# TAKS Tutorial by maclaren1

VIEWS: 25 PAGES: 72

• pg 1
```									 TAKS Tutorial
Algebra Objectives 1 – 4
Part 2
Remember…
This tutorial and all the ones presented
previously can be found on Mrs. Nelson’s
website.
There is a link to her site on the Spring High
website.
If you missed Objectives 1 – 4 part 1, you
definitely want to go to the website to go
through the lesson.
Today, we have a great deal to
cover! Topics include:
   Simplifying expressions
   Setting up & solving linear equations
   Setting up & solving linear systems
   Setting up & solving linear inequalities
   Writing linear equations from information
   Slope and intercepts
This problem was on the 2006 test.
This expression
certainly can be
simplified the

- 21x  12x  6x - 13  24x
2                       2
Distribute :
3x  18 x  13
2
Combine like terms :
The only problem with the
“traditional” way is that some of
you do not correctly distribute the
negative/subtraction signs!
So let’s look at an
alternate way to do
this problem with a
calculator.
It takes longer, but if
you are someone
who makes simple
mistakes…this is
for you!
The only variable in the expression is
x. Store a value into your calculator
for x—any number except 1, 0, or -1.
Select and press your number, press STO,
press X,T,Θ,n , and ENTER

Now, enter your
expression, just as you
see it, into your
calculator…
-3x(7x-4)+6x-(13-24x^2)
Be sure to double check
that you typed the
expression correctly!
Now, press 2ND MATH to get TEST
We are looking for equal
expressions so select =

You should see the = sign
Now, press ENTER. If this
appear after your
two expressions are equal,
theexpression
you will see a ―1‖ as an
(NO, do not press
Looks like option F
correct
by one, enter were          ENTER—the calculator
firstlucky the first time. just as it expressions are not equal in
answer choice You                  will not simplify this
appears. Double check to
might check the other           value, you will see ―0‖ as an
expression for you!)
options to see that you
make sureget “0”.
correctly.
That was a lot to grasp in one
problem. Let’s try another one and
practice with the calculator. (2003)
Type in the (2 option
Type variable used is
Try again withnd Math)B.
The in the expression
exactly Remember,
choice. as it appears.
You do NOTahave to ―1‖
―n‖. Select
and select = number
Double for ―n‖ and is
if it useeverything! Press
to is check
retypeequal; ―0‖ if itstore
not.
nd ENTER
correctness!
2it in the calculator.
That was a lot to grasp in one
problem. Let’s try another one and
practice with the calculator. (2003)
like
Lookswasn’t the correct go
Use the backspace
Try         with option
option D. Don’t nd
must beequal sign. Either
to the NOT have to
You do Check
assume!the first it out!
delete everything! the
Enter, backspace toPress
retype
=, nd ENTER option it.
2 and type in
choice or type over C.
We will now move on to solving equations…
This problem was on the 2006 test

We are looking
for C when
they have
given us F.
We will now move on to solving equations…
This problem was on the 2006 test

We can solve
this equation
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
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 could use
Or need to be
the to see in the
able graph and
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.
again. Let’s window
— at 50.
xmaxYou 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
Be careful!!! After
going through all      4   0
that work to get the
don’t want the
problem to be
scored as wrong
because you didn’t
bubble in the
This problem was on the 2003 test.
Let’s approach this one differently,
since it is multiple choice.

We could transform the equation so we can
use the calculator, but too many people
Option F is not it.
mess that up—especially with the
Neither is option G
subtraction sign!
Option H is the one!
Since we were given answer choices for y, we
will use the calculator to substitute and
simplify until we find the y-value that gives us
Here’s an inequality problem from the 2003
test where they ask you to graph, but they
don’t look at the graph! We’ll solve this
problem the same as the last one.

In other words, don’t be fooled by how
complicated a problem looks!
Study the problem. See what you know that
can be used to make the problem easy to do!
Let me again mention—the state
graders are not going to look in
the test booklets for your graph!
We are NOT going to use the grid
to do this problem!
We are going to substitute these
coordinates into the expression.
We want an answer that is less
than 12!

Option D gives
us 12. We want
an answer that     A is more than 12
is less than 12.   And so is B

Sure enough, C      Looks like C is the answer,
is the answer.      but let’s check to be sure.
TAKS will not always give you an
expression, equation or inequality.
You may just have to read a word problem and
come up with one of your own.

The next several problems fit in this category.
2006

First, you want to find the profit on ONE
tool set.
If it sells for \$19.95 and is made for
\$4.37, the profit is the difference in the
two prices.
19.95 – 4.37
Eliminate B & C
Now, the profit is made on every tool set
sold, which is s. We would multiply s to the
profit (19.95 – 4.37) on each tool set.
2006

Let’s reason. A total of
80 backpacks were
sold. That means, if 1
\$35 backpack was sold,
79 of the \$50 backpacks
were sold.
If 2 \$35 were sold, then
In each case, I subtracted the   78 \$50 were sold.
number of \$35 backpacks, x,      If 10 \$35 were sold,
from the total of 80.            then 70 \$50 were sold.
That is 80 – x .
2006

Since x is the number of
\$35 backpacks, I would
need to multiply 35 and
x together to get the
by those purchases.

Since (80 – x) is the number of
\$50 backpacks sold, I would
need to multiply 50 and (80 – x).
2006
―Total‖ implies
and c should be 220.
b + c = 220
2006
As for the
money…Every
brownie sold for \$.75
so \$.75 needs to be
multiplied to b, the
number of brownies.

note that
\$.50, the
cost of
each
multiplied
to c.
In some cases, you will be expected
to use the information given in a
problem situation to set up the
procedure and to solve for the
requested information.

How you do the problem is up to you and will
not be checked. That you come up with the
correct answer is the important piece this
time.
2006        Perimeter is the sum of the lengths of
the 3 sides: 5x + 10

Anytime a
figure is used,
DRAW &
LABEL it in the
2x + 5       2x + 5       test booklet!
We have no
idea how long
the base is so
5x + 10 = 95
x               that is ―x‖.
5x    = 85
Each leg is 5
x = 17                               more than
double the
base: 2x + 5
That is not the only way you can do
this problem. You can just use the

Let’s look at option A. If the base is 17,
then based on what the problem says, the
legs are each 2(17) + 5 = 39
The perimeter means to add the two
legs and the base:
17 + 39 + 39 = 95

95 is the perimeter we want, so A is
2006   This part means \$.11 times ―x‖

―x‖ is the number
of minutes Lisa
can talk. Notice: all
graphs have a
start at zero. That
is because Lisa
cannot talk for less
than 0 minutes,
which is no talking
at all.
The connection fee is
charged, no matter
what.
2006   This part means \$.11 times ―x‖

―Not more than‖
means we have
an inequality—this
value is the upper
limit. Lisa wants to
spend \$5 or less.
.50 + .11x ≤ 5
.11x ≤ 4.50
x ≤ 40.9090…
Again, on this problem we could use
the answer choices to work toward
the solution.

All of the graphs have 0
as a lower limit of
minutes. That makes
the 0 a ―non-issue‖.
We need to look at the
upper limit of the graphs
and see which one
keeps us at \$5 or less.
since it has the largest
upper limit.
Again, on this problem we could use
the answer choices to work toward
the solution.

If minutes is 50, then
.50 + .11(50) = 6. \$6 is
over Lisa’s limit.

If minutes is 45, then
.50 + .11(45) = 5.45 This
X                      value is also over Lisa’s
limit

X                    If minutes is 40, then
.50 + .11(40) = 4.9 \$4.90 is
under Lisa’s \$5 limit, so
option B is the correct one.
2003                                   Anna must get the
same amount of
money, m, for
selling the plates
as it takes to
make the plates
before she can
―x‖ represents the number of plates
make any profit.
Anna must sell

Her costs: m = 750 + 10x
Her revenue: m = 25x
As we discussed earlier, you can solve by graphing the
two equations and finding the intersection. Or you can use
the table and find where the two y values are the same.
Or you can use substitution and solve algebraically.
2003

750 + 10x = 25x
750    = 15x
50 = x
2003

And, of course, you always have the option of
working with the answer choices to see which
one gives you equal values for her costs and
how much she makes selling the plates.

20 plates is a NO
50 plates looks NO
30 plates is also like
a winner.
Now, it is time to move on to
the mechanics of lines.
 Slope
 Y-intercepts
 X-intercepts
 Equations of lines through points

If we do not get everything covered before the
end of the session, please visit Mrs. Nelson’s
website to complete the power point lesson!
The first thing you
need to note is
that the slope is

X    negative. That
means the line
should be going
downward.
Eliminate the
ones going up.
Now, look for the

X               point (4, -3) on the
remaining 2 graphs.
The point must be
ON the line.
Rate of change is slope

Graph the line and see what it
looks like.

The line is horizontal. It is ―running‖ but it
is NOT ―rising‖. It has 0 rate of change
because the y-coordinates of every point
on the line are exactly the same.
You want to remember:
   Horizontal lines have 0 slope
   Vertical lines have undefined slope
   Diagonal lines have some fraction for a slope
   If the diagonal line goes up as it goes right, the
slope is positive
   If the diagonal line goes down as it goes right, the
slope is negative
   The steeper the line (the closer it is to the y-axis),
the bigger the slope
   The flatter the line (the closer it is to the x-axis), the
closer the slope is to zero (which would be
horizontal).
2006

You are expected to know that
the x-intercept is where the
graph ―touches‖ the x-axis.
You are also expected to know
that the y-coordinate is 0 for an
x-intercept.
Option 1: put 0 in   2/3(0) = -6x + 12
for y and find x.
0 = -6x + 12
6x = 12
x=2
2006

You are expected to know that
the x-intercept is where the
graph ―touches‖ the x-axis.

This equation is not in the correct
form for our calculator. So, divide by
2/3—Not you! Tell the calculator to
Option 2: graph the         do it. Just be sure to use
line and see where          parentheses!
it crosses the x-
axis.
y1= (-6x+12)/(2/3)
x = 2 at this point
2003

Find the point
(5, -1) on the grid.
You need to use
the equation
x – 3y = 6 to find
the y-intercept.

There are a few
ways to do that!

NOT looking at your graphs in
your booklet. This grid is for you!
2003

The x-coordinate of the y-intercept is
always zero. Substitute 0 in for x and find y.
0 – 3y = 6       -3y = 6      y = -2
You could transform the equation x – 3y = 6
into slope-intercept form to find the y-intercept.
-3y = 6 – x       y = -2 + 1/3 x
You could put the equation into a form that
the calculator will graph and find the y-
intercept visually.
x = -2
-3y = 6 – x    y = (6 – x)/-3          here
2003

Eliminate A and D

X   since the b-value,
the y-intercept, is
NOT -2.
Make a point
where the y-
intercept is -2.

Now, count the
slope from (0,-2)      up 1    right 5

X   to (5,-1).            The slope is 1/5.
2006

and draw the line
between R and S.
You can see that the y-
intercept cannot be 4.5, so
eliminate those two choices.
up 12  3
Now, count the slope                   1.5
between R and S.              right 8 2
2004                There are
numerous ways to
do this problem.

You could type each answer choice
in your calculator, go to the table,
and look for BOTH points.

BOTH points are here—this is it!
2004                               Option 2

You are given graph paper at the
end of the math section. Make
yourself a set of axes and graph the
two points.           The y-intercept is
at 3.5
7/2 = 3.5

Draw the line between them.
Count the slope:
down 2  2  1
   
right 4   4   2
2004                                       Option 3

You could use the slope formula on
the formula chart to calculate the
slope. Then, you could use slope-
intercept form or point-slope form,
which is also on the formula chart to
calculate the y-intercept.
y  mx  b
1
2     (3)  b use the slope and (3,2) as(x, y)
4-2     2    1        2
          4   3  2b get rid of the fraction by multiplyin g everything by 2
-1 - 3  4   2    7  2b         add 3 to both sides
7
b          divide both sides by 2
2
Now, let’s talk “linear systems” 2003

X                   X         We – 3y needthe given
Neither 0
2x just = of the y by
equations is in
itself. Using parentheses
-3y = 0 – 2x
calculator the
will allow us form. We
opportunity – 2x)/-3 into
y = (0 for the
need to get them
that form ―calculate‖
calculator tofirst.
put this function in y1

X                                    That does is too
The slope in FNOT
mean compared to
steep as they have to
this graph.
be in slope-intercept
form.
The line going through (0, 0) must go
upward.
Now, let’s make sure…

X                 X    x + 2y = -7
2y = -7 – x
y = (-7 – x)/2
put this function in y2

X
Sure enough, we have a match.
Now, let’s make sure…

X               X         You were not asked,
but let’s find the point
of intersection for the
two lines—the solution
to the system.

X
Yes, this point is
(-3, -2)
2006