Mathematics Part 2

Quadratic Equations Question 1.Check whether the following are quadratic equations:(i) (x + 1)2 = 2(x – 3)(ii) x2 – 2x = (- 2)(3 – x)(iii) (x – 2)(x + 1) = (x – 1)(x + 3)(iv) (x – 3)(2x + 1) = x(x + 5)(v) (2x – 1)(x -3) = (x + 5)(x – 1)(vi) x2 + 3x […]

Pair of Linear Equations in Two Variables Question 1.The ages of two friends Ani and Biju differ by 3 years. Ani’s father Dharam is twice as old as Ani and Biju is twice as old as his sister Cathy.The ages of Cathy and Dharam differ by 30 years. Find the ages of Ani and Biju?

Question 1.Solve the following pairs of equations by reducing them to a pair of linear equations:1. 1/2x + 1/3y = 21/3x + 1/2y = 13/6 2. 2/√x + 3/√y = 24/√x – 9/√y = – 1 3. 4/x + 3y = 143/x – 4y = 23 4. 5/(x−1) + 1/(y−2) = 26/(x−1) – 3/(y−2) = 1 5. (7x−2y)/xy = 5(8x+7y)/xy = 15 6. 6x + 3y = 6xy2x + 4y = 5xy 7. 10/(x+y) + 2/(x−y) = 415/(x+y) – 5/(x−y) = – 2 8. 1/(3x+y) + 1/(3x−y) = 3/41/2(3x+y) – 1/2(3x−y) = −1/8 Solution:1. Taking 1/x = u and 1/y = v, the

Pair of Linear Equations in Two Variables Question 1.Which of the following pairs of linear equations has unique solution, no solution, or infinitely many solutions? In case there is a unique solution, find it by using cross multiplication method.1.  x – 3y – 3 = 03x – 9y – 2 = 0 2. 2x +

Pair of Linear Equations in Two Variables Question 1.Solve the following pair of linear equations by the elimination method and the substitution method: Solution:1. By elimination method:The given system of equations isx +y = 5 ……………….. (1) and2x – 3y = 4 ………………….. (2)Multiplying (1) by 3, we get3x + 3y = 15 ……………….. (3)Adding

Pair of Linear Equations in Two Variables Question 1.Solve the following pair of linear equations by the substitution method:1. x + y = 14x – y = 4 2. s – t = 3s/3 + t/2 = 6 3. 3x – y = 39x – 3y = 9 4. 0.2x + 0.3y = 1.30.4x + 0.5y = 2.3

Question 1.Form the pair of linear equations in the following problems, and find their solution graphically. 1. 10 students of Class X took part in a Mathematics quiz. If the number of girls is 4 more than the number of boys, If the number of girls is 4 more than the number of boys, find

Pair of Linear Equations in Two Variables Question 1.Aftab tells his daughter, “Seven years ago, I was seven times as old as you were then. Also, three years from now, I shall be three times as old as you will be”. (Isn’t this interesting)? Represent this situation algebraically and graphically.Solution:Let us denote the present age

Polynomials Question 1.Verify that the numbers given alongside of the cubic polynomials below are their zeros.Also verify the relationship between the zeroes and the coefficients in each case: Solution:1. Comparing the given polynomial with ax3 + bx2 + cx + d, we geta = 2, b = 1, c = – 5 and d = 2. p(1)

Polynomials Question 1.Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following: Solution:1. Here, dividend and divisor are both in standard forms. So, we have: 2. Here, the dividend is already in the standard form and the divisor is not in the standard form. It can