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

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 the following web pages on different stuff in math. 

WORD PROBLEMS

HCF and LCM  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