TAKS Tutorial

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TAKS Tutorial

• Objective 9 Probability Statistics
• Objective 5 Non-Linear Functions
• Part 2

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If you were unable to attend the tutorial over
the first part of these objectives on April 9th,
you will want to go to Mrs. Nelsons website.
That lesson, and all other TAKS tutorial lessons
presented after school, can be found there.BE
PREPARED FOR TAKS!
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Topics to be addressed today

• Circle and Bar Graphs
• Interpreting Data
• Using Percent and Proportion
• Laws of Exponents

4
2003
Notice that the scale on the graph is 10. The
numbers of votes is going up by 10 each line.
X
X
Too High
Too Low
X
The bars reflecting Jimmys votes are different
on two of the graphs, so lets start with Jimmy
Charlene and Lupe have the same height on all but
one graph.
Analyze the graphs first. Stephens bar is the
same on every graph, so dont worry about him.
After changing the to a decimal and
multiplying, we find that Jimmy received about 80
votes.
5
2006
Read all of the answer choices before you do any
work. Two of the choices refer to percents, so
lets work with them first.
6
2006
Choice A talks about combining credit card
payments, insurance, and food.
Less than 30 of the budget.
X
7
2006
Choice C talks about combining rent, food, and
utilities.
More than 50 of the budget.
X
X
8
2006
Choice B talks about combining utilities,
insurance, and car payment. But choice B refers
to an actual dollar amount and not a percent. We
will need to do that calculation by multiplying
the percent total to Richards total budget
amount.
X
This is the one!
X
9
2006
The orange sherbet received 10 out of the 30
tallies as favorite flavor. That fact eliminates
choices A C.
The 10 out of 30 ratio needs to equal the ratio
for the correct number of degrees for the central
angle out of the 360o total in the circle. That
fact eliminates choice B.
10
2003
We are going to create a proportion for this
problem just like in the last problem. To do
that, we need to know the total number of
sandwiches sold in that one day.
There were 75 out of 500 Ham-and-cheese
sandwiches sold. That is the number of degrees
for the central angle out of 360o in the circle.
11
2003
Read through all of the options first, paying
close attention to the wording. Two of the
choices say the ad is accurate two say
inaccurate. Pay attention to the reasoning given
for each answer.
X
Choice F It is true that 2 out of 8 is 25.
However, the ad refers to nutritionistsall of
them. There were 80, not 8
12
2003
Choice G We already determined that the ad was
inaccurate because its percentage is incorrect.
Whether you believe nutritionists are food
experts or not, which the ad does not mention,
you cannot get past the wrong information.
X
X
Choice J Since the ad specifies nutritionists,
a survey that includes non-nutritionists is not
necessary.
X
Verifying Choice H We already determined that
there were 2 out of 80 nutritionists who chose
Brand A tacos.
13
2004
Read through all of the options thoroughly! Two
of the choices refer to amounts that are not in
the table. The other two choices talk about cost
per pound.
X
X
Per is a division sign. So lets divide cost by
pounds to see if the last two choices are
accurate.
You can clearly see that the costs are NOT always
more than .35 per pound NOR less than .30 per
pound.
14
2004
X
X
X
10 lbs is between 5 lbs 20 lbs so its price
should be between .39 and .34 per pound.
Multiplying by 10, both amounts would be less
than the 4.00, as stated in choice A.
You can see that the more of the fertilizer that
is purchased, the cheaper it is.
15
2004
X
X
X
200 pounds of fertilizer should cost less than
.28 per pound.
At .28 per pound, the cost would be 56, so
certainly 200 pounds would cost less than 57.
16
2006
This problem can be done using a proportion.
A conversion is necessary 8 minutes 480
seconds
1.68 joules are lost in 8 minutes. 3.86 1.68
2.18 joules is the amount of energy the
particle has left after 8 minutes.
17
2004
Remember RT D Rate of Speed times Time equals
Distance traveled
Dividing by speed T D/R
The faster car covers 50 laps in the same time as
the slower car covers between 47 and 48 laps.
18
2004
The smallest rectangles are 3 in. by 5 in. 100
of the dimensions would produce the same sized
rectangle. With 125, we have a larger rectangle.
As a decimal, 125 is 1.25.
The dimensions of the second type of fabric are
3.75 in. by 6.25 in.
You then have to multiply the dimensions of the
second fabrics rectangles to get the dimensions
of the third type of fabrics rectangles.
19
2006
Expect that problems will require multiple steps
to get to the answer.
You need to multiply the 15 cost by 15 (changed
to a decimal) to get the amount of the tip.
Then you need to add the tip to the price of the
haircut to know how much Bruce had to pay.
Finally, you need to subtract that amount from
the 20 bill that Bruce paid with.
20
2006
2
7
5
Be sure to correctly enter the answer onto the
grid and to bubble the numbers correctly and
completely, staying within the circle.
21
2003
We can again use a proportion to find this answer.
5 is 6,975 just as 100 is the total price of
the house
22
2003
Or you can solve a simple algebraic equation
6,975 is 5 is the total price of the
house. 6975 .05x
23
2003
One way to do this problem is to follow the rules
for multiplying expressions with
exponents Multiply coefficients add exponents
of the same base
(3-4)(m-26)(n4-7) -12m4n-3
Since this answer is not one of the choices, we
need to deal with the negative exponent.
Negative exponents tell us to take the reciprocal
of the base.(In this case, n)
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A couple of things to think about

• First, negative signs for the coefficients can go
  in front of the fraction bar, with the numerator,
  or with the denominator. Just rememberif the
  fraction is negative, there is only one negative
  sign!

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A couple of things to think about

• Second, try to think of negative exponents as if
  they were tickets. You know that when you go
  somewhere, you turn in your ticket and then you
  move. Well, the same is true of the negative sign
  in an exponent.

n has a negative exponent. The negative sign is
the ticket it is turned in and then n moves to
the denominator with its exponent but without the
ticket negative sign.
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• Using the same thought processes

Had the expression looked like this one, the n
would turn in its ticket negative sign and move
up into the numerator.
27
2003
A second way to do this problem is to deal with
the negative exponents first.
In the first expression, m took a trip to the
denominator. In the second, n took the trip to
the denominator. Notice, now both negatives in
the exponents are gone.
As for the simplifying, now you need to multiply
the two expressions and then follow the rules for
dividingdivide coefficients and subtract
exponents of the same base.
28
2006
(-6)(2)(a32)(b53)
No negative exponents, so no trips! We do have a
multiplication and a division going on in this
problem. Fraction bars are grouping symbols, so
multiply first.
Largest power of a is in the numerator so that is
where the answer goes a5-4
Negatives cancel 12 and 18 have a factor of 6 in
common
b8-8 b0 1 1 times the rest of the expression
is the expression so we dont need to see the 1.
c3 remains as is since there is no other c term.
29
2006
Do not overlook this word!!!! Circle it,
underline it, highlight it. You need to realize
that 3 of the 4 choices will equal 212.
212
232
212
212
Choices F G are expressions raising a power to
a power. In these cases, you multiply exponents.
Choices H J are expressions involving
multiplication. In these cases, you add exponents.
30
2003
This problem refers to a rectangle. DRAW ONE and
label it!
We know that for a rectangle area is length times
width. (If you dont know, it is on the math
chart.) A lw To find length, we need
to divide the area by the width.
Divide coefficients and subtract exponents of the
same base
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What do you do if you just dont remember those
exponent rules?

• You use your calculator and check!
• You still have something to rememberthe
  calculator steps.
• These directions will work anytime on a multiple
  choice test.
• Although all 4 of the previous problems can be
  done with the calculator, we are only going to do
  a couple of them here.

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Lets do this problem first, since it doesnt
have a variable in it.
You will need to use the TEST feature of your
calculator. To get TEST, press 2nd MATH.
You see several options. We will be using the ,
which is automatically highlighted
For now, QUIT so we can work this problem out.
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Lets do this problem first, since it doesnt
have a variable in it.
You first need to enter the expression from the
problem
If you find a true statement, you will get 1
for an answer. If you find an untrue statement,
you will get 0.
Next, you want to use the TEST button and select
the equal sign.
Now, you want to type in the answer choices, one
by one, until you find the correct answer.
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Lets do this problem first, since it doesnt
have a variable in it.
You found a true statement. Remember, we are
looking for an untrue statement. NOT
And type the next option over the last one (or
delete if you prefer).
You do not need to retype the entire expression
for the next option. Use 2nd ENTER
And use the backspace button to go back to the
equal sign
The zero showed up so this is the untrue
statement.
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For the next problem, you will need to know how
to STORE a value in the calculator.

• To store a value, you need to select a number
  (but dont use 0, 1, or -1) put it into your
  calculator, press STO (lower left), press the
  letter of the alphabet for the variable you are
  working with and enter. Thats it. You just
  stored that number into the calculators memory
  for that variable.

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We will do this problem again
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This time we have 3 variables.

• You need to store a number for each variable.
  Pick a different number for each one. Remember,
  dont use 0, 1, or -1.

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Do you remember what needs to be done next?

• Type in the expression just as you see it.
  However, this one has a catch!
• When a fraction is involved, the entire numerator
  and the entire denominator MUST be in
  parentheses!
• ((-6a3b5)(2a2b3))/
• (-18a4b8c3)

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• then, 2nd MATH
• for TEST
• Select and enter
• And one by one, enter the answer choices
• When you get 1, you have the answer
• Entire numerators and entire denominators in
  parentheses!

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41
2006
Find 140 meters on the graph
Now, look at the time that is, what time does
the line hit the curved graph?
between 3.25 and 3.5 sec
42
2004
You could solve this equation algebraically by
substituting 200 in for y and then factoring
Be honest! How many of you would have remembered
how to do this?
43
2004
An easier way to do this problem is to use the
graphing calculator!
Enter the equations in y
Adjust the window so you can see higher than the
250.
Then, graph
Use the CALC feature to find the point of
intersection in quadrant I.
44
2004
After entering and getting the shown screen, use
the right and left arrows to move the cursor
close to the point of intersection and enter.
When asked about the 2nd curve, if you are close,
just enter.
At Guess? just enter again
The coordinates of the point of intersection are
shown. The equation is solved for x.
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Practice Problems

• Time to practice what we learned in the lesson.

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2004
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