# PSAT MATH PRACTICE TEST QUESTIONS

PSAT Math Practice Test Questions :

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 Math Practice Test

Question 11 :

What is the value of r in the equation 2r  = 102 ?

(A)  5  (B)  10  (C)  25  (D)  50  (E)  100

Solution :

2r  = 102

2r  = 100  ==>  r  =  100/2  ==>  50

Hence the value of r is 50.

Question 12 :

What is the area of a square with a perimeter of 16 ?

(A)  4  (B)  8  (C)  12  (D)  16  (E)  24

Solution :

Perimeter of square  =  16

4a  =  16

a  =  16/4  =  4

Area of square  =  a2

=  42  =  16

Question 13 :

What is 10% of a number whose square is 81 ?

(A)  0.81  (B)  0.9  (C)  8.1  (D)  9  (E)  10

Solution :

Let "x" be the unknown number

Given that:

Square of the unknown number  =  81

x2  =  81

x  =  9

10% of x  =  (10/100) ⋅ 9

=  9/10

=  0.9

Question 14 :

What is the range of the set {1, 2, 5, 10, 6, 12} ?

(A)  -16  (B)  -11  (C)  3  (D)  11  (E)  22

Solution :

To find the range of the given set, we have to subtract the smallest value from the largest value.

Range  =  L - S

Largest value  =  12, Smallest value  =  1

R  =  12 - 1  =  11

Hence the range is 11.

Question 15 :

Nancy found a formula for the area of a square in terms of its perimeter. Let A stand for the area and P for perimeter. What is the formula Nancy found ?

(A)  p2  (B)  p2/8  (C)  p2/4  (D)  p2/16  (E)  4p

Solution :

A - Area of square

P - Perimeter of square = 4a

A  =  a2 and P = 4a  ==> a  =  P/4

Applying the value of a in area of square formula, we get

A  =  (p/4)2  =  P2/16

Question 16 :

Anayet is driving to work from home and realizes he left his wallet at home when he is at workplace. He turns back to retrieve his wallet. His workplace and home are 45 miles apart and it takes him twice as long to get to workplace from his home than the other way around. It is a 30 minutes drive from his workplace to home. What is the average speed for the round trip in miles per minute ?

(A)  0.75   (B)  1.5  (C)  1  (D)  2  (E)  0.5

Solution :

Distance between workplace and home  =  45 miles

Time taken to drive from his workplace to home

=  30 minutes

Given that :

Going back to home, retrieving his wallet and coming back to workplace is twice as long.

Distance covered  =  2(45)  =  90 miles

Time taken  =  30 + 30 + 30  =  90 minutes

Average speed  =  Distance / Time

=  90/90

=  1 minute/mile.

Hence the average speed is 1 minute/mile.

Question 17 :

Given that a vector  =  a2 + a, what is a vector  ÷ a ?

(A)  a  (B)  a + 2  (C)  1  (D)  a + 1  (E)  2a

Solution :

a vector  ÷  a  =  (a2 + a) /a

=  a(a + 1)/a

=  a + 1

Question 18 :

Sarah has a trick coin that has heads on both sides. She asks he friend John, who believes the coin is fair, to guess what face it will land on. If they flip the coin 100 times, how many times bigger is Sarah's expected probability of the coin landing on heads than John's expected probability of the coin landing on heads ?

(A)  0.25  (B)  0.5  (C)  1  (D)  2  (E)  4

Solution :

According to Sarah's belief :

Probability of getting head =  1 (Sure event)

According to John's belief :

Probability of getting head =  1/2

1 is 2 times than 1/2.

Hence 2 times is the answer.

Question 19 :

What is the square of a number that when added to any number does not change that number's value ?

(A)  0  (B)  0.5  (C)  1  (D)  4  (E)  undefined

Solution :

0 is the number, when we add any number to zero, it will become the same number. By squaring 0, we get 0.

Question 20 :

How many non zero numbers are between 3 and 5 ?

(A)  0  (B)  2  (C)  8  (D)  9  (E)  undefined

Solution :

The question is, how many non zero numbers are between 3 and 5.

Note : There are infinite numbers between 3 and 5. If you would like to have more questions on PSAT math, please click on the links given below.

PSAT online practice test math - Paper 1

PSAT online practice test math - Paper 2

PSAT online practice test math - Paper 3

PSAT online practice test math - Paper 5

PSAT online practice test math - Paper 6

PSAT online practice test math - Paper 7

PSAT online practice test math - Paper 8

PSAT online practice test math - Paper 9

PSAT online practice test math - Paper 10

After having gone through the stuff given above, we hope that the students would have understood, how to solve problems in PSAT.

Apart from the stuff given above, if you want to know more about, please use our google custom search here.

You can also visit our following web pages on different stuff in math.

WORD PROBLEMS

Word problems on simple equations

Word problems on linear equations

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation

Word problems on unit price

Word problems on unit rate

Word problems on comparing rates

Converting customary units word problems

Converting metric units word problems

Word problems on simple interest

Word problems on compound interest

Word problems on types of angles

Complementary and supplementary angles word problems

Double facts word problems

Trigonometry word problems

Percentage word problems

Profit and loss word problems

Markup and markdown word problems

Decimal word problems

Word problems on fractions

Word problems on mixed fractrions

One step equation word problems

Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and venn diagrams

Word problems on ages

Pythagorean theorem word problems

Percent of a number word problems

Word problems on constant speed

Word problems on average speed

Word problems on sum of the angles of a triangle is 180 degree

OTHER TOPICS

Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

Time, speed and distance shortcuts

Ratio and proportion shortcuts

Domain and range of rational functions

Domain and range of rational functions with holes

Graphing rational functions

Graphing rational functions with holes

Converting repeating decimals in to fractions

Decimal representation of rational numbers

Finding square root using long division

L.C.M method to solve time and work problems

Translating the word problems in to algebraic expressions

Remainder when 2 power 256 is divided by 17

Remainder when 17 power 23 is divided by 16

Sum of all three digit numbers divisible by 6

Sum of all three digit numbers divisible by 7

Sum of all three digit numbers divisible by 8

Sum of all three digit numbers formed using 1, 3, 4

Sum of all three four digit numbers formed with non zero digits

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6 