PSAT PRACTICE QUESTIONS MATH

PSAT Practice Questions Math :

In this section, we are going to see some PSAT math practice questions.

Sample Questions on PSAT Math - Practice Questions

Please visit the page "PSAT Math Questions and Answers" to find thefirst 10 questions.

PSAT Practice Questions Math :

Question 11 :

(-39)2/133

Solution :

=  (-39)2/133

Since we have even power, so the negative sign will become positive.

=  (39 ⋅ 39) / (13 ⋅ 13 ⋅ 13)

=  (3 ⋅ 3) / 13

=   9/13

Question 12 :

In a scaled diagram, 1 inch represents 20 feet. How many square inches on the diagram represent 1 square foot ?

Solution :

1 inch  =  20 feet

1 feet  =  1/20 inch

1 square foot  =  (1/20)2

=  1/400

=  0.0025

Hence 0.0025 square inches represents 1 square foot.

Question 13 :

What is the greatest common factor of 2,240 and 3,360 ?

Solution :

To find the greatest common factor, we have to decompose the given numbers into the prime factors until we get prime numbers. To find the greatest common divisor, take all the common divisors of 2240 and 3360 and multiply them.

Greatest common factor  =  5 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 7

=  1120

Question 14 :

If 50% of 2y is 12, what is y2 ?

Solution :

50% of 2y  =  12

(50/100) ⋅ (2y)  =  12

(1/2) ⋅ (2y)  =  12

y  =  12

y2  =  12==>  144

Hence the value of y2 is 144.

Question 15 :

(15)  In the figure given below ∢ PRL is 150 degree. What is (a2 - b2)/(a - b) ? Solution :

To find the value of  (a2 - b2)/(a - b), first let us simplify this using algebraic identities.

(a2 - b2)/(a - b)  =  (a + b)(a - b)/(a - b)

(a2 - b2)/(a - b)  =  a + b

From the given picture, we have

<PRL  =  150

<PRL  =  <RPQ + <PQR

150  =  a + b

Hence the value of a + b is 150.

Question 16 :

If y = 3/4 and xy2  =  9/16, what is (x - 4)?

Solution :

Given that :

y = 3/4 and xy2  =  9/16

x(3/4)2  =  9/16

x(9/16)  =  9/16

x  =  1

then x - 4  =  1 - 4  =  -3

Hence the value of x - 4 is -3

Question 17 :

If P is an odd integer, which of the following must be an even number ?

Solution :

By observing the options, D is having an even number in the denominator. So we might have even number in the numerator.

Even number / even number  =  even number

Hence   (2p2 - 2P3) / 2P is the even number.

Question 18 :

If the diameter of a circle is P, and P2/4  =  2, what is the area of the circle ?

Solution :

Diameter of the circle  =  P

Radius of the circle  =  P/2

Area of the circle  =  π r2

=   π (P/2)2

=   π (P2/4)

=  2π

Hence the required area of the circle is 2π.

Question 19 :

If a regular polygon has (N - 10) sides, where, N = (40/10)2, what is the measure of one of its angles?

Solution :

N = (40/10)==>  4=  16

Number of sides in the given polygon

N - 10  ==>  16 -  10  =  6

So, the given polygon has 6 sides, it is hexagon.

Sum of the angles of a polygon  =  (n - 2) 180

=  (6 - 2) 180

=  4 (180)

=  720

Angle measure  =  720/6

=  120 degree

Question 20 : If the perimeter of the triangle shown above is the circumference of a circle, then what is the radius of the circle?

Solution :

Perimeter of triangle  =  Sum of lengths of all sides

Let "x" be the length of unknown side.

(5π)2  =  (4π)2 + x2

25π2 - 16π =  x2

x =  9π2

x  =  3π

Perimeter of triangle  =  3π + 5π + 4π

Circumference of circle  =  12 π

2π r  =  12π

r  =  6

Hence the radius of circle is 6 After having gone through the stuff given above, we hope that the students would have understood, how to solve math problems in PSAT.

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WORD PROBLEMS

Word problems on simple equations

Word problems on linear equations

Word problems on quadratic 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 