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# Praxis I Math Review

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```									Praxis I Math Review
By: Professor Peter Eley
Question 1
A scientist has a very sophisticated microscope and laser cutting
tool. She begins with a sample that is 0.23684 inches long and
cuts precisely three one-thousandths of an inch off the end. What
is the size of the remaining piece?

139230= 0.00384 inches
139231= 0.00684 inches
139232 = 0.23 inches
139229 = 0.23384 inches
139239 = 0.20684 inches
Explanation
This may seem complex, but it is a simple subtraction
problem if you construct it properly. Convert three one-
thousandths of an inch into a number form.

3 / 1000 = 0.003

Then subtract the size of the cut piece from the whole
sample.

0.23684 inches - 0.003 inches =0.23384 inches
Question 2
A man flipped a coin four times and got "heads" each
time. What is the probability that he will get "heads" on the
fifth time he flips the coin?

175968= 20%
175969= 25%
175870= 50%
175971= 80%
175972= More than 50% but less than 80%
Explanation
This can be a tricky question. Each time you flip a coin
there is a 50/50 or 50% chance of getting either
"heads" or "tails." It does not matter how many times
you flip the coin, the result of each flip has its own
probability of 50%. What makes this question tricky is
that people seem to think that if the coin lands on
"heads" or "tails" many times in a row that somehow it
is more likely to do the opposite on the next flip. This is
not true, it is always 50%.
Question 3

What is the value of x in this 30-60-90
triangle?
175978= 1
175979= 2
175980= 3
175981= √ 3
175982= √ 2
Explanation
This triangle is a special kind of right triangle called a 30-60-90
triangle. That means that the angles of it are 30, 60 and 90
degrees. This also means that the dimension of the sides
are special as well. They follow the one-two-square root of
three rule. This means that sides will be proportional to
each other where the shortest side equals n times one, the
hypotenuse equals n times two and the remaining side
equals n times the square root of three. In the question, the
shortest side is 1. Therefore, the shortest side can be
thought of as being n times 1. Since the shortest side is 1, n
must equal 1. Let’s check on the hypotenuse. n * 2 = 1 * 2 =
2. Now we have what we need for the answer. Since n = 1
then x = n * √ 3 = 1 * √ 3 = √ 3
Question 4
Solve for x: x/3 * 4/7 = 12/21

175954= 1

175955= 2

175956= 3

175957= 4

175913= 7
Explanation
 The numerators and denominators are multiplied separately
in order to get the product, so in this problem: x/3 * 4/7 =
12/21

Can be thought of as two equations:

Numerator: x * 4 = 12 and

Denominator: 3 * 7 = 21

When expressed like this it is easy to see that x = 3.
Question 5

What is the value of the angle x?
175973= 90
175974= 50
175975= 40
175976= 45
175977= None of the above
Explanation
If you add the internal angles of any triangle, no matter what
shape, they always equal 180 degrees. We know from the
square in the corner that this triangle is a right triangle, so one
angle is 90°. Another angle of the triangle is given as
50°. Adding 90° + 50° yields 140°. The angle that
remains must be 180° - 140° or 40°.
Question 6

In a shuffled, standard deck of playing cards, what is the
probability of drawing a red ace?

173570= 1/52

175958= ¼

175959= 1/13

175960= 1/26

175914= 2%
Explanation
Probability of drawing a red ace = the number of red aces
divided by the total number of cards. Since there are 2 red
aces in a standard playing deck of 52 cards, the chance of
drawing a red ace is 2 in 52 or 1 in 26. Therefore, 1/26.
Question 7

If 4x2 = y which of the following is true?

175993= x = 2

175994= x = √ (y/4)

175995= x = (√y) / 2

175996= x = √y * 4

= Both 175994 and 175995
Explanation
Solve the equation for x:

4x2 = y

Divide each side by 4:

x2 = (y/4)

Then take the square root of both sides.

x = √ (y/4) or Answer B.

However, that equation can also be expressed as:

x = (√y ) / (√4) OR x = (√y) / 2 which is Answer C.

Since Answer E states that both B and C are correct, this is the best choice.
Question 8

The ant wants to get back to his home, but there are several paths he
can follow, as shown in the diagram. Whenever he reaches a junction,
he is equally likely to choose any one path as he is to choose any
other.

He cannot turn back. What is the probability he reaches home?

171944=1/8   171945= 1/6   175878= ¼ 176013 = 1/2 176014=2/3
Explanation

To reach home, he either follows route ABEGH or route ACEGH.
P( He follows route ABEGH) = ½ × ½ × ½ = 1/8
P( He follows route ACEGH) = ½ × ½ × ½ = 1/8
Therefore, the probability he reaches home = 1/8 + 1/8 = 1/4.
Question 9

From the above diagram, what is the value of a/x?

175983= 2/3

175984= 9/8

175985= 4/3

175986=3/2

175987= 2/1
Explanation
The sides x and a both face a 75° angle. Of the remaining
sides in the two triangles, the two longer sides are in the ratio
24/16 = 3/2 and the two shorter sides are in the ratio 18/12 =
3/2.
Therefore, triangles ABC and XYZ are similar with ratio 3/2.
Therefore, a/x = 3/2 also.
Question 10

Jordan's teacher asked her to solve the equation x/3 + 3/x = -2. This was Jordan's answer:
x/3 + 3/x = -2
⇒ (x + 3)/(3 + x) = -2
⇒ x + 3 = -2(3 + x)
⇒ x + 3 = -6 -2x
⇒ 3x = -9
⇒ x = -3
Jordan has got the right answer, but she made some mistakes. How many mistakes did Jordan
make?

175988= 0

175989= 1

175990= 2

175991= 3

175992= 4
Explanation
1. In the first line she said x/3 + 3/x = (x + 3)/(3 + x).
Fractions are not added in this way. It is not generally true that a/b
+ c/d = (a + c)/(b + d).
Certainly in this case it is wrong because (unless x = -3) the left-
hand side would simplify to 1 and 1 ≠ -2. If x = -3, then the left-hand
side would be 0/0 and 0/0 is undefined.
2. In the second line she multiplied both sides by (3 + x) which
would be alright except for the case where x = -3. In that case both
sides would be multiplied by 0. And, of course, x does equal -3.
After making two mistakes, Jordan managed to get the right
Question 11

The table above shows the x and y coordinates of a straight line.
What is the equation of that line?

175963= x = 5*y + 6
175964= y = x + 11
175965= y = 6*x + 5
175966= y = 5*x + 6
175967= y =5*x + 11
Explanation
Recall that the equation of a straight line is y = mx + b.
When x = 1, y = 11 and when x = 2, y = 16
Slope is rise over run. Y "rises" 5 while x "runs" 1 so slope is 5.
Take any two points from the table and solve for b.
y = 16, m = 5, x = 2
16 = 5 * 2 + b
b=6
so y = 5*x + 6
Question 12

What percent of 80 is 20?

175939= 20%

175940= 25%

175941= ¼%

175942= 80%

175943= 50%
Explanation
First, convert the phrase into an equation where "of" is a multiplication sign
and "is" is an equal sign. Use a variable (in this case x) to describe the
number you are solving.
x% * 80 = 20
Solve for x by dividing both sides by 80
x% = 20 / 80
x% = 1 / 4
x% = 0.25
The percent sign means we need to multiply by 100.
x = 25%
Question 13

Which of the following is equal to a quarter of a million?

175934= 40,000

175935= 250,000

175936= 1/(4,000,000)

175937= 65

175938= 500,000
Explanation
Since one million is 1,000,000, quarter of a million is ¼ *
1,000,000 or 250,000
Question 14

Which of the following fractions is least?

175860= 11/10

175861= 99/100

175862= 25/24

175864= 3/2

175865= 501/500
Explanation
Of the five fractions given, for are greater than 1; that is the
numerators are greater than the denominators. Only one of
the fractions, 99/100, is less than 1, so it must be the least.
Question 15

Which of the following sales commission is greatest?

175944= 1% of \$1,000

175945= 10% of \$200

175946= 12.5% of \$100

175947= 15% of \$100

175948= 25% of \$40
Explanation
The five sales commissions are as follows:
1st choice: 1% of \$1,000 is \$10.
2nd choice 10% of \$200 is \$20.
3rd choice 12.5% of \$100 is \$12.50.
4th choice 15% of \$100 is \$15.
5th choice 25% of \$40 is \$10.
You can rule out certain choices by comparing them to the other
similar choices.
Question 16

If P/5 = Q, then P/10=

175867= 10Q

175868= 2Q

175869= Q/2

175961= Q/10

175962= Q/20
Explanation
Several ways to solve this problem exists.

p/5 = q

Then p=5q, and so P/10 = 5q/10 = q/2
Question 17
R
C is the center of the circle.
Q
Which of the following must
be true?

175949 = QC and RC have the same
C           length
175950=QR and RC have the same
length
175951=QC is perpendicular to QR
175952=QR is perpendicular to RC
175953=ΔQRC is equilateral
Explanation
Since “c” is the center of the circle, “QC” and “RC” are both radii
of the circle and therefore have the same length.
Question 18

In the Venn diagram above, black circle represent the integers 2
to 10, inclusive, and the blue circle represents 6 to 12, inclusive.
How many integers are represented by the intersection?

176015= one, 176016=two, 175930=three, 175931=four, 175932=five, 175933=six
Explanation
In the Venn diagram, the intersection region represents the
integers that are in both the Black and Blue circles that is the
integers that are among the integers 6 through 12, or 6, 7, 8,
9, and 10, which amount to five integers.

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