ACT Practice Paper1 Solution2

In this page ACT practice paper1 solution2 we are going to see solution of some practice questions.

Question 5:

Factorize 4 (a + b)² - 9

Solution:

To factorize this we can write the given question in the form of square.

                   = 4 (a + b)² - 9

                   = 2² (a + b)² - 3²

                   = [2 (a + b)]² - 3²

This looks like the formula a² - b². Expansion of a²-b²=(a + b) (a - b)

                   = [2 (a + b) + 3] [2 (a + b) - 3]                   


Question 6:

Find the median of the data 78,56,22,34,45,54.39,68,54,84.

Solution:

To find the median first we have to arrange the numbers in ascending order.Arranging the data in the ascending order we get 22,34,39,45,54,54,56,68,78,84.

Here the total number of terms (n) = 10,and even number

Median = [(n/2)th term + (n/2)+ 1 th term]/2

n = 10

         = [(10/2)th term + (10/2)+ 1 th term]/2

         = (5th term + 6th term]/2

need to select the numbers from the ascending order.

5th term = 54

6th term = 54

         = (5th term + 6th term]/2

         = (54 + 54)/2

         = 108/2

         = 54

Therefore the median is 54.


Question 7:

A person earns $ 2,400 per month. He saves 15% of his salary. How much does he save?

Solution:

Earning of a person = $ 2,400

Since he is saving 15% of his salary.

            his saving amount = 15% of 2400

                                        = (15/100) x 2400

                                        = 15 x 24

                                        = $ 360

So he is saving $ 360 per month.


Question 8:

Find the slope of line 3 x + 2 y - 12 = 0.

The given equation is in the form a x + b y + c = 0. Then the required formula to find the slope of the line is m = -coefficient of x/coefficient of y

From the given equation the coefficient of x is 3 and the coefficient of y is 2

                  m = -3/2

Therefore the required slope is -3/2.

ACT practice paper1 solution2 ACT practice paper1 solution2