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
1
2
+ 7
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
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
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 yvalues 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 variable
in 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
This problem refers to
AREA of the
rectangular kitchen.
The area formula for a
rectangle is A = length
times width.
Which expression represents
the area of Tammy’s kitchen
floor in square units?
F. 6x2 + 30x + 5
G. 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)
units
We are going to use “y=“ ,
since there is only the
variable x used in the
expressions.
Which expression represents
the area of Tammy’s kitchen
floor in square units?
Enter the expression (3x + 5)(2x + 1)
2
F. 6x + 30x + 5
in y1
G. 6x2 + 13x + 5
H. 10x + 12
J. 5x + 6
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 + 5
G. 6x2 + 13x + 5
H. 10x + 12 Changing to this
option allows you
J. 5x + 6
to follow along as
the 2nd function is
graphed. F
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.
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
2
G. 6x + 13x + 5
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 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  8 , 7  ?
3 3
Press the STAT
button.
A. Point K
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
nd y=)
GoWhen
to STAT
PLOT
(2
you enter, the
calculator will change the
Enter and turn on the plot by
fraction into a decimal.
entering again. You should see
xlist:
forinto
the L
x-coordinate &
EnterL17/3
2
ylist: L2 for the y-coordinate.
Set the window to the scale in
And
graph. so you can make a
the problem
good comparison.
,
A.
B.
C.
D.
Point K
Point M
Point R
Point U
And a ycoordinate
between 2 & 3.
This point has an
x-coordinate
between 2 and 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
Graph. Adjust the window,
if necessary to see the point
of intersection.
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.
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”
Looking at the answer choices,
the correct solution is not there.
A. (2, 0)
B. (0, 2)
C. (0.5, 0)
D. Not here
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.
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 back
to the home screen.
2nd QUIT will get you there
Be sure to use parentheses
when 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
where
x
=
4
3x - 1
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!
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 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.
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
Shows where the graph goes and
makes a regular line
These options come
from backspacing
and pressing
ENTER
Makes a dotted line
Shows where the graph
goes but makes NO line
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 x-intercept
appears to be 4
The 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 the
table of values. Let n = y and r = x, and you will be just fine.
Not answer choice B
Not 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-byone, 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.
Definitely not this one,
either. Looks like F is the
correct answer choice.
Doesn’t lookNOPE
like
NO
it, but let’s adjust
the window.
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.
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 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 xaxis 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.
Adjustifthe
Now,
youwindow
have noonclue
your
about
calculator
these points,
to
you will
match
thewant
scaletohere.
use the
YouSTAT
are going
buttonfrom
on
yourto
-2.5
calculator.
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.
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 looking
for C when
they have
given us F.
We can solve
this equation
the “traditional”
way—using the
“undo” process.
9
104  C  32
5
9
72  C
5
360  9C
40  C
Subtract 32
Multiplyby 5
Divide by 9
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
need
to be
Or we
could
use
able
to see and
in the
the graph
window
where the
CALC features
of
two
thelines
graphing
intersect.
calculatorThat
place looks way
Enter
off tothe
theequation
right.
in y1 and 104 in y2.
Adjust the window
Adjust
thetry
window
again.
Let’s
the
— at
You
xmax
50.need ymax to
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
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 on
your answer document. Be sure to use the
correct 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-1
B 3n 2 - 3n
C 10n 2 - 13n + 2
D 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
F
G
H
J
What is the effect on the graph of the equation
y  x 2 + 1 when it is changed to y  x 2 + 5 ?
The slope of the graph changes.
The curve translates in the positive
x direction.
The graph is congruent, and the vertex of
the graph moves up the y-axis.
The graph narrows.
Looking at the graph of the third equation with the tracer ball
lets 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  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 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 2n
G 2n
H 2n - 1
J 2n - 1
Build a table of values for the information given.
Stage # of circles
1
1
2
3
3
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 a
relationship in which every real number x
corresponds to a nonnegative real number?
F y=x
G y=x2
H y=x3
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 container
with the dimensions shown in the drawing.
Find the approximate volume of this oatmeal
container.
F 471 cm 3
G 566 cm 3
H 1413 cm 3
J 5655 cm 3
Remember, all past tutorials can be
found on SFHS Math TAKS
Resources.
• There is a link to that site on the Santa Fe
High webpage.
• Your teachers will be ready to answer any
questions you might have in class.
• Come to take the test RESTED!
• Look at the posted roll sheets to see what
day(s) you are testing and where.
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!
AIM For TAKS SUCCESS!!!