Calculator Strategies
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Calculator Strategies

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Calculator Strategies Calculator Strategies Presentation Transcript

  • TAKS TutorialCalculator Strategies
  • 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
  • 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
  • 2nd + 712
  • Use the “y=“ to match equations with graphs and/or tables.The table below shows various values for x and y. x y Enter the answer choices into −6 23 the calculator through the “y=“ −2 11 feature and then look at the 7 −16 tables to find a match. 11 −28Which equation best describes therelationship between x and y?A. y = −3x + 5B. y = −5x − 7C. y = −x + 17D. y = 3x + 41
  • If your table jumps around as the lastone did and you do not wish to scroll• You may set your table to “ASK” you for specific domain (x) values x y When “asking” it will not matter −6 23 where the table starts or what the −2 11 change in table is… 7 −16 Move the cursor 11 −28 to “Ask” for the Independent variable only
  • If your table jumps around as the lastone 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 x y will not see anything except the −6 23 cursor waiting for you to input an −2 11 x-value. Then, one at a time, 7 −16 enter the domain 11 −28 values from the given table. The corresponding y- values come up automatically.
  • 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.
  • The next problem couldalso be done on thecalculator.Since there is only one variablein this problem youcan use the y = key.
  • Tammy drew a floor plan for her kitchen as shown below. (3x + 5) units (2x + 1) This problem refers to units AREA of the rectangular kitchen. The area formula for aWhich expression represents rectangle is A = lengththe area of Tammy’s kitchen times width.floor in square units?F. 6x2 + 30x + 5G. 6x2 + 13x + 5 The expression for Area, then,H. 10x + 12 would be (3x + 5)(2x + 1)J. 5x + 6
  • Tammy drew a floor plan for her kitchen as shown below. (3x + 5) units (2x + 1) We are going to use “y=“ , units since there is only the variable x used in the expressions.Which expression representsthe area of Tammy’s kitchenfloor in square units? Enter the expression (3x + 5)(2x + 1)F. 6x2 + 30x + 5 in y1G. 6x + 13x + 5 2H. 10x + 12J. 5x + 6
  • Tammy drew a floor plan for her kitchen as shown below. (3x + 5) units One by one, enter the answer choices into y2. (2x + 1) units Then, graph. If both equations have exactly the same graph, the two expressions are equivalentWhich expression represents and you found your correctthe area of Tammy’s kitchen answer.floor in square units?F. 6x2 + 30x + 5G. 6x2 + 13x + 5H. 10x + 12 Changing to thisJ. 5x + 6 option allows you to follow along as the 2nd function is graphed. F is not the correct answer since the two graphs are different.
  • Tammy drew a floor plan for her kitchen as shown below. (3x + 5) units Replace choice F in y2 with choice G and graph. (2x + 1) units Which expression represents the area of Tammy’s kitchen floor in square units? F. 6x2 + 30x + 5 Did you watch as the little G. 6x + 13x + 5 2 circle made its way around the H. 10x + 12 same parabola? Option G is the J. 5x + 6 correct choice.To be safe, you can check options H & J. If you realize that those twooptions are linear (no seen exponents for x), their graphs could neverbe a parabola and thus are not correct answer choices.
  • Use STATPLOT to compare points or scatter plots. Which point on the grid below best represents the coordinates  8 , 7  ?  , 3 3 Press the STAT A. Point K button. B. Point M Select EDIT C. Point R D. Point U Enter 8/3 in L1
  • Which point on the grid below best represents the coordinates  8 , 7  ?   3 3 Go to STAT PLOT the y=) When you enter, (2nd calculator will change the Enter and turn on the plot by fraction into a decimal., entering again. You should see xlist: L1 forinto L Enter 7/3 the x-coordinate & 2 ylist: L2 for the y-coordinate. Set the window to the scale in Andproblem so you can make a the graph. good comparison. And a y- This point has an A. Point K coordinate x-coordinate between 2 & 3. B. Point M between 2 and 3. C. Point R D. Point U
  • To clear any numbers in a list, you may…• Reset the calculator (2nd + 7 1 2) 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!
  • Use the calculator to solve systems.If the system of linear equations 2x + y = 1 is not yet2x + y = 1 and y = − x + 1 are calculator friendly!graphed on the same coordinate Get the y by itself bygrid, which of the following is the subtracting 2x fromsolution to this system of linear each side.equations?A. (2, 0) y = 1 – 2xB. (0, 2)C. (0.5, 0) Enter both equationsD. Not here using the y= feature. Graph. Adjust the window, if necessary to see the point of intersection.
  • You want to go to the CALC feature (2nd TRACE)Select intersect since that is whatyou 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,Looking at the answer choices, which is the solution,the correct solution is not there. are shown at the bottom of the window. A. (2, 0) (0, 1) is the point B. (0, 2) where these two lines C. (0.5, 0) intersect. D. Not here
  • 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
  • Know how to get backto the home screen.2nd QUIT will get you there
  • Be sure to use parentheseswhen fractions are involved. Correct way 2 - 5x y= 7 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.
  • x+6 3x - 1 where x = 4MUST 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! Correct Incorrect
  • 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.
  • Let’s use this equation. You willsee different tables for this samefunction based upon how you setthe 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.
  • There are different settings you can use on thegraphs 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 Shows where the graph goes and ENTER makes a regular line Makes a dotted line Shows where the graph goes but makes NO line
  • Practice Problems
  • The first thing you shouldThere are several things you notice is that all of thecan do with these answer inequalities have 5 as thechoices to eliminate a few so y-intercept and a negativeyou won’t have to graph so slope and no equal sign.many.
  • Then, whether you plan to use the graphing calculator ornot, you need to know that when the inequality sign pointsto y, as in B and C, the shading is below the line. Since ourshading is above the line, we can eliminate these twographs.
  • For the remaining two choices, you either need to count theslope, starting at the y-intercept or you test the x-interceptof 4 by substituting 4 in for x to see if you get y = 0 or usethe calculator to graph and see if the x-intercept is 4.Since today’s tutorial is on calculator usage, that is themethod we are going to use.
  • Shaded above To be safe, fraction The x-intercept is NOT in ( ). 4. Wrong choice
  • Shaded above To be safe, fraction The x-intercept IS 4. in ( ). Choice D is verified.
  • This problem can be done a few ways, also.Remember, x-intercepts have y = 0, so you cansubstitute 0 for y and solve for x. Y-intercepts havex = 0, so you can substitute 0 for x and solve for y.Or you can graph. If you want to do the graphing byhand, remember that there is a blank sheet of graphpaper at the end of the math section for you to use asyou choose.
  • Since this tutorial is about using the calculator, that is the way we are going to do this problem.The given equation is not You do NOT have tocalculator friendly. We need put the equation into put the equation in y = slope-intercept form,form. Remember, there is an just calculator friendlyunderstood -1 in front of y, form. The calculatordue to the subtraction sign. will do the rest.
  • 2x – y = 8 is 2x – 1y = 8.Subtracting 2x, we get -1y = 8 – 2xThen, dividing by -1, we get thecalculator friendly formy = (8 – 2x)/-1 You absolutely MUST have the parentheses around the numerator!
  • The x-interceptappears to be 4The y-intercept is negative. We have no choices with negatives. Let’s eliminate the y-intercept choices.
  • 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 thetable of values. Let n = y and r = x, and you will be just fine.
  • Not answer choice BNot answer choice A ALL 4 of the ordered pairs match. This is the one!
  • 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!Allows me to watch as the Check the others to graph is plotted. be sure, though.
  • Definitely not this one, either. Looks like F is the correct answer choice.Doesn’t lookNOPE like NOit, but let’s adjustthe window.
  • If this graph is shifted UP, the y-intercept/vertexshould be higher. Logically, you should eliminate Jbecause -8 is lower than -3.
  • Let’s type the original function in y1 and the answerchoices, one at a time, in y2 and see which parabolashifted UP 5 units.
  • Count the hash marks. The new graph shift up 8 units. Too high!Answer choices will have a thicker line
  • Count the hash marks.The new graph shift up 5 units. This is it!
  • If you count, you can see that between 0 and1, there are 4 spaces—on each axis. Thatmeans 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 meanswe are looking at options G and H.
  • T is located on the 5rd space below 0 on they-axis so its y-coordinate is -5/4 . Thatmeans the correct option is G.
  • Adjust you have no clue about these toNow, ifthe window on your calculatorpoints,match the scale use You are going fromyou will want tohere.the STAT button on-2.5 calculator.yourto 2.5 by ¼ or .25 on each axis.
  • Recall, when you enter fractions into the calculator, they are changed into decimal form.Be sure thatthe STATPLOT isturned onwith theproper lists.
  • And then graph.This point is way too low to be point T.
  • 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
  • We are lookingfor C whenthey havegiven us F.
  • We can solve this equation the “traditional” way—using the “undo” process. 9104 = C + 32 Subtract 32 5 9 72 = C Multiply by 5 5360 = 9C Divide by 9 40 = C
  • 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
  • Alternate method You we couldbe Or need to use able to see and the graph in the window features of CALC where the two lines the graphing intersect. That calculator place looks way Enter the equation off to the right. in y1 and 104 in y2. Adjust the window Adjust the window again. Let’s try the xmax at 50.need ymax to — You be higher than 104 Graph
  • 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?
  • This problem was NOT multiple choice. You have to bubble in your answer correctly!Be careful!!! After 4 0 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!
  • • 28 An equation can be used to find the total cost of buying square-foot floor tiles to cover an area of floor. Using the table below, find the equation that best represents y, the total cost, as a function of x, the number of square feet to be covered.• F x = 0.35y• G y = 0.35x• H x = 2.86y• J y = 2.86x• Verify the correct selection by using the table.••
  • Which graph best represents all the pairs of num bers (x, y) suchthat x + y < −6? Solve for y = y < - x - 6 then use the y = key on the calculator
  • Solve the equation 2a − 6 + 5a = 3a + 1 0 for a.Record your answer and fill in the bubbles onyour answer d ocum ent. Be sure to use thecorrect place value. Look at the table for the value of x for which y1 = y 2.
  • 25 Which expression is equivalent to(5n - 2)3n - (5n - 2)(n - 1)?A n-1B 3n 2 - 3nC 10n 2 - 13n + 2D 10n2 + n - 2To confirm the solution, check the table to see if you get the same values for the two expressionsindicating that they are equivalent or check to see if they generate the same graph.
  • 23 Valerie purchased x tubes of lipstick at $4 each and y bottles of nail polishat $2 each. She spent less than $1 2, not includ ing tax. U se the grid below to graphthe inequality 4x + 2y < 1 2.Which point represents a reasonable num ber of lipsticks and bottlesof nail polish that Valerie purchased ?A (1 , 5) B (2, 3) C (1 , 3) D (2, 2)Use the home screen to calculate and compare the answers to see which is less than 12.
  • 4 What is the effect on the graph of the equation y = x 2 + 1 when it is changed to y = x 2 + 5 ?F The slope of the graph changes.G The curve translates in the positive x d irection.H The graph is congruent, and the vertex of the graph m oves up the y-axis.J The graph narrows.Looking at the graph of the third equation with the tracer balllets you know that the second equation is the moved up the y-axis.
  • 15 What are the x-intercepts of the graph of the equation y = x 2 + x − 1 2? A x = 4, x = 3 B x = −4, x = 3 C x = −4, x = −3 D x = 4, x = −3 Looking at the graph, you can see that the x-intercepts are at about –4 and 3.Looking at the tables, you can see that the values of x for which the values of y are 0 are –4 and 3.
  • 47 What is the solution set for the equation 4(3x - 2) 2 = 36?Since the solutions are the values for x for which the value of y = 36, the table showsthat the solutions must be between 0 and –1 and between 1 and 2. This eliminateschoices A and B.Using the table set in “ASK” and entering the values for x as fractions shows that thevalue for x for which y=36 is –1/3. C is the correct answer
  • 49 Which shows the functions correctly listed in order from widest to narrowest graph?Using the graph will allow the student to compare. Using the decimal window (zoom 4)will make the comparison easier to analyze visually.
  • 34 The figure below shows the first 3 stages of a fractal.How many circles will the nth stage of this fractal contain?F 2nG 2nH 2n - 1J 2n - 1Build a table of values for the information given.Stage # of circles1 12 33 7Enter the three possible equations and, using the “ASK” table set, look for theequation that will give the correct values for number of circles.
  • 6 Which graph best represents a line parallel to the line with the equationy = 3x + 4? Using a square standard window, you can see that J is the parallel line.
  • 22 Which of these equations describes arelationship in which every real number xcorresponds to a nonnegative real number?F y=xG y=x2H y=x3J y = -xLook in the table for the equation that gives nonnegative values for both positive andnegative values of x.
  • Using a square window, you can see that only F can be perpendicular to the given line.
  • 42 Oatmeal is packaged in a cylindrical containerwith the dimensions shown in the drawing.Find the approximate volume of this oatmealcontainer.F 471 cm 3G 566 cm 3H 1413 cm 3J 5655 cm 3