Praxis I Math Review

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					Praxis I Math Review
     By: Professor Peter Eley
                    Question 1
                  Text answers to 22333
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
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  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
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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
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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
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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
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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
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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
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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
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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
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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
Jordan made two mistakes:
  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
  answer!
                     Question 11
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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
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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
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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
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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
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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
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    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
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        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
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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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