SELF ASSESSMENT – TERM 1 MODEL PAPER – 2025-2026
Exam Code: 955 MR – 22
UDISE Code: _____________ PEN ID: _____________
Child Name: _________________________________________
Roll No.: ___________ Class: 10 Subject: Mathematics
Total Marks: 100 Time: 3 Hours
No. of Questions: 33
విభాగం – A / SECTION – A
(Each question carries 1 mark / ప్రతీ ప్రశ్నకు 1 మార్కు)
20 × 1 = 20 Marks
- The HCF of 65 and 117 is _____
A) 1 B) 13 C) 5 D) 7 (65 మరియు 117 యొక్క గ.సా.ని ఏది?) [ ] - The decimal expansion of 1/8 is _____
A) Terminating B) Non-terminating C) Irrational D) Repeating [ ] - If α and β are the zeros of x² – 5x + 6, then αβ = _____ [ ]
A) –5 B) 6 C) 11 D) 2 - Graph of a pair of inconsistent linear equations represents _____
A) Parallel lines B) Coincident lines C) Intersecting lines D) Perpendicular lines [ ] - The roots of x² + 5x + 6 = 0 are _____
A) –2, –3 B) 2, 3 C) 3, –2 D) –3, 2 [ ] - The common difference of A.P. 2, 7, 12, 17,… is _____ [ ]
A) 2 B) 5 C) 7 D) 3 - In ΔABC, if AD ⊥ BC, then AD is called _____
A) Median B) Altitude C) Bisector D) Radius [ ] - If ΔABC ~ ΔDEF, then AB/DE = _____
A) AC/EF B) BC/DE C) AD/EF D) AB/DF [ ] - Distance between (3, –4) and (0, 0) = _____ [ ]
A) 5 B) 4 C) 3 D) √10 - The midpoint of (2, 3) and (4, 7) is _____ [ ]
A) (3, 5) B) (2, 4) C) (4, 6) D) (1, 5) - Mode = _____ (3 × Median – 2 × Mean) [ ]
A) Empirical relation B) Pythagoras theorem C) Euclid axiom D) Area formula - tan 45° = _____ [ ]
A) 0 B) 1 C) √3 D) 1/√3 - sin²A + cos²A = _____ [ ]
A) 0 B) 1 C) 2 D) 3 - The ratio of sides in a 30°–60°–90° triangle is _____ [ ]
A) 1 : √3 : 2 B) 1 : 1 : √2 C) 2 : 1 : √3 D) √2 : 1 : 1 - The sum of n terms of an A.P. is given by _____
A) n/2 [2a + (n – 1)d] B) a + nd C) a + d/2 D) n a [ ] - In ΔABC, if AD is the median, then AB² + AC² = 2(AD² + _____²) [ ]
A) BD B) DC C) BC/2 D) None - If a/b = c/d, then ad = _____ [ ]
A) bc B) ac C) bd D) cd - Sum of zeros of x² – 7x + 12 is _____ [ ]
A) 7 B) 12 C) –7 D) –12 - tan θ = sin θ / _____ [ ]
A) cos θ B) tan θ C) cot θ D) sec θ - The formula for mode in continuous data is _____
A) l + (h × f₁ – f₀)/(2f₁ – f₀ – f₂) B) (l +h)/2 C) 3 Median – 2 Mean D) None [ ]
విభాగం – B / SECTION – B
(Each question carries 2 marks / ప్రతీ ప్రశ్నకు 2 మార్కులు)
6 × 2 = 12 Marks
- Find the HCF of 26 and 91 using Euclid’s algorithm.
(యూక్లిడ్ విధానాన్ని ఉపయోగించి 26 మరియు 91 యొక్క గ.సా.ని కనుగొనండి.) - If a polynomial p(x) = x² – 4x + 3, find its zeros.
(p(x) = x² – 4x + 3 యొక్క శూన్యాలను కనుగొనండి.) - Solve 2x + 3y = 12, x – y = 1 by substitution method.
(ప్రతిస్థాపన పద్ధతితో సమీకరణాలను పరిష్కరించండి.) - Find the value of k if x = 2 is a root of 2x² + kx + 3 = 0.
(x = 2 సమీకరణానికి మూలమైతే k విలువ కనుగొనండి.) - Find the 10th term of the A.P. 5, 9, 13, 17,…
(5, 9, 13, 17,… A.P. లో 10వ పదం కనుగొనండి.) - Find the coordinates of the midpoint joining (4, –3) and (–2, 5).
విభాగం – C / SECTION – C
(Each question carries 4 marks / ప్రతీ ప్రశ్నకు 4 మార్కులు)
7 × 4 = 28 Marks
- Divide the polynomial p(x) = 2x³ + 3x² – 2x – 3 by (x + 1).
- Using Pythagoras theorem, prove that the triangle formed on the diameter of a circle is right angled.
- Find the sum of the first 20 terms of A.P. whose first term = 7 and common difference = 3.
- Find the coordinates of the centroid of the triangle with vertices (2, 3), (4, –1), (6, 5).
- Draw the graph of 2x + 3y = 6 and x – y = 1 on the same graph.
- A boy observes the top of a tower at an angle of elevation 30°. If the boy is 50 m away from the foot of the tower, find its height.
- The following table shows the daily wages of workers. Find the mean by direct method.
| Wages (Rs.) | 100-120 | 120-140 | 140-160 | 160-180 | 180-200 |
|————–|———-|———-|———-|———-|
| No. of Workers | 4 | 6 | 10 | 8 | 2 |
విభాగం – D / SECTION – D
(Each question carries 8 marks / ప్రతీ ప్రశ్నకు 8 మార్కులు)
5 × 8 = 40 Marks
- Solve the quadratic equation x² – 7x + 10 = 0 by factorization method.
- Prove that √2 is irrational.
- Prove that the areas of two similar triangles are in the ratio of the squares of their corresponding sides.
- From the top of a building 30 m high, the angle of depression of a car on the road is 30°. Find the distance of the car from the foot of the building.
- The following table gives the distribution of heights of students in a class. Draw an ogive to find the median height.
| Height (cm) | 140-150 | 150-160 | 160-170 | 170-180 | 180-190 |
|————–|———-|———-|———-|———-|
| No. of Students | 5 | 8 | 10 | 6 | 1 |
ANSWER KEY
- B 2) A 3) B 4) A 5) A 6) B 7) B 8) A 9) A 10) A
- A 12) B 13) B 14) A 15) A 16) C 17) A 18) A 19) A 20) A
- 13 22) 1, 3 23) x = 3, y = 2 24) k = –7 25) 41 26) (1, 1)
- Quotient = 2x² + x – 3; Remainder = 0
- ∵ Angle in a semicircle = 90°, proved.
- Sₙ = n/2 [2a + (n – 1)d] = 20/2 [14 + 57] = 710
- Centroid = (4, 7/3)
- Lines intersect at (1.8, 0.8)
- tan 30° = h/50 ⇒ h = 50/√3 = 28.9 m
- Mean = Σ(fx)/Σf = (4×110 + 6×130 + 10×150 + 8×170 + 2×190)/30 = 150 Rs.
- (x – 2)(x – 5) = 0 ⇒ x = 2, 5
- Assume √2 = p/q → contradiction → irrational.
- If ΔABC ~ ΔDEF, then (AB/DE)² = ar(ΔABC)/ar(ΔDEF). Hence proved.
- tan 30° = 30/x ⇒ x = 30√3 = 51.96 m
- Median class = 160-170 → Median ≈ 163 cm.