**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"

**Question 11 :**

If A = 3r^{2}h^{2} and (rh) increases by 100%, then the new A is what times of the old A ?

**Solution :**

A = 3r^{2}h^{2}

A = 3(rh)^{2 } ----(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(4r^{2}h^{2})

A = 4(3r^{2}h^{2})

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

**Question 12 :**

If x^{a} = ^{q}√x^{p}, what is p^{2}/q^{2} ?

**Solution :**

x^{a} = ^{q}√x^{p}

x^{a} = (x^{p})^{1/q}

x^{a} = x^{p/q}

Since base are equal, powers are also equal

a = p/q

Taking squares on both sides, we get

a^{2} = (p/q)^{2}

a^{2} = p^{2}/q^{2}

Hence the value of p^{2}/q^{2} is a^{2}.

**Question 13 :**

Set A = {1, 2, 3, a} set B = {2, 4, 5, a^{2}, 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 - √(25⋅3)

= 2√75 - √75

= √75

= √(5⋅5⋅3)

= 5 √3

Hence the answer is 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 = x^{3}

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 (x^{3}y^{2}z^{4}) / (z^{3}y^{3}) equal to ?

**Solution :**

(x^{3}y^{2}z^{4}) / (z^{3}y^{3})^{ } = x^{3}y^{2-3 }z^{4-3}

= x^{3}y^{-1 }z^{1}

= x^{3}z/y

Hence the answer is x^{3}z/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 = √(x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}

R(0, 3) L(4, 0)

d = √(4 - 0)^{2} + (0 - 3)^{2}

d = √4^{2} + 3^{2}

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.

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