9-ஆம் வகுப்பு கணிதம்:
காலாண்டுத் தேர்வு
வினாத்தாள் மற்றும்
விடைகள் 2026
தமிழகப் பள்ளிகளில் நடைபெறும் 9-ஆம் வகுப்பு மாணவர்களுக்கான 2026-ஆம் ஆண்டு காலாண்டுத் தேர்வு (Quarterly Examination) கணித வினாத்தாள் (ஆங்கில வழி) மற்றும் ஒரு மதிப்பெண் வினாக்களுக்கான விடைகள் கீழே கொடுக்கப்பட்டுள்ளது. இதனை மாணவர்கள் எளிதில் படிக்கும் வகையிலும், மொபைல் போனில் பார்ப்பதற்கு வசதியாகவும் வடிவமைத்துள்ளோம்.
| வகுப்பு | 9-ஆம் வகுப்பு |
|---|---|
| பாடம் | கணிதம் (Mathematics - EM) |
| தேர்வு | காலாண்டுத் தேர்வு 2026 |
| மொத்த மதிப்பெண்கள் | 100 மதிப்பெண்கள் |
QUARTERLY EXAMINATION - 2026
MATHEMATICS
Part - I
I. Answer all the questions. Choose the most appropriate from the give four alternatives. 14 x 1 = 14
1. If $U = \{x/x \in \mathbb{N}, x < 10\}$, $A = \{x/x \in \mathbb{N}, 2 \le x < 6\}$ then $(A')'$ is
a) $\{1, 6, 7, 8, 9\}$ b) $\{1, 2, 3, 4\}$ c) $\{2, 3, 4, 5\}$ d) $\{\}$
விடை: c) $\{2, 3, 4, 5\}$
2. Let $A = \{\phi\}$ and $B = P(A)$, then $A \cap B$ is
a) $\{\phi, \{\phi\}\}$ b) $\{\phi\}$ c) $\phi$ d) $\{0\}$
விடை: b) $\{\phi\}$
3. For any three sets $P, Q$ and $R$, $P - (Q \cap R)$ is
a) $P - (Q \cup R)$ b) $(P \cap Q) - R$ c) $(P - Q) \cup (P - R)$ d) $(P - Q) \cap (P - R)$
விடை: c) $(P - Q) \cup (P - R)$
4. For any three sets $A, B$ and $C$, $(A - B) \cap (B - C)$ is equal to
a) A only b) B only c) C only d) $\phi$
விடை: d) $\phi$
5. The shaded region in the Venn diagram is [Diagram shows region in Z excluding X and Y]
விடை: a) $Z - (X \cup Y)$
6. An irrational number between 2 and 2.5 is
a) $\sqrt{11}$ b) $\sqrt{5}$ c) $\sqrt{2.5}$ d) $\sqrt{8}$
விடை: b) $\sqrt{5}$
7. Find the odd one out of the following
a) $\sqrt{32} \times \sqrt{2}$ b) $\frac{\sqrt{27}}{\sqrt{3}}$ c) $\sqrt{72} \times \sqrt{8}$ d) $\frac{\sqrt{54}}{\sqrt{18}}$
விடை: d) $\frac{\sqrt{54}}{\sqrt{18}}$
8. If $\sqrt{80} = k\sqrt{5}$ then $k = ?$
a) 2 b) 4 c) 8 d) 16
விடை: b) 4
9. If $\sqrt{9^x} = \sqrt[3]{9^2}$ then $x =$
a) $\frac{2}{3}$ b) $\frac{4}{3}$ c) $\frac{1}{3}$ d) $\frac{5}{3}$
விடை: b) $\frac{4}{3}$
10. The zero of the polynomial $2x + 5$ is
a) $\frac{5}{2}$ b) $-\frac{5}{2}$ c) $\frac{2}{5}$ d) $-\frac{2}{5}$
விடை: b) $-\frac{5}{2}$
11. Degree of the polynomial $(y^3 - 2)(y^3 + 1)$ is
a) 9 b) 2 c) 3 d) 6
விடை: d) 6
12. If $P(a) = 0$ then $(x - a)$ is a ............ if $p(x)$
a) divisor b) quotient c) remainder d) factor
விடை: d) factor
13. Degree of the constant polynomial is ............
a) 3 b) 2 c) 1 d) 0
விடை: d) 0
14. In the quadrilateral ABCD, AB = BC and AD = DC, measure of $\angle BCD$ is [Diagram given with $\angle B = 108^\circ$ and $\angle D = 42^\circ$]
விடை: c) $105^\circ$
Part - II
II. Answer any 10 questions, question No. 28 is compulsory. 10 x 2 = 20
15. Are $A = \{x : x \in \mathbb{N}, 4 \le x \le 8\}$ and $B = \{4, 5, 6, 7, 8\}$ equal sets?
16. Find the number of subsets and the number of proper subsets of the following set. $W = \{\text{red, blue, yellow}\}$.
17. If $P = \{7, 8\}$, $Q = \{7, -3, -11\}$ then represent P and Q in Venn diagram and hence find $P \cup Q$.
18. If $n(A) = 25$, $n(B) = 40$, $n(A \cup B) = 50$ and $n(B') = 25$ find $n(A \cap B)$.
19. Find any two rational numbers between $\frac{1}{2}$ and $\frac{2}{3}$.
20. Classify the numbers as rational or irrational : i) $\sqrt{10}$ ii) $\sqrt{49}$
21. Find the value of $(243)^{\frac{2}{5}}$.
22. Represent the number in scientific notation 569430000000.
23. Write the co-efficient of $x^2$ and $x$ in the following polynomial $6 - 2x^2 + 3x^3 - \sqrt{7}x$.
24. Find the zeros of the polynomial $f(x) = 3x - 5$.
25. Find the number of zeros of the following polynomials represented by their graphs.
i)
26. Expand : $(a - b + c)^2$.
27. The angles of a triangle are in the ratio $1 : 2 : 3$ find the measure of each angle of the triangle.
28. Evaluate : $98^3$.
Part - III
III. Answer any 10 questions. Question No. 42 is compulsory. 10 x 5 = 50
29. If $A = \{b, c, e, g, h\}$, $B = \{a, c, d, g, i\}$ and $C = \{a, d, e, g, h\}$ then show that $A - (B \cap C) = (A - B) \cup (A - C)$.
30. Verify $A \cap (B \cup C) = (A \cap B) \cup (A \cap C)$ using Venn diagram.
31. In a group of 100 students, 85 students speak Tamil, 40 students speak English, 20 students speak French, 32 speak Tamil and English, 13 speak English and French and 10 speak Tamil and French. If each student knows atleast any one of these languages, then find the number of students who speak all these three languages.
32. If $U = \{x : x \in \mathbb{N}, x \le 10\}$, $A = \{2, 3, 4, 8, 10\}$ and $B = \{1, 2, 5, 8, 10\}$ then verify that $n(A \cup B) = n(A) + n(B) - n(A \cap B)$.
33. Simplify : $2\sqrt[3]{40} + 3\sqrt[3]{625} - 4\sqrt[3]{320}$.
34. Arrange surds in descending order : $\sqrt[3]{5}, \sqrt[9]{4}, \sqrt[6]{3}$.
35. Rationalise the denominator : $\frac{5 + \sqrt{3}}{5 - \sqrt{3}}$
36. Simplify : $(8.41 \times 10^4) \div (4.3 \times 10^5)$
37. Find the product $(4x - 5)$ and $(2x^2 + 3x - 6)$.
38. Determine the value of $m$, if $(x + 3)$ is a factor of $x^3 - 3x^2 - mx + 24$.
39. Expand : $(x - 5)(x - 6)(x + 2)$.
40. If $x^2 + \frac{1}{x^2} = 23$, then find the value of $x + \frac{1}{x}$ and $x^3 + \frac{1}{x^3}$.
41. Find all the three angles of the $\Delta ABC$.
[படத்தில் $\angle A = (x+35)^\circ$, $\angle B = (2x-5)^\circ$ மற்றும் $C$-ன் வெளிக்கோணம் $(4x-15)^\circ$ எனக் கொடுக்கப்பட்டுள்ளது]
42. Factorise : $2x^2 + 15x - 27$.
Part - IV
IV. Answer all the questions. 2 x 8 = 16
43. a) Construct the $\Delta LMN$ such that $LM = 7.5\text{cm}, MN = 5\text{cm}$ and $LN = 8\text{cm}$, Locate its centroid.
(OR)
b) Construct the circum centre of the $\Delta ABC$ with $AB = 5\text{cm}, \angle A = 60^\circ$ and $\angle B = 80^\circ$. Also draw the circumcircle and find the circum radius of the $\Delta ABC$.
44. a) Construct $\Delta PQR$ whose sides are $PQ = 6\text{cm}, \angle Q = 60^\circ$ and $QR = 7\text{cm}$ and locate its orthocentre.
(OR)
b) Draw an equilateral triangle of side $6.5\text{cm}$ and locate its incentre. Also draw the incircle.