#### Term 1 Algebra Five Marks Questions

9th Standard

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Maths

Time : 01:00:00 Hrs
Total Marks : 50
10 x 5 = 50
1. The cost of a chocolate is Rs. (x + y) and Amir bought (x + y) chocolates. Find the total amount paid by him in terms of x and y. If x =10, y =5 find the amount paid by him.

2. The length of a rectangle is (3x+2) units and it’s breadth is (3x–2) units. Find its area in terms of x. What will be the area if x = 20 units.

3. If two polynomials 2x3 + ax2 + 4x – 12 and x3 + x2 –2x+ a leave the same remainder when divided by (x – 3), find the value of a and also find the remainder.

4. If the polynomials f(x) = ax3 + 4x2 + 3x –4 and g(x) = x3 – 4x + a leave the same remainder when divided by x–3, find the value of a. Also find the remainder.

5. Classify the following polynomials.

S.No Polynomial Based on number of terms Based on their degree
1 $\frac { { x }^{ 2 } }{ \sqrt { 2 } } +x+1$
2 $\sqrt { 5 } { x }^{ 2 }-\frac { 6 }{ 5 } x$
3 1
4 ${ m }^{ 4 }-\frac { 6 }{ 7 } { m }^{ 2 }-6m+2.7$
5 $\frac { { t }^{ 3 } }{ \sqrt { 6 } } +\frac { { t }^{ 4 } }{ 4 } -t$
6. Find the quotient and remainder when  5x3 - 9x2 + 10x + 2 is divided by x + 2 using synthetic division

7. Find the quotient and remainder when 4x3 + 6x2 + 7x + 2 is divided by x - 2

8. Find the quotient and remainder when 5x3 + 7x2 + 3x + 2 is divided by 3x + 2

9. Factorise  2x3- x2 - 12x - 9 into linear factors

10. Prove that x -1 is a factor x5 - 45x4 + 36x3 + 45x2 - 36x-1