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.
• 2nd, Memory (+), Reset (7), All RAM (1),
Reset (2)
• 2nd, +, 7, 1, 2
5. 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 −28
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
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
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
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
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.
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. 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.
10. 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 a
Which expression represents rectangle is A = length
the area of Tammy’s kitchen times width.
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
11. 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 represents
the area of Tammy’s kitchen
floor in square units? Enter the expression (3x + 5)(2x + 1)
F. 6x2 + 30x + 5 in y1
G. 6x + 13x + 5
2
H. 10x + 12
J. 5x + 6
12. 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 equivalent
Which expression represents and you found your correct
the area of Tammy’s kitchen answer.
floor in square units?
F. 6x2 + 30x + 5
G. 6x2 + 13x + 5
H. 10x + 12 Changing to this
J. 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.
13. 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 two
options are linear (no seen exponents for x), their graphs could never
be a parabola and thus are not correct answer choices.
14. 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
15. 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
16. 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!
17. Use the calculator to solve systems.
If the system of linear equations
2x + y = 1 is not yet
2x + y = 1 and y = − x + 1 are
calculator friendly!
graphed on the same coordinate
Get the y by itself by
grid, which of the following is the
subtracting 2x from
solution to this system of linear
each side.
equations?
A. (2, 0) y = 1 – 2x
B. (0, 2)
C. (0.5, 0) Enter both equations
D. Not here using the y= feature.
Graph. Adjust the window,
if necessary to see the point
of intersection.
18. 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,
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
19. 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
20. Know how to get back
to the home screen.
2nd QUIT will get you there
21. 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.
22. x+6
3x - 1 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!
Correct
Incorrect
23. 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.
24. 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.
25. 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
Shows where the graph goes and ENTER
makes a regular line
Makes a dotted line
Shows where the graph
goes but makes NO line
27. The first thing you should
There are several things you
notice is that all of the
can do with these answer
inequalities have 5 as the
choices to eliminate a few so
y-intercept and a negative
you won’t have to graph so
slope and no equal sign.
many.
28. 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.
29. 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.
30. Shaded above
To be safe, fraction The x-intercept is NOT
in ( ). 4. Wrong choice
31. Shaded above
To be safe, fraction The x-intercept IS 4.
in ( ). Choice D is verified.
32. 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.
33. 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 to
calculator friendly. We need put the equation in
to put the equation in y = slope-intercept form,
form. Remember, there is an just calculator friendly
understood -1 in front of y, form. The calculator
due to the subtraction sign. will do the rest.
34. 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!
35. 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.
36. 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.
37. Not answer choice B
Not answer choice A
ALL 4 of the
ordered pairs
match. This is the
one!
38. 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.
39. 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.
40. If this graph is shifted UP, the y-intercept/vertex
should be higher. Logically, you should eliminate J
because -8 is lower than -3.
41. 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.
42. Count the hash marks.
The new graph shift up
8 units. Too high!
Answer choices
will have a
thicker line
43. Count the hash marks.
The new graph shift up
5 units. This is it!
44.
45. 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.
46. 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.
47. Adjust you have no clue about these to
Now, ifthe window on your calculatorpoints,
match the scale use You are going from
you will want tohere.the STAT button on
-2.5 calculator.
yourto 2.5 by ¼ or .25 on each axis.
48. 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.
52. We can solve
this equation
the “traditional”
way—using the
“undo” process.
9
104 = C + 32 Subtract 32
5
9
72 = C Multiply by 5
5
360 = 9C Divide by 9
40 = C
53. 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
54. 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
55. 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?
56. 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!
57. • 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.
•
•
58. Which graph best represents all the pairs of num bers (x, y) such
that x + y < −6?
Solve for y =
y < - x - 6 then use
the y = key on the
calculator
59. Solve the equation 2a − 6 + 5a = 3a + 1 0 for a.
Record your answer and fill in the bubbles on
your answer d ocum ent. Be sure to use the
correct place value.
Look at the table for the value of x for which y1 = y 2.
60. 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.
61. 23 Valerie purchased x tubes of lipstick at $4 each and y bottles of nail polish
at $2 each. She spent less than $1 2, not includ ing tax. U se the grid below to graph
the inequality 4x + 2y < 1 2.
Which point represents a reasonable num ber 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.
62. 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 ball
lets you know that the second equation is the moved up the y-axis.
63. 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.
64. 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
65. 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.
66. 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.
67. 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.
68. 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.
69. Using a square window, you can see that only F can be perpendicular to the given line.
70. 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
