**SHSAT Practice Questions With Answers :**

Here we are going to see some practice questions of SHSAT exams.

**Question 1 :**

For how many values of x is the function is not equal to 1 ?

f(x) = (x - 3)/(x - 3)

**Solution :**

The terms in the numerator and denominator are same, we always get 1 for f(x) by applying any value of x.

Hence the answer is undefined.

**Question 2 :**

If today is Monday, what day will it be in 49^{2} from now?

**Solution :**

First let us find the value of 49^{2}

49^{2 }= 49 ⋅ 49 = 2401

To find the day after 2401 days from now, we have to divide 2401 by 7 to get the remainder.

By dividing 2401 by 7, we get 0 as remainder. According day arithmetic 0 stands for Sunday. Hence the day after 2401 from now is Sunday.

**Question 3 :**

If f(x) = x^{3}, then how many times greater is f(4) then f(2) ?

**Solution :**

To find how many times f(4) greater than f(2), first let us find the values of f(4) and f(2).

f(x) = x f(4) = 4 f(4) = 64 |
f(x) = x f(2) = 2 f(2) = 8 |

f(4) / f(2) = 64/8

= 8

Hence f(4) is 8 times greater than f(2).

**Question 4 :**

Convert 3/40 to a decimal.

**Solution :**

Inorder to convert 3/40 into decimal, let us convert the denominator as 100, 1000 etc.

For that, we have to multiply both numerator and denominator by 25.

(3/40) ⋅ (25/25) = 75/1000

= 0.075

**Question 5 :**

How many prime numbers are between 4 and 16 inclusive ?

**Solution :**

4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16

Prime numbers are 5, 7, 11, 13

Hence the number of prime numbers between 4 and 16 is 4.

**Question 6 :**

How many perfect squares are between 9 and 25 exclusive.

**Solution :**

9, 16, 25

Hence the number of perfect square between 1.

**Question 7 :**

An octagon, a triangle and a circle all have same perimeter (circumference for the circle). Which is true of the areas of these shapes? (O=area of octagon, T= area of triangle and C = area of circle)

**Solution :**

Given that :

Perimeter of octagon = perimeter of triangle = perimeter of circle

Note : The more sides of the figure have more area.So,

Area of octagon is largest than area of triangle.

Area of triangle is more than area of circle.

Hence the correct answer is C > O > T.

**Question 8 :**

If (x/y) = x^{2}, then what is (x/y) - (x/y)^{2} ?

**Solution :**

(x/y) - (x/y)^{2 }= x^{2} - (x^{2})^{2}

= x^{2} - x^{4}

= x^{2} (1 - x^{2})

Question 9 :

In scaled drawing, 1 millimeter represents 150 meters. How many square millimeters on the drawing represent 1 square meter ?

Solution :

If 1 mm represents 150 m, then 1 sq.mm represents 22,5 00 sq.m.

1 sq.m = (1/22500) sq.mm

**Question 10 :**

A rectangle is drawn on the coordinate plane. If the coordinates of one corner of the rectangle is (0, -5) and the coordinates of the opposite corner is (7, 3), then what is the area of the rectangle ?

**Solution :**

To solve this problem, first let us draw a rectangle in a coordinate plane with given conditions.

From the given picture, the length of rectangle is 7 units and width of the rectangle is 8 units.

Area of rectangle = length (width)

= 7(8)

= 56 square inches.

After having gone through the stuff given above, we hope that the students would have understood, "SHSAT Practice Questions With Answers".

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