PSAT ONLINE PRACTICE TEST MATH

Question 1 :

The perimeter of a square is four times the circumference of a circle with radius of 1 m. What is the area of the square ?

(A)  4π  (B)  8π  (C)  4π²  (D)  8π²  (E)  16π²

Solution : 

Perimeter of square  =  4 Circumference of circle

Radius of circle  =  1 m

4a  =  4(2π r)

4a  =  8π(1)

a  =  8π/4  ==>  2π

Area of square  =  a²

  =  (2π)²

  =  4π²

Question 2 :

(A)  24  (B)  66  (C)  67  (D)  68  (E)  1120

Solution :

Since the given shapes are similar, we may equate the corresponding angles.

<a  =  4, <b  =  5, <c  =  7 and <d  =  8

bc + ad  =  5(7) + 4(8)

  =  35 + 32

  =  67

Question 3 :

Convert 3/40 to a decimal.

(A)  0.0075  (B)  0.075  (C)  0.06  (D)  0.75  (E)  7.5

Solution :

To present the given fraction in decimal form, we have to convert the denominator as 10, 100 or 1000 etc.

When we multiply 40 by 25, we get 1000.

  =  (3/40) ⋅ (25/25)

=  75/1000

=  0.075

Question 4 :

For what value of q is 6(q + 3)  =  2(q + 4) ?

(A)  -1/2  (B)  -4/9  (C)  -5/2  (D)  -3  (E)  -2/5

Solution :

6(q + 3)  =  2(q + 4) 

6q + 18  =  2q + 8

6q - 2q  =  8 - 18

4q  =  -10

q  =  -10/4

q  =  -5/2

Question 5 :

What is angle x of the circle O?

(A)  45 degree  (B)  60 degree (C)  75 degree 

(D)  150  degree  (E)  90 degree

Solution :

OA  =  OB  =  r

OA  =  OB (Equal sides makes an equal angle) 

The sum of the angles in a triangle.

x + x + 30  =  180

2x + 30  =  180

2x  =  180 - 30

2x  =  150

x  =  150/2  =  75

Question 6 :

For how many values of x is -3x²/4 > 0

(A)  0  (B)  1   (C)  3  (D)  5  (E)  6

Solution :

For all positive and negative values of x, x² will be positive, but in front 3x²/4 we have negative sign. For no values of x, we will have negative.

Hence the answer is 0.

Question 7 :

x is 40% of y and y is the square of x, which is x ?

(A)  √x  (B)  0.4√x  (C)  0.4x²  (D)  x²  (E)  0.4 x

Solution :

x  =  40% of y  ----(1)

y  =  x² -----(2)

Applying the value of y in (1), we get

x  =  40% of x²

x  =  0.4 x²

Hence the answer is 0.4 x².

Question 8 :

If x  =  7 and 4x (3y - 2x)  =  112, what is the value of y ?

(A)  4  (B)  6  (C)  7  (D)  28  (E)  84

Solution :

By applying x  =  7, we get

4x (3y - 2x)  =  112

4(7) [3y - 2(7)]  =  112

28 (3y - 14)  =  112

3y - 14  =  112/28

3y  - 14  =  4

3y  =  4 + 14 

3y  =  18

y  =  18/3  =  6

Hence the value of y is 6.

Question 9 :

If x ⟩ y  =  (x + y)/(x - y), what is a ⟩ (a - b) ?

(A)  2a/b  (B)  (2a - b)/2a  (C)  (2a - b)/b 

(D)  (2a - b)/2b  (E)  (a + b)/(a - 2b)

Solution :

Given that :

  x ⟩ y  =  (x + y)/(x - y)

We need to find, a ⟩ (a - b).

Here, x  =  a and y  =  a - b

 a ⟩ (a-b)  =  (a + a - b)/(a - (a - b))

=  (2a - b)/(a - a + b)

=  (2a - b)/b

Question 10 :

What is the value of √25 + √64?

(A)  10  (B)  13  (C)  14  (D)  89  (E)  100

Solution :

√25 + √64  =  √(5 ⋅ 5) + √(8 ⋅ 8)

  =  5 + 8

  =  13

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