Mathematics 10TH AP SA1 Question paper 202-26

Mathematics 10TH AP SA1 Question paper 202-26 |10TH Class Maths Ap sa1 exam paper 2025 answer

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Table of Contents

Andhra Pradesh SA-1 Model Question Paper 2025-26

Subject: Mathematics  Class: 10  Exam Code: 954MATHS-10
Total Marks: 100  Time: 3 Hours
No. of Questions: 33  Medium: English

Instructions

  1. The question paper contains four sections (A to D).
  2. Read all questions carefully and write answers in your answer booklet.
  3. Diagrams and steps carry marks.
  4. Calculators are not allowed.
  5. Attempt all questions unless internal choice is given.

SECTION A – Multiple Choice Questions (20 × 1 = 20 Marks)

Choose the correct option and write it in your answer booklet.

  1. The zeros of the polynomial x² − 5x + 6 are
     A) 1 and 6 B) 2 and 3 C) −2 and −3 D) 3 and 5
  2. If α and β are zeros of ax² + bx + c, then α + β = ____
     A) −b/a B) b/a C) c/a D) −c/a
  3. The pair of equations x + 2y = 5 and 2x + 4y = 10 has
     A) One solution B) No solution C) Infinitely many solutions D) Two solutions
  4. The sum of first n natural numbers is
     A) n(n − 1)/2 B) n(n + 1)/2 C) n² D) 2n
  5. The distance between points (3, 4) and (7, 1) is
     A) 5 B) 6 C) √25 D) √34
  6. If tan θ = 3/4, then sin θ = ?
     A) 3/5 B) 4/5 C) 5/3 D) 1/2
  7. The area of triangle with vertices (0, 0), (4, 0), (0, 3) is
     A) 6 sq. units B) 12 sq. units C) 7 sq. units D) 10 sq. units
  8. In an A.P. 5, 8, 11, …, the 10th term = ?
     A) 32 B) 35 C) 38 D) 41
  9. If the sum of n terms of an A.P. is 5n² + 3n, then the common difference = ?
     A) 10 B) 5 C) 3 D) 8
  10. A circle with radius 7 cm has circumference = ? (π = 22/7)
     A) 22 cm B) 44 cm C) 154 cm D) 14 cm
  11. Volume of a sphere of radius r is
     A) 4/3 πr³ B) πr²h C) 2πr D) πr³/2
  12. Mean of 10, 20, 30, 40, 50 =
     A) 30 B) 35 C) 25 D) 40
  13. The probability of getting a head when a coin is tossed = ?
     A) 1/3 B) 1/2 C) 1/4 D) 2/3
  14. The coordinate of midpoint of (2, −3) and (4, 5) is
     A) (3, 1) B) (3, 4) C) (6, 2) D) (4, 1)
  15. The roots of x² − 2x − 8 = 0 are
     A) −2, 4 B) 2, −4 C) 4, 2 D) −4, −2
  16. 1, 4, 7, 10, … form an A.P. with common difference = ?
     A) 3 B) 4 C) 2 D) 1
  17. sin²θ + cos²θ = ?
     A) 0 B) 1 C) 2 D) sin θ
  18. The area of circle is 154 cm². Its radius = ? (π = 22/7)
     A) 7 cm B) 5 cm C) 6 cm D) 4 cm
  19. Standard deviation of 2, 4, 6, 8, 10 = ?
     A) 2 B) 3 C) 4 D) 5
  20. In similar triangles, ratio of areas = ?
     A) ratio of corresponding sides B) square of ratio of corresponding sides C) cube of ratio D) equal

SECTION B – Short Answer Questions (4 × 2 = 8 Marks)

  1. Find the zeros of the polynomial x² − 4.
  2. Solve the pair of equations: 2x + 3y = 12 and x − y = 1.
  3. Find the 10th term of the A.P. 2, 7, 12, 17, ….
  4. Find the distance between the points (1, 2) and (4, 6).

SECTION C – Long Answer Questions (5 × 6 = 30 Marks)

  1. Prove that √5 is irrational.
  2. Solve the quadratic equation x² − 3x − 10 = 0 by factorization.
  3. Draw the graph of y = 2x + 3 and find the y-intercept.
  4. Find the sum of first 20 terms of the A.P. 4, 9, 14, ….
  5. From the top of a tower 30 m high, the angle of depression of a car on the ground is 30°. Find the distance of the car from the foot of the tower. (tan 30° = 1/√3)

SECTION D – Essay / Application Questions (5 × 8 = 40 Marks)

  1. (a) Derive the quadratic formula for solving ax² + bx + c = 0.
      or
     (b) If x + y = 6 and xy = 5, find the value of x³ + y³.
  2. (a) In a right triangle ABC, tan A = 3/4. Find the values of sin A and cos A.
      or
     (b) Prove that (1 + cot²A) = cosec²A.
  3. (a) Find the coordinates of the centroid of a triangle whose vertices are (2, 3), (−1, 0), (2, −4).
      or
     (b) Find the area of triangle whose vertices are (−2, −3), (3, 2), (−1, 8).
  4. (a) The radius of a sphere is 7 cm. Find its surface area and volume.
      or
     (b) Find the volume and surface area of a cylinder of radius 7 cm and height 10 cm.
  5. (a) Find the mean, median and mode of the following data:
Class Interval0–1010–2020–3030–4040–5050–60
Frequency571518105

  or
 (b) A card is drawn at random from a pack of 52 cards. Find the probability of getting
  (i) a king (ii) a red card.

10th Mathematics AP SA1 Question paper 202-26
10th Mathematics AP SA1 Question paper 202-26 | 10TH Class Maths Ap sa1 exam paper 2025 answer key real

MODEL ANSWER KEY (Outline)

Section A
1 – B 2 – A 3 – C 4 – B 5 – D 6 – A 7 – A 8 – A 9 – A 10 – B 11 – A 12 – A 13 – B 14 – A 15 – A 16 – A 17 – B 18 – A 19 – A 20 – B

Section B
21 → x = ±2.
22 → x = 3, y = 2.
23 → a = 2, d = 5 ⇒ t₁₀ = 2 + 9×5 = 47.
24 → Distance = √[(4 − 1)² + (6 − 2)²] = √(9 + 16) = 5.

9th Mathematics AP SA1 Question paper 202-26
9th Mathematics AP SA1 Question paper 202-26 | 9TH Class Maths Ap sa1 exam paper 2025 answer key real

Section C (answers outline)
25 → Proof by contradiction; √5 is irrational.
26 → (x − 5)(x + 2) = 0 ⇒ x = 5, −2.
27 → y = 2x + 3 ⇒ y-intercept = 3.
28 → S₂₀ = 20/2[2×4 + 19×5] = 10(8 + 95) = 1030.
29 → tan 30° = h/d ⇒ 1/√3 = 30/d ⇒ d = 30√3 m.

Section D (answers outline)
30 (a) x = [−b ± √(b² − 4ac)]/(2a); (b) x³ + y³ = ( x + y )³ − 3xy( x + y ) = 6³ − 3×5×6 = 216 − 90 = 126.
31 (a) sin A = 3/5, cos A = 4/5; (b) Identity proved.
32 (a) Centroid G( (2 − 1 + 2)/3, (3 + 0 − 4)/3 ) = (1, −1/3); (b) Area = ½| x₁(y₂ − y₃) + x₂(y₃ − y₁) + x₃(y₁ − y₂) | = ½| (−2)(2 − 8) + 3(8 + 3) + (−1)(−3 − 2) | = ½| 12 + 33 + 5 | = 25.
33 (a) Surface area = 4πr² = 4×3.14×49 = 615.44 cm²; Volume = 4/3 πr³ = 4/3×3.14×343 = 1436.03 cm³.
 (b) Cylinder surface area = 2πr(h + r) = 2×3.14×7×17 = 747.74 cm²; Volume = πr²h = 3.14×49×10 = 1538.6 cm³.
34 (a) Mean ≈ 32.3, Median ≈ 33, Mode ≈ 34 (class 30–40 modal class).
 (b) P(king) = 4/52 = 1/13; P(red) = 26/52 = 1/2.