9th Standard Syllabus & Materials
9th Standard
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Published on: 06/09/2019
Term 2 Algebra
Download Tamil Nadu 9th Standard Maths question papers, model tests, one-mark questions, important questions, and public exam papers in PDF format. Free study materials and answer keys for TN State Board students.
Questions + Answers key
Take MCQ Maths Test1.
Expand the following: (2a-3b+4c)2
2.
Expand the following: (x+2y+3z)2
3.
Expand (a -b +c)2
4.
If the quotient obtained on dividing (8x4- 2x2 + 6x - 7) by (2x +1) is (4x3+ px2- qx + 3), then find p, q and also the remainder.
5.
Find the quotient and remainder when (3x3- 4x2- 5) is divided by (3x + 1) using synthetic division
6.
Find the area of square whose side length is 3m +2n −4l.
7.
Factorise 2x2 - 15x - 27
8.
Simplify: \(\left[ \frac { ({ x }^{ 2 }-{ y }^{ 2 })^{ 3 }+({ y }^{ 2 }-{ z }^{ 2 })^{ 3 }+({ z }^{ 2 }-{ x }^{ 2 })^{ 3 } }{ (x-y)^{ 3 }+(y-z)^{ 3 }+(z-x)^{ 3 } } \right] \) by using identity
9.
Cubic polynomial may have maximum of ________ linear factors.
1
2
3
4
10.
If (x + 5) and (x - 3) are the factors of ax2+bx+c, then values of a, b and c are _______.
1, 2, 3
1, 2,15
1, 2, −15
1, −2,15
11.
If x - 3 is a factor of p(x), then the remainder is _______.
3
-3
p(3)
p(-3)
12.
Which of the following has x -1 as a factor?
2x -1
3x -3
4x -3
3x -4
13.
If p(a)= 0 then (x-a) is a _____ of p(x).
divisor
quotient
remainder
factor
1.
(2a-3b+4c)2= (2a+(-3b)+4c)2 = (2a)2+(-3b)2+(4c)2+2(2a)(-3b)+2(-3b)(4c)+2(4c)(2a)
= 4a2+9b2+16c2+(-12ab)+(-24bc)+16ca
= 4a2+9b2+16c2-12ab-24bc+16ca
2.
(a+b+c)2= a2+ b2+ c2+ 2ab + 2bc + 2ca
роГ (x + 2y + 3z)2= (x)2+(2y)2+(3z)2+2(x)(2y)+2(2y)(3z)+2(3z)(x)
= x2 + 4y2 + 9z2 + 4xy + 12yz + 6xz
3.
Replacing ‘b’ by ‘-b ’ in the expansion
(a+b+c)2 = a2+ b2+ c2+ 2ab + 2bc + 2ca
(a+(-b)+c)2 = a2+(-b)2+ c2+ 2a(-b) + 2(-b)c+ 2ca
= a2+ b2- 2ab - 2bc + 2ca
4.
Let p(x) = 8x4- 2x2 + 6x-7
Standard form = 8x4+ 0x3- 2x2+ 6x - 7
Co-efficients are 8 0 - 2 6 -7
Q(x) = 2x+1,
To find zero of 2x + 1, put 2x + 1 = 0; 2x = -1, x = \(-\frac{1}{2}\)
Synthetic division
Quotient = \(\frac{1}{2}\)[8x3-4x2+6] = 4x3-2x2+3
Quotient 4x3 - 2x2 + 3 is compared with the given quotient 4x3-px2-qx+3
Co-efficients of x2 is p = -2
Co-efficients of x is q = 0
Remainder is - 10
5.
Let p(x) = 3x3- 4x2- 5
d(x) = (3x+1)
Standard form of p(x) = 3x3- 4x2+ 0x - 5 and d(x) = 3x + 1
To find the zero of 3x+1;
put 3x + 1 = 0 we get 3x = –1
x = \(-\frac{1}{3}\)
\(3x^3-4x^2-5-\left(x+{1\over 3}\right)\left(3x^2-5+{5\over 3}\right)-{50\over 9}\)
\(3x^3-4x^2-5={(3x+1)\over 3}\times3\left(x^2-{5\over3}x+{5\over9}\right)-\left(50\over9\right)\)
\(=(3x+1)\left(x^2-{5\over3}x+{5\over9}\right)-\left(50\over9\right)\) (since, p(x) = d(x) q(x) + r
Hence the quotient is \(\left(x^2-{5\over3}x+{5\over9}\right)\) and remainder is \(-50\over 9\)
6.
Area of square = side x side
= (3m +2n −4l) \(\times\)(3m +2n −4l) [substituting a = 3m, b = 2n, c = -4l]
= (3m+2n-4l)2
We know that, (a+b+c)2 = a2+b2+c2+2ab+2bc+2ca
[3m+2n+(-4l)]2 = (3m)2+(2n)2+(-4l)2+2(3m)(2n) +2(2n)(-4l)+2(-4l)(3m)
= 9m2+4n2+16l2+12mn-16ln-24lm
Therefore, Area of square = [9m2+4n2+16l2+12mn -16ln - 24lm] sq.units.
7.
Compare with ax2 + bx + c
Here, a = 2, b = -15, c = −27
product ac = 2\(\times\) –27 = –54, sum b = –15
| Product of numbers ac = -54 |
Product of numbers b = 15 |
Product of numbers ac = -54 |
Product of numbers b = 15 |
| -1 \(\times\) 54 | 53 | 1 \(\times\) -54 | -53 |
| -2 \(\times\) 27 | 25 | 2 \(\times\) -27 | -25 |
| -3 \(\times\) 18 | 15 | 3\(\times\) -18 | -15 |
| -6 \(\times\) 9 | 3 | 6 \(\times\) -9 | -3 |
The required factors are 3 and -18
∴ we split the middle term as –18x and 3x
2x2 - 15x -27 = 2x2 - 18x + 3x - 27
= 2x (x − 9) + (3x − 9)
= (x - 9) (2x + 3)
Therefore, (x − 9) (2x + 3) and are the factors of 2x2 - 15x - 27
8.
Let \(\frac{(x^2-y^2)^3+(y^2-z^2)^3+(z^2-x^2)^3}{(x-y)^3+(y-z)^3+(z-x)^3}\) ...(1)
(x2-y2)3+(y2-z2)3+(z2-x2)3=3(x2-y2)(y2-z2)(z2-x2)
(x-y)3+(y-z)3+(z-x)3=3(x-y)(y-z)(z-x)
=(x+y)(y+z)(z+x)
9.
(c)
3
10.
(c)
1, 2, −15
11.
(c)
p(3)
12.
(b)
3x -3
13.
(d)
factor
9th Standard Syllabus & Materials
9th Standard
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NEW9th Standard
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Tamilnadu Stateboard 9th Standard Subjects
Tamilnadu Stateboard Standards
