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**Calculator Strategies**

TAKS Tutorial Calculator Strategies

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**When it comes to the calculator, you are on your own…**

Most teachers who will monitor the test know absolutely nothing about these calculators Even if they did know about the calculator, they are not allowed to assist you in any way

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**Know how to clear the memory of your calculator**

If something goes “funky” with the calculator, reset it. 2nd, Memory (+), Reset (7), All RAM (1), Reset (2) 2nd, +, 7, 1, 2

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2nd 1 2

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**Use the “y=“ to match equations with graphs and/or tables.**

The table below shows various values for x and y. x y −6 23 −2 11 7 −16 −28 Enter the answer choices into the calculator through the “y=“ feature and then look at the tables to find a match. Which equation best describes the relationship between x and y? A. y = −3x + 5 B. y = −5x − 7 C. y = −x + 17 D. y = 3x + 41

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**Move the cursor to “Ask” for the Independent variable only**

If your table jumps around as the last one did and you do not wish to scroll You may set your table to “ASK” you for specific domain (x) values x y −6 23 −2 11 7 −16 −28 When “asking” it will not matter where the table starts or what the change in table is… Move the cursor to “Ask” for the Independent variable only

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**If your table jumps around as the last one did and you do not wish to scroll**

You may set your table to “ASK” you for specific domain (x) values Now, when you go to TABLE, you will not see anything except the cursor waiting for you to input an x-value. x y −6 23 −2 11 7 −16 −28 Then, one at a time, enter the domain values from the given table. The corresponding y-values come up automatically.

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**To put your calculator table back to the way it was, either reset or…**

Go back to TBLSET and put Auto back on for the Indpnt: variable.

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Use the “STO” key to store values for variables to match equivalent expressions with more than one variable. You will need to select numbers of your choosing to be the values for the variables in the expression. Please do NOT use 0, 1, or -1 as sometimes things are true of those numbers but not of anything else. Each variable should have a different value stored for it.

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Which expression represents the area of a rectangle with sides measuring 2x2y4z units and 5xy4z3 units? F. 7x2y8z3 units2 G. 7x3y8z4 units2 H. 10x3y8z4 units2 J. 10x2y8z3 units2 Select 3 different numbers to store for x, y, and z. Press the button for the first number, press the “STO” button, press the letter of the alphabet representing the variable, and then enter. Repeat this procedure for each variable.

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**Press the button for the first number,**

press the “STO” button, press the letter of the alphabet representing the variable, and then enter. Repeat this procedure for each variable.

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**The figure described is a rectangle. Draw and label one.**

2x2y4z 5xy4z3 The problem asked which expression represents the AREA. Area of a rectangle is length times width. (The formula is on the math chart.) You are going to enter into the home screen of your calculator the expressions found here for length times width: (2x^2y^4z)(5xy^4z^3)

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**Now, you want to go to TEST (2nd MATH)**

2x2y4z 5xy4z3 Now, you want to go to TEST (2nd MATH) Since you want the equal sign and it is already highlighted, press ENTER. Notice, the equal sign appears after your expression for area. And, one by one, type in the answer choices into the calculator just as they appear.

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**Option F is not the correct answer.**

If the answer choice has an expression that is EQUAL to the area expression, when you ENTER you will get “1” for an answer. If the answer choice has an expression that in NOT EQUAL to the area expression, when you ENTER you will get “0” for an answer. Option F is not the correct answer. Since we have a “0”, answer choice F is not correct and we need to repeat this procedure using G. Repeating the procedure does NOT mean that you have to retype everything! Press 2nd ENTER.

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**Repeating the procedure does NOT mean that you have to retype everything! Press 2nd ENTER.**

Notice that the step above just reappears. Now, backspace until you get to the equal sign Another zero! Repeat with option H. 2nd ENTER, backspace to the equal, type in option H, and ENTER. And type over the old choice with the new choice or delete the old choice and type in the new. Looks like H is the answer. Repeat with J just to be sure! ENTER

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Which expression represents the area of a rectangle with sides measuring 2x2y4z units and 5xy4z3 units? F. 7x2y8z3 units2 G. 7x3y8z4 units2 H. 10x3y8z4 units2 J. 10x2y8z3 units2 Sure enough, option H is the correct answer. Do you have to do ALL of this work? NO. If you know that 2 times 5 is 10, you could have eliminated entering in choices F and G. If you know the rules for when you add, subtract, and multiply exponents for same bases and trust your own memories and work, then make your selection.

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**This next problem could be done the same way as the last problem.**

However, since there is only one variable in this problem (instead of 3 as in the last one) there is another way we can work this one out on the calculator without having to use the STO and TEST keys.

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**Tammy drew a floor plan for her kitchen as shown below.**

(3x + 5) units (2x + 1) units Once again, this problem refers to AREA of the rectangular kitchen. We already know that means finding length times width. Which expression represents the area of Tammy’s kitchen floor in square units? F. 6x2 + 30x + 5 G. 6x2 + 13x + 5 H. 10x + 12 J. 5x + 6 The expression for Area, then, would be (3x + 5)(2x + 1)

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**Tammy drew a floor plan for her kitchen as shown below.**

(3x + 5) units (2x + 1) units But this time, we are going to use “y=“ instead of STO, since there is only the variable x used in the expressions. Which expression represents the area of Tammy’s kitchen floor in square units? F. 6x2 + 30x + 5 G. 6x2 + 13x + 5 H. 10x + 12 J. 5x + 6 Enter the expression (3x + 5)(2x + 1) in y1

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**Tammy drew a floor plan for her kitchen as shown below.**

(3x + 5) units (2x + 1) units One by one, enter the answer choices into y2. Then, graph. If both equations have exactly the same graph, the two expressions are equivalent and you found your correct answer. Which expression represents the area of Tammy’s kitchen floor in square units? F. 6x2 + 30x + 5 G. 6x2 + 13x + 5 H. 10x + 12 J. 5x + 6 Changing to this option allows you to follow along as the 2nd function is graphed. F is not the correct answer since the two graphs are different.

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**Tammy drew a floor plan for her kitchen as shown below.**

(3x + 5) units (2x + 1) units Replace choice F in y2 with choice G and graph. Which expression represents the area of Tammy’s kitchen floor in square units? F. 6x2 + 30x + 5 G. 6x2 + 13x + 5 H. 10x + 12 J. 5x + 6 Did you watch as the little circle made its way around the same parabola? Option G is the correct choice. To be safe, you can check options H & J. If you realize that those two options are linear (no seen exponents for x), their graphs could never be a parabola and thus are not correct answer choices.

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**Use STATPLOT to compare points or scatter plots.**

Which point on the grid below best represents the coordinates ? Press the STAT button. , A. Point K B. Point M C. Point R D. Point U Select EDIT Enter 8/3 in L1

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**Which point on the grid below best represents the coordinates ?**

Go to STAT PLOT (2nd y=) When you enter, the calculator will change the fraction into a decimal. Enter and turn on the plot by entering again. You should see xlist: L1 for the x-coordinate & ylist: L2 for the y-coordinate. , Enter 7/3 into L2 Set the window to the scale in the problem so you can make a good comparison. And graph. And a y-coordinate between 2 & 3. This point has an x-coordinate between 2 and 3. A. Point K B. Point M C. Point R D. Point U

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**To clear any numbers in a list, you may…**

Reset the calculator (2nd ) which will also reset the window on the graph. 2nd + 4 ClrAllLists Or while in the list, highlight the list name, press CLEAR, and enter. Do NOT delete!

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**Use the calculator to solve systems.**

If the system of linear equations 2x + y = 1 and y = − x + 1 are graphed on the same coordinate grid, which of the following is the solution to this system of linear equations? A. (2, 0) B. (0, 2) C. (0.5, 0) D. Not here 2x + y = 1 is not yet calculator friendly! Get the y by itself by subtracting 2x from each side. y = 1 – 2x Enter both equations using the y= feature. Graph. Adjust the window, if necessary to see the point of intersection.

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**You want to go to the CALC feature (2nd TRACE)**

Select intersect since that is what you are looking for. Since there is only 1 point of intersection, Enter when the calculator says “First curve?”, “Second curve?”, and “Guess” The coordinates of the point of intersection, which is the solution, are shown at the bottom of the window. (0, 1) is the point where these two lines intersect. Looking at the answer choices, the correct solution is not there. A. (2, 0) B. (0, 2) C. (0.5, 0) D. Not here

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**Know how to use the calculator to change decimals to fractions and vice-versa.**

Typing in a fraction and pressing ENTER automatically gives you a decimal. To get a fraction from a decimal, use the MATH button. The highlighted option is convert to Fraction Frac

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**Know how to get back to the home screen.**

2nd QUIT will get you there

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**Be sure to use parentheses when fractions are involved.**

must go into the calculator as y = (2 – 5x)/7 or else you will get the wrong graph! Check it out! The two lines are NOT the same.

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**where x = 4 MUST go into the calculator as (4 + 6)/(3•4-1)**

or else you will get the wrong answer. Check it out and see what happens when you don’t have the parentheses—both sets!

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**Know how to change your table settings.**

You set the number where you want the table to start You set the scale that you want the values in the table to go by You determine whether you want the table to be filled in automatically as you set it up or to have it wait for you to give it x-values to find.

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**Let’s use this equation**

Let’s use this equation. You will see different tables for this same function based upon how you set the table to appear. Starting with -3 and going by 1. Starting with -5 and going by 10. Starting with 2 and going by 0.1.

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**There are different settings you can use on the graphs**

Makes a thicker line Makes a regular line Makes a regular line and shades above the line Makes a regular line and shades below the line These options come from backspacing and pressing ENTER Shows where the graph goes and makes a regular line Makes a dotted line Shows where the graph goes but makes NO line

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Practice Problems

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The first thing you should notice is that all of the inequalities have 5 as the y-intercept and a negative slope and no equal sign. There are several things you can do with these answer choices to eliminate a few so you won’t have to graph so many.

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Then, whether you plan to use the graphing calculator or not, you need to know that when the inequality sign points to y, as in B and C, the shading is below the line. Since our shading is above the line, we can eliminate these two graphs.

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For the remaining two choices, you either need to count the slope, starting at the y-intercept or you test the x-intercept of 4 by substituting 4 in for x to see if you get y = 0 or use the calculator to graph and see if the x-intercept is 4. Since today’s tutorial is on calculator usage, that is the method we are going to use.

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**To be safe, fraction in ( ). The x-intercept is NOT 4. Wrong choice**

Shaded above To be safe, fraction in ( ). The x-intercept is NOT 4. Wrong choice

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**To be safe, fraction in ( ). **

Shaded above To be safe, fraction in ( ). The x-intercept IS 4. Choice D is verified.

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**This problem can be done a few ways, also**

This problem can be done a few ways, also. Remember, x-intercepts have y = 0, so you can substitute 0 for y and solve for x. Y-intercepts have x = 0, so you can substitute 0 for x and solve for y. Or you can graph. If you want to do the graphing by hand, remember that there is a blank sheet of graph paper at the end of the math section for you to use as you choose.

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**Since this tutorial is about using the calculator, that is the way we are going to do this problem.**

The given equation is not calculator friendly. We need to put the equation in y = form. Remember, there is an understood -1 in front of y, due to the subtraction sign. You do NOT have to put the equation in slope-intercept form, just calculator friendly form. The calculator will do the rest.

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2x – y = 8 is 2x – 1y = 8. Subtracting 2x, we get -1y = 8 – 2x Then, dividing by -1, we get the calculator friendly form y = (8 – 2x)/-1 You absolutely MUST have the parentheses around the numerator!

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**Let’s eliminate the y-intercept choices.**

The x-intercept appears to be 4 The y-intercept is negative. We have no choices with negatives. Let’s eliminate the y-intercept choices.

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You can either substitute the r-values, by hand or on the calculator home screen, one-by-one to make sure that you get the corresponding n-values. And yes, you must check all of them until you find a value that does not work. Or, you can type the answer choices in y = and match the table of values. Let n = y and r = x, and you will be just fine.

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**ALL 4 of the ordered pairs match. This is the one!**

Not answer choice B Not answer choice A ALL 4 of the ordered pairs match. This is the one!

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**Allows me to watch as the graph is plotted.**

There is only one variable in these expressions. Put the problem’s expression in y1 and the answer choices, one-by-one, in y2. Remember, you want matching graphs. They matched! Check the others to be sure, though. Allows me to watch as the graph is plotted.

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**Definitely not this one, either**

Definitely not this one, either. Looks like F is the correct answer choice. Doesn’t look like it, but let’s adjust the window. NOPE NO

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**These expressions have more than 1 variable**

These expressions have more than 1 variable. We want to store a number into the calculator for each of these variables and use the TEST feature. Remember, you pick whatever numbers you want, except 0, 1, or -1.

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**Type in the expression for the problem. BE CAREFUL**

Type in the expression for the problem. BE CAREFUL! You need extra parentheses around the entire numerator and around the entire denominator.

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**Remember, when you get a zero, the two expressions are NOT EQUAL**

You now want TEST (2nd MATH) and enter to get the equal sign. Now, type in your answer choices, one at a time. Again, extra parentheses around the numerator and the denominator. Remember, when you get a zero, the two expressions are NOT EQUAL

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**We have a 1. That means the two expression ARE EQUAL**

Press 2nd ENTER to get the last step again. Backspace to the equal sign and either delete or type over the old option. We have a 1. That means the two expression ARE EQUAL

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Verify that the two remaining answer choices are NOT EQUAL before you select G as the correct answer. Be careful that you correctly type in all expressions! Remember to put those extra parentheses around both the numerator and the denominator.

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Since these problems are kind of complicated to do on the calculator and since you probably haven’t used this procedure very much, here is another problem. You can either use those same 3 values that you already have stored in for a, b, and c, or you can change them.

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Remember, correctly type in the expression from the problem, using an extra set of parentheses around both the numerator and the denominator. Then, go to TEST, select the equal sign, and type in the answer choices, one at a time. Extra parentheses are needed around entire numerators and entire denominators. NOT A

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**2nd ENTER to get the previous operation**

2nd ENTER to get the previous operation. Backspace to the equal sign and enter the next answer choice. NOT B Not C, either

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**If this graph is shifted UP, the y-intercept/vertex should be higher**

If this graph is shifted UP, the y-intercept/vertex should be higher. Logically, you should eliminate J because -8 is lower than -3.

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Let’s type the original function in y1 and the answer choices, one at a time, in y2 and see which parabola shifted UP 5 units.

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**Count the hash marks. The new graph shift up 8 units. Too high!**

Answer choices will have a thicker line

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**Count the hash marks. The new graph shift up 5 units. This is it!**

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If you count, you can see that between 0 and 1, there are 4 spaces—on each axis. That means that the grid is divided into fourths. T is located on the 3rd space past 0 on the x-axis so its x-coordinate is ¾ . That means we are looking at options G and H.

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T is located on the 5rd space below 0 on the y-axis so its y-coordinate is -5/4 . That means the correct option is G.

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**Adjust the window on your calculator to match the scale here**

Adjust the window on your calculator to match the scale here. You are going from to 2.5 by ¼ or .25 on each axis. Now, if you have no clue about these points, you will want to use the STAT button on your calculator.

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**Recall, when you enter fractions into the calculator, they are changed into decimal form.**

Be sure that the STAT PLOT is turned on with the proper lists.

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**This point is way too low to be point T.**

And then graph. This point is way too low to be point T.

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**This point looks better. Count.**

5 below zero Try again. 3 to the right of zero This point looks better. Count. 5 below zero 3 to the right of zero

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**We are looking for C when they have given us F.**

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**We can solve this equation the “traditional” way—using the “undo” process.**

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Alternate method We can solve this equation by using the table feature of the graphing calculator. Enter the equation. Go to the table. Scroll down the table until you find 104 in the y-column

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Alternate method You need to be able to see in the window where the two lines intersect. That place looks way off to the right. Or we could use the graph and CALC features of the graphing calculator Enter the equation in y1 and 104 in y2. Adjust the window again. Let’s try the xmax at 50. Adjust the window — You need ymax to be higher than 104 Graph

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Alternate method Press 2nd TRACE so that you get CALC. Now, select Intersect. Move the cursor to be close to the point of intersection. Enter again for the second curve? And guess?

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**This problem was NOT multiple choice**

This problem was NOT multiple choice. You have to bubble in your answer correctly! Be careful!!! After going through all that work to get the correct answer, you don’t want the problem to be scored as wrong because you didn’t bubble in the answer properly! 4

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