# Frank solutions for Class 9 Maths ICSE chapter 6 - Changing the subject of a formula [Latest edition]

## Chapter 6: Changing the subject of a formula

Exercise 6.1Exercise 6.2Exercise 6.3
Exercise 6.1

### Frank solutions for Class 9 Maths ICSE Chapter 6 Changing the subject of a formula Exercise 6.1

Exercise 6.1 | Q 1

The simple interest on a sum of money is the product of the sum of money, the number of years and the rate percentage. Write the formula to find the simple interest on Rs A for T years at R% per annum.

Exercise 6.1 | Q 2

The volume V, of a cone is equal to one third of π times the cube of the radius. Find a formula for it.

Exercise 6.1 | Q 3

The fahrenheit temperature, F is 32 more than nine -fifths of the centigrade temperature C. Express this relation by a formula.

Exercise 6.1 | Q 4

The arithmetic mean M of the five numbers a, b, c, d, e is equal to their sum divided by the number of quantities. Express it as a formula.

Exercise 6.1 | Q 5

Make a formula for the statement:"The reciprocal of focal length f is equal to the sum of reciprocals of the object distance u and the image distance v."

Exercise 6.1 | Q 6

Make a formula for the statement:"The number of diagonals, d, that can be drawn from one vertex of an n sided polygon to all the other vertices is equal to the number of sides of the polygon less 3"

Exercise 6.1 | Q 7

The area A of a circular ring is π times the difference between the squares of outer radius R and inner radius r. Make a formula for this statement.

Exercise 6.1 | Q 8

A man bought 25a articles at 30p paisa each and sold them at 20q paisa each. Find his profit in rupees.

Exercise 6.1 | Q 9

How many minutes are there in x hours, y minutes and z seconds.

Exercise 6.1 | Q 10

Apple cost x rupees per dozen and mangoes cost y rupees per score. Write a formula to find the total cost C in rupees of 20 apples and 30 mangoes.

Exercise 6.2

### Frank solutions for Class 9 Maths ICSE Chapter 6 Changing the subject of a formula Exercise 6.2

Exercise 6.2 | Q 1

Make R the subject of formula A = "P"(1 + "R"/100)^"N"

Exercise 6.2 | Q 2

Make L the subject of formula T = 2pisqrt("L"/"G")

Exercise 6.2 | Q 3

Make a the subject of formula S = "ut" + (1)/(2)"at"^2

Exercise 6.2 | Q 4

Make x the subject of formula "a"x^2/"a"^2 + y^2/"b"^2 = 1

Exercise 6.2 | Q 5

Make a the subject of formula S = ("a"("r"^"n" - 1))/("r" - 1)

Exercise 6.2 | Q 6

Make r2 the subject of formula (1)/"R" = (1)/"r"_1 + (1)/"r"_2

Exercise 6.2 | Q 7

Make a the subject of formula x = sqrt(("a" + "b")/("a" - "b")

Exercise 6.2 | Q 8

Make y the subject of formula W = "pq" + (1)/(2)"wy"^2

Exercise 6.2 | Q 9

Make N the subject of formula I = "NG"/("R" + "Ny")

Exercise 6.2 | Q 10

Make V the subject of formula K = (1)/(2)"MV"^2

Exercise 6.2 | Q 11

Make d the subject of formula S = "n"/(2){2"a" + ("n" - 1)"d"}

Exercise 6.2 | Q 12

Make R2 the subject of formula R2 = 4π(R12 - R22)

Exercise 6.2 | Q 13

Make A the subject of formula R = ("m"_1"B" + "m"_2"A")/("m"_1 + "m"_2)

Exercise 6.2 | Q 14

Make c the subject of formula x = (-"b" ± sqrt("b"^2 - 4"ac"))/(2"a")

Exercise 6.2 | Q 15

Make k the subject of formula T = 2pisqrt(("k"^2 + "h"^2)/"hg"

Exercise 6.2 | Q 16

Given: mx + ny = p and y = ax + b. Find x in terms of m, n, p, a and b.

Exercise 6.2 | Q 17

If A =  pr2 and C = 2pr, then express r in terms of A and C.

Exercise 6.2 | Q 18

If V = pr2h and S = 2pr2 + 2prh, then express V in terms of S, p and r.

Exercise 6.2 | Q 19

If 3ax + 2b2 = 3bx + 2a2, then express x in terms of a and b. Also, express the result in the simplest form.

Exercise 6.2 | Q 20

If b = (2"a")/("a" - 2), and c = (4"b" - 3)/(3"b" + 4), then express c in terms of a.

Exercise 6.3

### Frank solutions for Class 9 Maths ICSE Chapter 6 Changing the subject of a formula Exercise 6.3

Exercise 6.3 | Q 1

Make h the subject of the formula R = "h"/(2)("a" - "b"). Find h when R = 108, a = 16 and b = 12.

Exercise 6.3 | Q 2

Make s the subject of the formula v2 = u2 + 2as. Find s when u = 3, a = 2 and v = 5.

Exercise 6.3 | Q 3

Make y the subject of the formula x = (1 - y^2)/(1 + y^2). Find y if x = (3)/(5)

Exercise 6.3 | Q 4

Make a the subject of the formula S = "n"/(2){2"a" + ("n" - 1)"d"}. Find a when S = 50, n = 10 and d = 2.

Exercise 6.3 | Q 5

Make x the subject of the formula a = 1 - (2"b")/("cx" - "b"). Find x, when a = 5, b = 12 and

Exercise 6.3 | Q 6

Make h the subject of the formula K = sqrt("hg"/"d"^2 - "a"^2. Find h, when k = -2, a = -3, d = 8 and g = 32.

Exercise 6.3 | Q 7

Make x the subject of the formula y = (1 - x^2)/(1 + x^2). Find x, when y = (1)/(2)

Exercise 6.3 | Q 8

Make y the subject of the formula x/"a" + y/"b" = 1. Find y, when a = 2, b = 8 and x = 5.

Exercise 6.3 | Q 9

Make m the subject of the formula x = "my"/(14 - "mt"). Find m, when x = 6, y = 10 and t = 3.

Exercise 6.3 | Q 10

Make I the subject of the following M = "L" /"F"(1/2"N" - "C") xx "I". Find I, If M = 44, L = 20, F = 15, N = 50 and C = 13.

Exercise 6.3 | Q 11

Make g the subject of the formula v2 = u2 - 2gh. Find g, when v = 9.8, u = 41.5 and h = 25.4.

Exercise 6.3 | Q 12

Make f the subject of the formula D = sqrt((("f" + "p")/("f" - "p")). Find f, when D = 13 and P = 21.

Exercise 6.3 | Q 13

Make z the subject of the formula y = (2z + 1)/(2z - 1). If x = (y + 1)/(y - 1), express z in terms of x, and find its value when x = 34.

Exercise 6.3 | Q 14

Make c the subject of the formula a = b(1 + ct). Find c, when a = 1100, b = 100 and t = 4.

Exercise 6.3 | Q 15

"The volume of a cylinder V is equal to the product of π and square of radius r and the height h". Express this statement as a formula. Make r the subject formula. Find r, when V = 44cm3, π = (22)/(7), h = 14cm.

Exercise 6.3 | Q 16

"The volume of a cone V is equal to the product of one third of π and square of radius r of the base and the height h". Express this statement as a formula. Make r the subject formula. Find r, when V = 1232cm3, π = (22)/(7), h = 24cm.

Exercise 6.3 | Q 17

The pressure P and volume V of a gas are connected by the formula PV = C; where C is a constant. If P = 4 when V = 2(1)/(2); find the value of P when V = 4?

Exercise 6.3 | Q 18.1

The total energy E possess by a body of Mass 'm', moving with a velocity 'v' at a height 'h' is given by: E = (1)/(2) "m" "u"^2 + "mgh". Make 'm' the subject of formula.

Exercise 6.3 | Q 18.2

The total energy E possess by a body of Mass 'm', moving with a velocity 'v' at a height 'h' is given by: E = (1)/(2) "m" "u"^2 + "mgh". Find m, if v = 2, g = 10, h = 5 and E = 104.

Exercise 6.3 | Q 19

If s = "n"/(2)[2"a" + ("n" - 1)"d"], the n express d in terms of s, a and n. find d if n = 3, a = n + 1 and s = 18.

Exercise 6.3 | Q 20

"Area A oof a circular ring formed by 2 concentric circles is equal to the product of pie and the difference of the square of the bigger radius R and the square of the bigger radius R and the square of the smaller radius r. Express the above statement as a formula. Make r the subject of the formula and find r, when A = 88 sq cm and R = 8cm.

## Chapter 6: Changing the subject of a formula

Exercise 6.1Exercise 6.2Exercise 6.3

## Frank solutions for Class 9 Maths ICSE chapter 6 - Changing the subject of a formula

Frank solutions for Class 9 Maths ICSE chapter 6 (Changing the subject of a formula) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the CISCE Class 9 Maths ICSE solutions in a manner that help students grasp basic concepts better and faster.

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Concepts covered in Class 9 Maths ICSE chapter 6 Changing the subject of a formula are Changing the Subject of a Formula.

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