**PSAT Practice Questions Math :**

In this section, we are going to see some 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}/13^{3}

**Solution :**

= (-39)^{2}/13^{3}

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 y^{2} ?

**Solution :**

50% of 2y = 12

(50/100) ⋅ (2y) = 12

(1/2) ⋅ (2y) = 12

y = 12

y^{2} = 12^{2 }==> 144

Hence the value of y^{2 }is 144.

**Question 15 :**

(15) In the figure given below ∢ PRL is 150 degree. What is (a^{2} - b^{2})/(a - b) ?

**Solution :**

To find the value of (a^{2} - b^{2})/(a - b), first let us simplify this using algebraic identities.

(a^{2} - b^{2})/(a - b) = (a + b)(a - b)/(a - b)

(a^{2} - b^{2})/(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 xy^{2} = 9/16, what is (x - 4)?

**Solution :**

Given that :

y = 3/4 and xy^{2} = 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 (2p^{2} - 2P^{3}) / 2P is the even number.

**Question 18 :**

If the diameter of a circle is P, and P^{2}/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 r^{2}

= π (P/2)^{2}

= π (P^{2}/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)^{2 }==> 4^{2 }= 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} + x^{2}

25π^{2 }- 16π^{2 } = x^{2}

x^{2 } = 9π^{2}

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.

Apart from the stuff given in this section, please use our google custom search here.

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