About "PSAT Practice Test Math"

PSAT Practice Test Math :

Here we are going to see some sample questions for PSAT exams. For each and every questions, you will have solutions with step by step explanation.

PSAT Practice Test Math

PSAT Practice Test Math - Practice questions

Question 11 :

The average of 7 consecutive even integers is 20. What is the median ?

Solution :

Let "x" be the even integer

1st even integer  =  x 

2nd even integer  =  x + 2

3rd even integer  =  x + 4

4th, 5th, 6th, 7th numbers are x + 6, x + 8, x + 10 and  x + 12 respectively.

Average of 7 consecutive even integer 

=  (x + x + 2 + x + 4 + x + 6 + x + 8 + x + 10 + x + 12)/7

20  =  (7x + 42)/7

140  =  7x + 42

7x  =  140 - 42

7x  =  98

x  =  14

Median  =  x + 6  

  =  14 + 6

  =  20

Question 12 :

What is 0.003815 in scientific notation ?

Solution :

In order to convert the given number in scientific notation, we have to move the decimal point to the right side

 0.003815  =  3.815 x 10-3

Question 13 :

In the figure above, what is the length of AC ?

Solution :

Since the given triangle is right triangle, we may use the Pythagorean theorem.

BC2  =  AB2 + AC2

172  =  52 + AC2

AC=  289 - 25

AC2  =  264

AC  =  √264

AC  =  √(2 ⋅ 2 ⋅ 66)

AC  =  2√66

Question 14 :

What time will it be 53 hours after 3 : 30 P.M on Thursday ?

Solution :

First let us divide 53 by 24.

3 : 30 PM - 3 : 30 PM (Thursday - Friday)

3 : 30 PM - 3 : 30 PM (Friday - Saturday)

53  =  2 (24) + 5

5 hours after 3 : 30 P.M on Saturday

8 : 30 PM on Saturday

Question 15 :

If x represents the circumference of the above figure and y represents the area, what is x/y ?

Solution :

Radius of the circle  =  5

Circumference of circle (x) =  2πr  =  2 π (5)  =  10 π

Area of circle (y) =  πr2

x/y  =  10 π/πr2

  =  10/r2

  =  10/52

  =  10/25  =  2/5

Question 16 :

A certain substance has a mass of 98 milligrams. What is the mass of this substance in kilograms ?

Solution :

1 milligram  =  (1/106) kilograms

98  =  98/106 kilogram

  =  9.8 x 101 x 10-6

  =  9.8 x 10-5 kilogram

Question 17 :

Samuel scored a 72, 92 and 80 on his first three exams. What is the minimum score he needs to get an average of 85 ?

Solution :

Let "x" be the required score.

(72 + 92 + 80 + x)/4  =  85

(244 + x)  =  340

x  =  340 - 244

x  =  96

Question 18 :

Five out of 10 marbles in a bag are red. What percentage of the marbles is not red ?

Solution :

Total number of marbles  =  10

Number of red marble  =  5

Percentage of red marble  =  (5/10) x 100 %

  =  50%

What percentage of the marbles it is not red  =  50%

Question 19 :

In the figure above, the rectangle ABCD is inscribed in the circle.Where E is the center and the radius is 5. If the length of BD is 6, what is the area of rectangle ABCD ?

Solution :

In order to find the area of rectangle, we must know the dimension of rectangle.

width of rectangle  =  6

radius of circle  =  5 (EB)

EB  =  EC   =  5  

CB  =  10

In right triangle CDB,

CB2 = CD2 + DB2

102 = CD2 + 62

100 - 36 = CD2

CD=  64

CD  =  8 (length of rectangle)

Area of rectangle  = length (width)

  =  8 (6)  =  48

Question 20 : 

 √81 √25 + √16  =  

Solution :

  =  √81 √25 + √16

  =  √(9 ⋅ 9) √(5 ⋅ 5) + √(4 ⋅ 4)

  =  (9 ⋅ 5) + 4

  =  45 + 4

  =  49

Hence the answer is 49.

After having gone through the stuff given above, we hope that the students would have understood "PSAT Practice Test Math". 

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