of y?

Answer:  8

Explanation: Slope is computed by the formula (y2 – y1) / (x2 – x1) … the change in y divided by the change in x.

So,

(y – 6) / (1 – -3) = 1 / 2

(y – 6) / 4 = 1 / 2

Multiply both sides by 4 and you have:

y – 6 = 2

y = 8

BUT, if you’re taking a test and having trouble remembering the method above, try this instead: Plot the point (-3,6) on a graph and move from that point with a slope of 1/2. Move up 1, right 2, up1, right 2… and repeat this pattern until your x-value is 1. Then, read the y-value at the same point. This is not my favorite way, but it works!

And one more thing!  If this were a multiple choice question, you could use my TI-84 Plus program ‘DISTANCE’ (which finds distance, midpoint, and slope for any two ordered pairs).  Substitute one of the answer choices for x, and see if the program reports that slope is 1/2.

 

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09.10.14
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SAT – Counting and Ordering

Q:  20 students are to choose a president and vice president from among themselves. How many possible ways can they be chosen?

Answer:  380

Explanation 1:  Using the Counting Principle, set up two blanks to represent the president and vice president, from left to right:

____    ____

There are 20 choices for the president.  Put 20 in the first blank:

_20_    ____

The same person cannot be chosen for both positions, so there are 19 left to choose from for the vice president.  Put 19 in the second blank:

_20_    _19_

Now, multiply these numbers.  20 x 19 = 380.

Explanation 2:  This is a permutation problem since you are choosing 2 people from a total of 20 people, and the order is important.  The order is important because the two people chosen must be given specific positions, and switching those positions results in a different scenario.  Do  20 nPr 2 , or use the formula for nPr.  On the TI-84 Plus, find nPr in MATH-PRB-2.  The result is 380.

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09.07.14
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SAT – number properties

Q: What is the sum of all of the integers from 1 to 100?

Answer: 5050

Explanation: Don’t add 1 + 2 + 3 + 4 + … all the way up to 100! While it will work, it is a giant waste of time. Look for a pattern of numbers to pair up:

 1 + 99 = 100

2 + 98 = 100

3 + 97 = 100

…

49 + 51 = 100

 That’s 49 one hundreds. 49×100 = 4900. Now, add the numbers we have not counted yet: 100 and 50.

4900 + 100 + 50 = 5050.

 My TI-84 Plus program ‘SUMATOB’ will find this sum, too.

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