Quiz on Number Sense

Play this quiz on NUMBER SENSE. Check how much do you know??

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Substitution method-Pair of linear equations in two variables- Class 10

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A very nice explanation of the concept is here!!!

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Solve the following pairs of linear equations in two variables by Substitution method.
1.) x = - 5y - 53 x + 3y = - 35
2.) y = - 2x + 22 - x = 10 - 3y
3.) x = - 3y + 27 x = - 4y + 35
4.) x = - 5y - 12 x = - 2y + 0
5.) - 5y - 5x = 35 y = - 2x - 17
6.) y = - x - 17 - x = -1 - y
7.) y + x = 2 y = x + 4
8.) x = - 5y + 50 x - 4y = - 40
9.) y = - 5x + 40 5x = 40 - 3y
10.) x = y + 2 x + 5y = 44

Splitting the middle term of a quadratic polynomial

This task is based on the concept of factorising a quadratic polynomial by splitting the middle term.

Example Factorise by splitting the middle term x^2 + 6x + 8

Solution:

Step 1: Observe the product of coefficient of x^2 and constant term. It is (1)(8) = 8

Step 2: Observe the coefficient of x. It is 6

Step3: Think of two numbers whose product is 8 and sum is 6.
2x4 = 8
2+4 = 6

Step 4: Write 6x = 2x+4x
x^2 + 6x+ 8
=x^2 + 2x + 4x + 8

Step 5: Take out the common factors as shown below
x(x + 2) + 4(x + 2)

=(x + 4)(x + 2)

Watch this Interactive lesson

Watch this Video for explanation:


Factorise the following by splitting the middle term:
1. 1 - 6x + 9x^2
2.x^2 - 7x – 18
3. 4x^2 + 5x + 1
4. x^2 + 4x + 3
5.2x^2 + 3x + 1
6. 4x^2 + 8x + 3
7. x^2 + 7x +12

Questions on Remainder theorem and Factor theorem : Polynomials class 9

Remainder theorem: Let P(x)be a polynomial of degree greater or equal to 1. Let a be any real number. If P(x) is divided by (x-a) then the remainder is P(a).

Factor Theorem :Let P(x)be a polynomial of degree greater or equal to 1. Let a be any real number.
(1) If (x-a) is a factor of P(x) then P(a)=0
(2) If P(a) = 0 then (x-a) is a factor of P(x)

For understanding the concept click here!!!
Do the following questions in your note book.

Q1 Using Remainder theorem, find the remainder when P(x) = 3x^2+ 5x − 8 is divided by
(x − 2).
Q2 By using the remainder theorem, find the remainder when 3x^3 − x^2 − 20x + 5 is divided by (x + 4).
Q3 Is (x + 1) a factor of f(x) = x^3+ 2x^2 - 5x - 6 ?
Q4 Use the factor theorem to find if (x - 2) is a factor of
P(x) = x^5 - 2x^4 + 3x^3 - 6x^2 - 4x + 8.

Also, practice atleast 10 questions based on Remainder theorem from here in your notebook.

Solve by elimination method- Pair of linear equations in tqo variables- Class 10

Example 1 9x-4y=2000 …..(1) 7x-3y=2000 …..(2) Multiplying equation (1) by 3 and equation (2) by 4 we get 27x-12y=6000 …..(3) 28x-12y=8000 …..(4) Eliminate y by subtracting equation (3) from equation (4) (28x-27y)-(12y-12y)=8000-6000 x= 2000 …..(5) Put value of x from equation(5) in (1) to get y y= 4000

Ans x= 2000, y=4000

Example 2

Can we solve the given pair of equations ?

2x+3y=8 4x+6y=7

2x+3y=8 …..(1) 4x+6y=7…..(2) Multiplying equation (1) by 2 and equation (2) by 1 we get 4x+6y=16 ….(3) 4x+6y=7 …..(4) Eliminate y by subtracting equation (4) from equation (3) (4x-4y)-(6y-6y)=16-7 0= 9 …..(5) It is a false statement. So, no solution

Solve the following pairs of linear equations in two variables by elimination method. 1.) - 4x + y = - 30 4x - 3y = 34 2.) 2x + 4y = 52 - 2x + y = - 12 3.) - 3x + 2y = 0 - 2x + 2y = 4 4.) x + 4y = - 30 x + 5y = - 40 5.) x + 4y = 3 - x - 2y = - 5 6.) 5x - 2y = - 22 5x - 3y = - 28 7.) 3x + y = 22 x - 2y = 5 8.) - 4x - 3y = - 26 - 8x + 5y = 14 9.) 4x - 5y = 47 x + 4y = - 4 10.) - 3x + y = - 9 3x - 5y = - 3 11.) 4x + 5y = - 17 2x + 5y = - 21 12.) - 3y + 5x = - 57 y = 4x + 33 13.) - 5x = - y - 29 x = 5y + 1 14.) y = 5x - 5 - 4x = - 4 + 3y