9th Standard Syllabus & Materials
9th Standard
TN 9ஆம் வகுப்பு கணிதம் ஆயத்தொலை வடிவியல்,முக்கோணவியல் முக்கியமான 2,3,&5 மதிப்பெண் வினாக்கள் விடைகளுடன் TN 9th Maths Coordinate Geometry,Trigonometry Important 1 Mark Questions with Answers 2,3,&5 Marks Questions with Answers
NEW9th Standard
TN 9ஆம் வகுப்பு கணிதம் அளவியல்,புள்ளியியல்&நிகழ்தகவு முக்கியமான 2,3,&5 மதிப்பெண் வினாக்கள் விடைகளுடன் TN 9th Maths Mensuration,Statistics&Probability Important 1 Mark Questions with Answers 2,3,&5 Marks Questions with Answers.
NEW9th Standard
TN 9ஆம் வகுப்பு சமூக அறிவியல் வரலாறு - செவ்வியல் உலகம் முக்கியமான 2,3,&5 மதிப்பெண் வினாக்கள் விடைகளுடன் TN 9th Social Science HIS - The Classical World Important 1 Mark Questions with Answers 2,3,&5 Marks Questions with Answers.
NEW9th Standard
TN 9ஆம் வகுப்பு சமூக அறிவியல் வரலாறு - தொடக்ககாலத் தமிழ்ச் சமூகமும் பண்பாடும்முக்கியமான 2,3,&5 மதிப்பெண் வினாக்கள் விடைகளுடன் TN 9th Social Science HIS - Early Tamil Society and Culture Important 1 Mark Questions with Answers 2,3,&5 Marks Questions with Answers.
NEW9th Standard
TN 9ஆம் வகுப்பு சமூக அறிவியல் வரலாறு - தொழிற்புரட்சி முக்கியமான 2,3,&5 மதிப்பெண் வினாக்கள் விடைகளுடன் TN 9th Social Science HIS - Industrial Revolution Important 1 Mark Questions with Answers 2,3,&5 Marks Questions with Answers.
NEW9th Standard
TN 9ஆம் வகுப்பு சமூக அறிவியல் வரலாறு - நவீன யுகத்தின் தொடக்கம் முக்கியமான 2,3,&5 மதிப்பெண் வினாக்கள் விடைகளுடன் TN 9th Social Science HIS - The Beginning of the Modern AgeImportant 1 Mark Questions with Answers 2,3,&5 Marks Questions with Answers.
Published on: 12/06/2021
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Questions + Answers key
Take MCQ Maths Test1.
Solve graphically
x = –3; y = 3
2.
Factorise the following:
(i) x2+10x + 24
(ii) z2+ 4z -12
(iii) p2- 6p -16
(iv) t2+72 -17t
(v) y2-16 - 80
(vi) a2+10a - 600
3.
Expand the following:
(i) (x+5)(x+6)(x+4)
(ii) (3x-1)(3x+2)(3x-4)
4.
Add the following polynomials and find the degree of the resultant polynomial.
| Sl.No | Polynomial | Addition | Degree of the resultant polynomial |
|---|---|---|---|
| 1 | p(x) = 5x3 - 3x + x2 + 4 q(x) = 7x - 4x2 + 2 |
||
| 2 | p(m) = 6m - 7 q(m) = 7m2 - 12 + 4m |
||
| 3 | p(x) = 4x2 - 6x3 - 4x + 6 q(x) = 8x3 + 2x2 - 2 |
||
| 4 | r(y) = 7y4 + 5y2 + 4y s(y) = 2y - 3y2 |
||
| 5 | p(m) = 12m3 - 10m2 - 7 q(m) = 7m3 + 5m2 - 3 |
5.
The polynomial ax3 - 3x2 + 4 and 2x3 - 5x +a when divide by (x - 2) leave the remainders p and q respectively if p - 2q = 4 ; find the value of a.
6.
Find p(0), p(1), and (p(-1) for each of the following polynomials.
| S.no | Polynominal | p(0) | p(1) | p(-1) |
| 1 | \(p(x)={ x }^{ 2 }+2x-1\) | |||
| 2 | \(p(x)={ x }^{ 3 }-1\) | |||
| 3 | \(p(x)=x+1\) |
7.
The area of a rectangle is x2 + 7x + 12. If its breadth is (x + 3), then find its length.
8.
Without actual division , prove that f(x) = 2x4- 6x3 + 3x2 + 3x - 2 is exactly divisible by x2 – 3x + 2
9.
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.
10.
Classify the following polynomials based on number of terms.
1.
Let us form table of values for each line and then fix the ordered pairs to be plotted.
Graph of x = -3
| x | -3 | -3 | -3 | -3 | -3 |
| y | -2 | -1 | 0 | 1 | 2 |
Points to be plotted : (-3, -2), (-3,-1), (-3, 0), (-3,1), (-3, 1), (-3, 2)
Graph of y = 3
| x | -2 | -1 | 0 | 1 | 2 |
| y | 3 | 3 | 3 | 3 | 3 |
Points to be plotted: (-2, 3), (- 1, 3), (0, 3), (1, 3), (2, 3)
\(\therefore\) The solution is (-3, 3)
2.
(i) x2+10x + 24 = x2+ 6x + 4x + 24
= x(x + 6) + 4(x + 6)
= (x + 6)(x + 4)
(ii) z2+ 4z -12
= z2+ 6z - 2z -12
= z(z + 6) -2(z + 6)
= (z + 6)(z - 2)
(iii) p2- 6p -16 = p2- 8p + 2p -16
= p(p - 8)+2(p - 8)
= (p - 8)(p + 2)
(iv) t2+ 72 -17t = t2-17t + 72
= t2- 9t - 8t + 72
= t(t - 9) - 8 (t - 9)
= (t - 9)(t - 8)
(v) y2 -16y- 80 = y2 - 20y + 4y - 80
= y(y - 20) + 4 (y - 20)
= (y - 20) (y + 4)
(vi) a2 + 10a - 600
= a2 + 30a - 20a - 600
= a(a + 30)- 20(a + 30)
= (a + 30)(a - 20)
3.
We know that (x +a)(x +b)(x +c) = x3 + (a +b +c)x2 + (ab +bc + ca) x +abc .....(1)
(i) (x+5)(x+6)(x+4)
= x3 + (5 + 6 + 4) x2+ (30 + 24 + 20) x + (5)(6)(4)
= x2 + 15x2+74x + 120
[Replace a by 5 b by 6 c by 4 in (1)]
(ii) (3x-1)(3x+2)(3x-4)
(3x)3+(-1+2-4)(3x)2+(-2-8+4)(3x)+(-1)(2)(-4)
= 27x3+(-3)9x2+(-6)(3x)+8
= 27x3- 27x2-18x + 8
[Repalce x by 3x, a by -1, b by 2, c by -4 in (1)]
4.
| Sl.No | Polynomial | Addition | Degree of the resultant polynomial |
|---|---|---|---|
| 1 | p(x) = 5x3 - 3x + x2 + 4 q(x) = 7x - 4x2 + 2 |
p(x) + q(x) = 5x3 + x2 - 3x + 4 (+)0x3 - 4x2 + 7x + 2 __________________ 5x3 - 3x2 + 4x + 6 |
3 |
| 2 | p(m) = 6m - 7 q(m) = 7m2 - 12 + 4m |
p(m) + q(m) = 0m2 + 6m - 7 (+) 7m2 + 4m - 12 _______________ 7m2 + 10m - 19 |
2 |
| 3 | p(x) = 4x2 - 6x3 - 4x + 6 q(x) = 8x3 + 2x2 - 2 |
p(x) + q(x) = -6x3 + 4x2 - 4x + 6 (+) 8x3 + 2x2 + 0x - 2 ___________________ 2x3 + 6x2 - 4x + 4 |
3 |
| 4 | r(y) = 7y4 + 5y2 + 4y s(y) = 2y - 3y2 |
r(y) + s(y) = 7y4 + 5y2 + 4y (+) 0y4 - 3y2 + 2y _________________ 7y4 + 2y2 + 6y |
4 |
| 5 | p(m) = 12m3 - 10m2 - 7 q(m) = 7m3 + 5m2 - 3 |
p(m) + q(m) = 12m3 - 10m2 - 7 (+) 7m3 + 5m2 - 3 _________________ 19m3 - 5m2 - 10 |
3 |
5.
p(x) = ax3 - 3x2 + 4
When it is divided by x - 2
p(2) = a(2)3 - 3(2)2 + 4
p = 8a-12 + 4
p = 8a- 8
q(x) = 2x3 - 5x + a
When it is divided by x - 2
q(2) = 2(2)3 - 5(2) + 8
q = 16-10+a
q = 6+a
Given p - 2q = 4
8a - 8 - 2 (6 + a) = 4
8a- 8 -12 -2a = 4
6a-20 = 4
6a = 24
a = 24/6 = 4
The value of a = 4
6.
| S.no | Polynominal | p(0) | p(1) | p(-1) |
| 1 | \(p(x)={ x }^{ 2 }+2x-1\) | \(p(0)=\left( { 0 } \right) ^{ 2 }+2(0)-1\\ =0+0-1\\ =-1\) | \(p(1)=(1)^{ 2 }+2(1)-1\\ 1+2-1\\ =2\) | \(p(-1\_ =(-1)^{ 2 }+2(-1)-1\\ =+1-2-1\\ =-2\) |
| 2 | \(p(x)={ x }^{ 3 }-1\) | \(p(0)={ 0 }^{ 3 }-1\\ =-1\) | \(p(1)={ 1 }^{ 3 }-1\\ 1-1\\ =0\) | \(p(-1)=(-1)^{ 3 }-1\\ =-1-1\\ =-2\) |
| 3 | \(p(x)=x+1\) | \(p(0)=0+1\\ =1\) | \(\quad p(1)=1+1\\ =2\) | \(p(-1)=-1+1\\ =0\) |
7.
Let the length of the reactangle be '' l ''
The Breadth of the reactangle = x + 3
Area of rectangle = Length \(\times\) breadth
x2 + 7x + 12 = l (x + 3) or
l = \(\frac { { x }^{ 2 }+7x+12 }{ x+3 } \)
= \(\frac { \left( x+4 \right) \left( x+3 \right) }{ x+3 } =x+4\)
Length of the rectangle = x + 4
8.
Let f(x) = 2x4- 6x3+3x2+3x-2
g(x) = x2 –3x + 2
= x2-2x-x+2
= x(x-2)-1(x-2)
= (x-2)(x-1)
we show that f(x) is exactly divisible by (x–1) and (x–2) using remainder theorem
f(1) = 2(1)4-6(1)3+3(1)2+3(1)-2
= 2 – 6 + 3 + 3 – 2 = 0
f(2) = 2(2)4-6(2)3+3(2)2+3(2)-2
= 32 – 48 + 12 + 6 – 2 = 0
f(x) is exactly divisible by (x – 1) (x – 2)
i.e., f(x) is exactly divisible by x2 –3x + 2
If p(x) is divided by (x -a) with the remainder p(a) = 0 , then (x -a) is a factor of p(x). Remainder Theorem leads to Factor Theorem.
9.
Length of the rectangle = 3x + 2 units
Breadth of the rectangle = 3x - 2 units
Area of the rectangle = (3x + 2 ) (3x - 2)
= 9x2 - 6x + 6x - 4
= 9x2- 4
When x = 20
Area of the rectangle = 9(20)2 - 4
= 9(400) - 4
= 3600 - 4 = 3596 sq.units.
10.
| S.No. | Polynomial | No of Terms | Type of polynomial based of terms |
| (i) | 5t3+6t+8t2 | 3 Terms | Trinomial |
| (ii) | y-7 | 2 Terms | Binomial |
| (iii) | \(\frac{2}{3}r^4\) | 1 Terms | Monomial |
| (iv) | 6y5+3y-7 | 3 Terms | Trinomial |
| (v) | 8m2+7m2 | Like Terms. So, it is 15m2 which is 1 term on | Monomial |
9th Standard Syllabus & Materials
9th Standard
TN 9ஆம் வகுப்பு சமூக அறிவியல் வரலாறு - பண்டைய நாகரிகங்கள் முக்கியமான 2,3,&5 மதிப்பெண் வினாக்கள் விடைகளுடன் TN 9th Social Science HIS - Ancient . Civilisations Important 1 Mark Questions with Answers 2,3,&5 Marks Questions with Answers.
NEW9th Standard
TN 9ஆம் வகுப்பு சமூக அறிவியல் வரலாறு - புரட்சிகளின் காலம் முக்கியமான 2,3,&5 மதிப்பெண் வினாக்கள் விடைகளுடன் TN 9th Social Science HIS - The Age of Revolutions Important 1 Mark Questions with Answers 2,3,&5 Marks Questions with Answers.
NEW9th Standard
TN 9ஆம் வகுப்பு சமூக அறிவியல் வரலாறு - இடைக்கால இந்தியாவில் அரசும் சமூகமும் முக்கியமான 2,3,&5 மதிப்பெண் வினாக்கள் விடைகளுடன் TN 9th Social Science HIS - State and Society in Medieval India Important 1 Mark Questions with Answers 2,3,&5 Marks Questions with Answers.
NEW9th Standard
TN 9ஆம் வகுப்பு சமூக அறிவியல் வரலாறு - ஆசிய ஆப்பிரிக்க நாடுகளில் காலனியாதிக்கம் முக்கியமான 2,3,&5 மதிப்பெண் வினாக்கள் விடைகளுடன் TN 9th Social Science HIS - Colonialism in Asia and Africa Important 1 Mark Questions with Answers 2,3,&5 Marks Questions with Answers.
Tamilnadu Stateboard 9th Standard Subjects
Tamilnadu Stateboard Standards
