TAKS Tutorial

Calculator 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 + 7

2

1

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

11 −28

Which equation best describes the relationship between x and y?A. y = −3x + 5B. y = −5x − 7C. y = −x + 17D. y = 3x + 41

Enter the answer choices into the calculator through the “y=“ feature and then look at the tables to find a match.

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

11 −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

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

11 −28

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.

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 could also be done on the calculator.

Since there is only one variablein this problem you can use the y = key.

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

(3x + 5) units

(2x + 1)units

Which expression represents the area of Tammy’s kitchen floor in square units?F. 6x2 + 30x + 5G. 6x2 + 13x + 5H. 10x + 12J. 5x + 6

This problem refers to AREA of the rectangular kitchen.

The area formula for a rectangle is A = length times width.

The expression for Area, then, would be (3x + 5)(2x + 1)

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

(3x + 5) units

(2x + 1)units

Which expression represents the area of Tammy’s kitchen floor in square units?F. 6x2 + 30x + 5G. 6x2 + 13x + 5H. 10x + 12J. 5x + 6

We are going to use “y=“ , since there is only the variable x used in the expressions.

Enter the expression (3x + 5)(2x + 1) in y1

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

(3x + 5) units

(2x + 1)units

Which expression represents the area of Tammy’s kitchen floor in square units?F. 6x2 + 30x + 5G. 6x2 + 13x + 5H. 10x + 12J. 5x + 6

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.

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.

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

(3x + 5) units

(2x + 1)units

Which expression represents the area of Tammy’s kitchen floor in square units?F. 6x2 + 30x + 5G. 6x2 + 13x + 5H. 10x + 12J. 5x + 6

Replace choice F in y2 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.

Use STATPLOT to compare points or scatter plots.

Which point on the grid below best represents the coordinates ?

,

3

7,

3

8

A. Point KB. Point MC. Point RD. Point U

Press the STAT button.

Select EDIT

Enter 8/3 in L1

Which point on the grid below best represents the coordinates ?

,

3

7,

3

8

A. Point KB. Point MC. Point RD. Point U

When you enter, the calculator will change the fraction into a decimal.

Enter 7/3 into L2

Set the window to the scale in the problem so you can make a good comparison.

Go to STAT PLOT (2nd y=)

Enter and turn on the plot by entering again. You should see xlist: L1 for the x-coordinate & ylist: L2 for the y-coordinate.

And graph.

This point has an x-coordinate

between 2 and 3.

And a y-coordinate

between 2 & 3.

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 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.

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.

A. (2, 0)B. (0, 2)C. (0.5, 0)D. Not here

Looking at the answer choices, the correct solution is not there.

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 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.

7

5x-2y

Correct way

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!

1 -3x

6 x

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.

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.

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

Practice Problems

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.

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.

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.

Shaded above

To be safe, fraction in ( ).

The x-intercept is NOT 4. Wrong choice

Shaded above

To be safe, fraction in ( ).

The x-intercept IS 4. Choice D is verified.

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.

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.

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!

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

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.

Not answer choice ANot answer choice B

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.

Allows me to watch as the graph is plotted.

They matched! Check the others to be sure, though.

NOPEDoesn’t look like it, but let’s adjust the window.

NO

Definitely not this one, either. Looks like F is the correct answer choice.

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

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.

Answer choices will have a thicker line

Count the hash marks. The new graph shift up

8 units. Too high!

Count the hash marks. The new graph shift up

5 units. This is it!

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.

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.

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.

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.

And then graph.

This point is way too low to be point T.

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

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

C40

9by Divide9C360

5by Multiply 5

972

32Subtract 325

9104

C

C

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

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

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 — You need ymax 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 xmax at 50.

Alternate method

Enter again for the second curve? And guess?

Press 2nd TRACE so that you get CALC. Now, select Intersect.

Move the cursor to be close to the point of intersection.

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

• 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 numbers (x, y) such that x + y 6?

Solve for y =

y < - x - 6 then use the y = key on the calculator

Solve the equation 2a 6 + 5a 3a + 10 for a.Record your answer and fill in the bubbles onyour answer document. 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 - 2

To confirm the solution, check the table to see if you get the same values for the two expressions indicating 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 polish at $2 each. She spent less than $12, not including tax. Use the grid below to graph the inequality 4x + 2y 12.

Which point represents a reasonable number of lipsticks and bottles of 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 direction.H The graph is congruent, and the vertex of the graph moves 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 12?A x 4, x 3B x 4, x 3C x 4, x 3D x 4, x 3Looking 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 shows that the solutions must be between 0 and –1 and between 1 and 2. This eliminates choices A and B.

Using the table set in “ASK” and entering the values for x as fractions shows that the value 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 2n

H 2n - 1J 2n - 1Build a table of values for the information given.Stage # of circles1 12 33 7 Enter the three possible equations and, using the “ASK” table set, look for the equation that will give the correct values for number of circles.

6 Which graph best represents a line parallel to the line with the equation y 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 = x 2

H y = x 3

J y = -x

Look in the table for the equation that gives nonnegative values for both positive and negative 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