This document provides strategies and tips for using a graphing calculator on the TAKS test, including: - Clearing the calculator memory if something goes wrong - Using the "y=" feature to match equations and graphs/tables - Setting the calculator table to "ASK" for specific x-values - Storing values in variables to match equivalent expressions - Using the "STO" key to represent variables in expressions - Clearing lists using "ClrAllLists" or highlighting and clearing - Using the "Calc" feature to find the intersection point of graphs - Converting between decimals and fractions - Ensuring proper use of parentheses with fractions and operations - Changing table settings for starting

1. TAKS Tutorial Calculator Strategies

2. 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

3. Know how to clear the memory of your calculator If something goes “funky” with the calculator, reset it. 2 nd , Memory (+), Reset (7), All RAM (1), Reset (2) 2 nd , +, 7, 1, 2

4. 2 nd + 7 2 1

5. Use the “y=“ to match equations with graphs and/or tables. The table below shows various values for x and y. 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 Enter the answer choices into the calculator through the “y=“ feature and then look at the tables to find a match. − 28 11 − 16 7 11 − 2 23 − 6 y x

6. 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 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 − 28 11 − 16 7 11 − 2 23 − 6 y x

7. 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. Then, one at a time, enter the domain values from the given table. The corresponding y-values come up automatically. − 28 11 − 16 7 11 − 2 23 − 6 y x

8. 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.

9. 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.

10. Which expression represents the area of a rectangle with sides measuring 2x 2 y 4 z units and 5xy 4 z 3 units? F. 7x 2 y 8 z 3 units 2 G. 7x 3 y 8 z 4 units 2 H. 10x 3 y 8 z 4 units 2 J. 10x 2 y 8 z 3 units 2 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.

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

12. The figure described is a rectangle. Draw and label one. 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) 2x 2 y 4 z 5xy 4 z 3

13. Now, you want to go to TEST (2 nd 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. 2x 2 y 4 z 5xy 4 z 3

14. 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. Since we have a “0”, answer choice F is not correct and we need to repeat this procedure using G. Option F is not the correct answer. Repeating the procedure does NOT mean that you have to retype everything! Press 2 nd ENTER.

15. Notice that the step above just reappears. Now, backspace until you get to the equal sign And type over the old choice with the new choice or delete the old choice and type in the new. ENTER Repeating the procedure does NOT mean that you have to retype everything! Press 2 nd ENTER. Another zero! Repeat with option H. 2 nd ENTER, backspace to the equal, type in option H, and ENTER. Looks like H is the answer. Repeat with J just to be sure!

16. Which expression represents the area of a rectangle with sides measuring 2x 2 y 4 z units and 5xy 4 z 3 units? F. 7x 2 y 8 z 3 units 2 G. 7x 3 y 8 z 4 units 2 H. 10x 3 y 8 z 4 units 2 J. 10x 2 y 8 z 3 units 2 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.

17. 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.

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

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

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

21. Tammy drew a floor plan for her kitchen as shown below. Which expression represents the area of Tammy’s kitchen floor in square units? F. 6x 2 + 30x + 5 G. 6x 2 + 13x + 5 H. 10x + 12 J. 5x + 6 Replace choice F in y 2 with choice G and graph. 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. (3x + 5) units (2x + 1) units

22. Use STATPLOT to compare points or scatter plots. Which point on the grid below best represents the coordinates ? , A. Point K B. Point M C. Point R D. Point U Press the STAT button. Select EDIT Enter 8/3 in L 1

23. Which point on the grid below best represents the coordinates ? , A. Point K B. Point M C. Point R D. Point U When you enter, the calculator will change the fraction into a decimal. Enter 7/3 into L 2 Set the window to the scale in the problem so you can make a good comparison. Go to STAT PLOT (2 nd y=) Enter and turn on the plot by entering again. You should see xlist: L 1 for the x-coordinate & ylist: L 2 for the y-coordinate. And graph. This point has an x-coordinate between 2 and 3. And a y-coordinate between 2 & 3.

24. To clear any numbers in a list, you may… Reset the calculator (2 nd + 7 1 2) which will also reset the window on the graph. 2 nd + 4 ClrAllLists Or while in the list, highlight the list name, press CLEAR, and enter. Do NOT delete!

25. 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.

26. You want to go to the CALC feature (2 nd 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. A. (2, 0) B. (0, 2) C . (0.5, 0) D . Not here Looking at the answer choices, the correct solution is not there.

27. 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

28. Know how to get back to the home screen. 2 nd QUIT will get you there

29. 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.

30. 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!

31. 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.

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

33. There are different settings you can use on the graphs Makes a regular line Makes a thicker line Makes a regular line and shades above the line Makes a regular line and shades below the line Shows where the graph goes and makes a regular line Shows where the graph goes but makes NO line Makes a dotted line These options come from backspacing and pressing ENTER

34. Practice Problems

35. There are several things you can do with these answer choices to eliminate a few so you won’t have to graph so many. 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.

36. 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.

37. 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.

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

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

40. 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.

41. 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.

42. 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!

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

44. 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.

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

46. There is only one variable in these expressions. Put the problem’s expression in y 1 and the answer choices, one-by-one, in y 2 . Remember, you want matching graphs. Allows me to watch as the graph is plotted. They matched! Check the others to be sure, though.

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

48. 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.

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

50. You now want TEST (2 nd 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

51. Press 2 nd 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

52. 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.

53. 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.

54. 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

55. 2 nd ENTER to get the previous operation. Backspace to the equal sign and enter the next answer choice. NOT B Not C, either

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

57. Let’s type the original function in y 1 and the answer choices, one at a time, in y 2 and see which parabola shifted UP 5 units.

58. Answer choices will have a thicker line Count the hash marks. The new graph shift up 8 units. Too high!

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

61. 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 3 rd space past 0 on the x-axis so its x-coordinate is ¾ . That means we are looking at options G and H.

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

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

64. 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.

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

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

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

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

69. 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

70. Alternate method Or we could use the graph and CALC features of the graphing calculator Enter the equation in y 1 and 104 in y 2 . Adjust the window — You need y max to be higher than 104 Graph You need to be able to see in the window where the two lines intersect. That place looks way off to the right. Adjust the window again. Let’s try the x max at 50.

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

72. 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 0

73. Remember, all past tutorials can be found on Mrs. Nelson’s website. There is a link to that site on the Spring High webpage. Your teachers will be ready to answer any questions you might have in class tomorrow and Monday. Come to take the test RESTED! Look at the posted roll sheets to see what day(s) you are testing and where.

74. We have confidence in YOU! You should have confidence in YOU! Remember, you only need to get a few more than half of the problems correct to pass this test! Do what you know how to do FIRST!