# PSAT MATH TEST

PSAT Math Test :

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

To find the set of first 10 questions please visit "PSAT math questions"

## Sample Questions on PSAT Math Test - Practice Questions and Solution

Question 11 :

If A  =  3r2h2 and (rh) increases by 100%, then the new A is what times of the old A ?

Solution :

A  =  3r2h2

A  =  3(rh) ----(1)

rh increases by 100%  =  rh + 100% of rh

=  rh + rh

=  2rh

By applying the increase rate in (1)

A  =  3(2rh)2

A  =  3(4r2h2)

A  =  4(3r2h2)

Hence, the new A is 4 times of the old A.

Question 12 :

If xa  =  q√xp, what is p2/q2 ?

Solution :

xa  =  q√xp

xa  =  (xp)1/q

xa  =  xp/q

Since base are equal, powers are also equal

a  =  p/q

Taking squares on both sides, we get

a2  =  (p/q)2

a2  =  p2/q2

Hence the value of p2/q2 is a2.

Question 13 :

Set A  =  {1, 2, 3, a} set B  =  {2, 4, 5, a2, b}, what is AnB ?

Solution :

AnB is the set of common elements of both sets A and B.

AnB  =  { 2 }

Hence the answer is { 2 }.

Question 14 :

2√75 - (√25) (√3)

Solution :

2√75 - (√25) (√3)

=  2√75 - √(253)

=  2√75 - √75

=  √75

=  √(5⋅53)

=  5 √3

Question 15 :

Express 0.0345/10 in scientific notation.

Solution :

0.0345/10

Since we have 10 in the denominator, we have to move the decimal point 1 digit to the left.

0.0345/10   =  0.00345

In order to represent in scientific notation, we have to move the decimal point three digits to the right side.

0.00345  =  3.45 x 10-3

Hence the answer is 3.45 x 10-3.

Question 16 :

If q  =  x + y and x  =  y + z, what is z in terms of y and q ?

Solution :

q  =  x + y -----(1)

x  =  y + z  ----(2)

From (2),

z  =  x - y  ----(3)

From (1),

x  =  q - y

By applying the value of x in (3), we get

z  =  q - y - y

z  =  q - 2y

Question 17 :

y = x3

The only possible values of x are those in the set {-1/3, 1/2, 1/3} what is the maximum value of y ?

Solution :

The largest element of the given set is 1/2. To get the maximum value of y, we have to apply 1/2 instead of x.

y = (1/2)3

y = 1/8

Hence the maximum value of y is 1/8.

Question 18 :

What is (x3y2z4/ (z3y3) equal to ?

Solution :

(x3y2z4/ (z3y3)  =  x3y2-3 z4-3

=  x3y-1 z1

=  x3z/y

Question 19 :

What is the length of RL ? Solution :

To find the length of RL, we have to use the formula for distance between two points.

d  =  √(x2 - x1)2 + (y2 - y1)2

R(0, 3) L(4, 0)

d  =  √(4 - 0)2 + (0 - 3)2

d  =  √42 + 32

d  =  √(16 + 9)  =  √25

d = 5

Question 20 :

In a triangle, the first angle is two times the second angle and the second angle is three times the third angle. Find the measure of the third angle.

Solution :

Let x be the measure of the third angle.

Then,

Measure of the second angle  =  3x

Measure of the second angle  =  2(3x)  =  6x

In a triangle, sum of the three angles is equal to 180°.

Then,

6x + 3x + x  =  180°

10x  =  180°

Divide each side by 10.

x  =  18°

So, the measure of the third angle is 18°. 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 need any other stuff in math, 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 