Practice the questions given in the worksheet on framing a formula.
I. Frame a formula for each of the following statements:
1. The side ‛s’ of a square is equal to the square root of its area A.
2. The selling price ‛x’ of a article is (1 – 1/10) times its marked price ‛y’ after a discount of 10%.
3. The sum ‛s’ of the first ‛n’ natural numbers is half of the product of ‛n’ and the next natural number.
4. The reciprocal of the focal length ‛f’ equals the sum of the reciprocals of the object distance ‛u’ and the image distance ‛v’.
5. The length ‛l’ of the diagonal of a cube is √3 times the length of an edge measuring ‛p’.
6. The temperature of a body in Fahrenheit ‛F’ is 32 more than nine-fifths of the temperature in centigrade ‛C’.
II. Establish an equation for each of the following statements.
1. One-fifth of a number ‛a’ exceeds one-seventh of the number by 2.
2. The fraction obtained by adding ‛m’ to the numerator and also to the denominator of ¾ equals the fraction obtained by subtracting ‛m’ from both the numerator and denominator of 5/6.
3. A father is 30 year older than his son. After 5 years from now, the age of the father will become four times his son’s age. The present age of the son is ‛y’ years.
4. A two-digit number is 7 more than three times the sum of the digits. If ‛a’ is the digit at the tens place and ‛b’ is the digit at the units place, write an equation in a and b.
5. The sum of a number of two digits and the number obtained by reversing the digits, is 99. Write an equation if the digit at the one’s place is ‛a’ and that at the ten’s place is ‛b’.
Answers for the worksheet on framing a formula are given below:
I. 1. s = √A
2. x = (1 – 1/10)y
3. s = n(n + 1)/2
4. 1/f = 1/u + 1/v
5. l = √3p
6. F = 9/5C + 32
II. 1. a/5 – a/7 = 2
2. 3 + m/4 + m = 5 – m/6 - m
3. 30 + y + 5 = 4(y + 5)
4. 10a + b = 7 + 3(a + b)
5. (10b + a) + (10a + b) = 99