# Distance, Midpoint, and Slope

### This week’s topic has been Distance, Midpoint, and Slope.

Let’s go through that blue SAT book everyone has, http://amzn.to/1wADKLS, or http://amzn.to/1wtPZuD, and this ACT book for problems about distance, midpoint, and slope that can be solved using my TI-84 Plus programs DISTANCE. Sorry, I won’t post the actual problems here.  But go dig out your books and calculator (buy them here: SAT, ACT , TI-84 Plus) and follow along.

## SAT book

ISBN-13: 9780874478525.  The page numbers included here are from that book, but if you have the other one (9780874479799), please refer to the Test number and Section number instead.

Test 1, Section 3, p. 397, problem # 6

Test 1, Section 3, p. 400, problem #15

Test 3, Section 8, p. 546, problem #10

Test 4, Section 6, p. 596, problem #10

Test 5, Section 8, p. 669, problem #8

Test 7, Section 3, p. 769, problem #4

Test 8, Section 3, p. 830, problem #2

Test 9, Section 5, p. 905, problem #8

Test 10, Section 2, p. 953, problem #17

## ACT book

I’m working out of an older edition that only has 3 tests.  I believe they are the same as the first 3 tests of the 2nd and 3rd editions.  Once I have the newer book, I’ll add to this list.

Test 1, Section 2, problems #35, 45

Test 2, Section 2, problem #33

Test 3, Section 2, problems #38, 48

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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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Algebraic solution by hand:

Use the slope formula:

Solution using my TI-84 Plus program DISTANCE:

Run DISTANCEHow?

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.

Lorem ipsum dolor sit amet, consectetur adipisicing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat.

# 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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Solution by hand:

Use the distance formula:

Solution using my TI-84 Plus program DISTANCE:

Draw a picture:

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

Run DISTANCEHow?

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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# Ratios and Proportions

### This week’s topic has been Ratios and Proportions.

Let’s go through that blue SAT book everyone has, http://amzn.to/1wADKLS, or http://amzn.to/1wtPZuD, and this ACT book for problems about ratios that can be solved using my TI-84 Plus programs RATIO and PROPORTN.  (See these posts for examples: 10/27, 10/28, 10/29, 10/30)

Sorry, I won’t post the actual problems here.  But go dig out your books and calculator (buy them here: SAT, ACT , TI-84 Plus) and follow along.

## SAT book

ISBN-13: 9780874478525.  The page numbers included here are from that book, but if you have the other one (9780874479799), please refer to the Test number and Section number instead.

Test 1, Section 7, p. 417, problem # 13

Test 4, Section 6, p. 594, problem #6

Test 10, Section 2, p. 953, problem #16

Test 10, Section 8, p. 980, problem #12

Math Multiple-Choice Sample Questions, p. 307, problem #6

Math Student-Produced Response Sample Questions, p. 347, problem #1

Test 1, Section 7, p. 417, problems # 11, 13

Test 2, Section 2, p. 452, problem #2

Test 3, Section 5, p. 528, problem #9

Test 3, Section 8, p. 543, problem #1

Test 4, Section 3, p. 583, problem #6

Test 5, Section 2, p. 639, problem #5

Test 6, Section 4, p. 715, problem #10

Test 7, Section 3, p. 768, problem #1

Test 9, Section 8, p. 916, problem #4

Test 9, Section 8, p. 918, problem #11

Test 10, Section 2, p. 950, problem #7

## ACT book

I’m working out of an older edition that only has 3 tests.  I believe they are the same as the first 3 tests of the 2nd and 3rd editions.  Once I have the newer book, I’ll add to this list.

Test 2, Section 2, problem #15

Test 1, Section 2, problems #19, 39, 44

Test 2, Section 2, problems #3

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# Ratios

Q: Last month, the ratio of sunny days to rainy days was 3:2.  How many rainy days  were there last month, if the month had 30 days?  (Assume all days were either sunny or rainy.)

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Solution by hand:

Number of sunny days = 3x

Number of rainy days = 2x

3x + 2x = 30

5x=30

x = 6

There were 2x rainy days, so there were 12 rainy days.

Solution using my TI-84 Plus Program RATIO:

Run RATIOHow?

Total number of items (days) = 30

Number of categories of items = 2  (sunny and rainy)

Ratio part for category 1 (sunny) = 3

Ratio part for category 2 (rainy) = 2

Distribution is: sunny = 18 and rainy = 12.

Lorem ipsum dolor sit amet, consectetur adipisicing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat.

# Proportions

### Q:  x is inversely proportional to w.  If x = 6 when w = 8, what is x when w = 12?

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Solution by hand:

For inverse proportions, (x1)(w1) = (x2)(w2)

(6)(8) = (x)(12)

48 = 12x

x=4

Solution using my TI-84 Plus Program PROPORTN:

Run PROPORTN.  How?

x1 = 6

y1 = 8  (here, we have renamed w1 as y1)

Have y2 (really w2)

y2 = 12

Choose ‘Inverse’ proportion.

Then, x2 = 4.

Lorem ipsum dolor sit amet, consectetur adipisicing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat.

# Proportions

### Q:  Wandering around blindly in a parking lot (don’t try it, please), the probability that the first car you bump into is blue is 2/5.  If there are 500 blue cars, how many cars are in the parking lot?

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Solution by hand:

Set up the proportion using the concept ‘blue / total = blue / total’:

2/5 = 500/x

2x = 2500

x = 1250

Solution using my TI-84 Plus Program PROPORTN:

Run PROPORTN.  How?

x1 = 2  (blue)

y1 = 5  (total)

Have x2 (blue)

x2 = 500

Choose ‘Direct’ proportion (because it doesn’t say ‘inverse’ in the problem).

Then, y2 (the total) = 1250.

Lorem ipsum dolor sit amet, consectetur adipisicing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat.

# 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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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 RATIOHow?

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.

Lorem ipsum dolor sit amet, consectetur adipisicing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat.

# 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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# 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!!)