In short: This is a solved AP SSC 2027 practice paper set built on the BSEAP model paper structure. Maths is a full 100-mark paper (33 questions across four sections of 1, 2, 4 and 8 marks), with complete solutions. Physical Science and Biological Science have 50-mark practice sets (17 questions each) with answers. Social Studies has a mixed question set with answer points. Questions follow the NCERT-based AP Class 10 syllabus. After this, solve the official BSEAP model papers from bse.ap.gov.in. To see which chapters carry the most marks, check our AP SSC chapter-wise weightage guide.
Maths Model Paper — 100 Marks
Time: 3 hours 15 minutes (including 15 minutes reading) | Max Marks: 100
| Section | Marks per Q | Questions | Total |
|---|---|---|---|
| I | 1 | 12 | 12 |
| II | 2 | 8 | 16 |
| III | 4 | 8 | 32 |
| IV (internal choice) | 8 | 5 | 40 |
Section I — 12 × 1 = 12 marks
- Write 156 as a product of prime factors.
- If one zero of x² − kx + 6 is 2, find k.
- State the condition for a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0 to have a unique solution.
- Find the discriminant of 3x² − 2x + 1/3 = 0.
- Which term of the AP 3, 8, 13, ... is 78?
- Find the distance between (2, 3) and (4, 1).
- If △ABC ~ △DEF with AB/DE = 2/3, what is ar(ABC) : ar(DEF)?
- Find the value of sin²30° + cos²30°.
- What is the angle of elevation of the sun when the shadow of a pole equals its height?
- Find the perimeter of a semicircle of radius 7 cm (π = 22/7).
- Write the formula for the mode of grouped data.
- A die is thrown once. What is the probability of getting a number greater than 4?
Section II — 8 × 2 = 16 marks
- Find the HCF of 336 and 54 by prime factorisation.
- Find the zeroes of 6x² − 3 − 7x.
- Solve: x + y = 5 and 2x − 3y = 4.
- Find the roots of 2x² − 7x + 3 = 0 by factorisation.
- Find the coordinates of the point dividing (4, −3) and (8, 5) internally in the ratio 3 : 1.
- In △ABC, DE ∥ BC. If AD = 1.5 cm, DB = 3 cm and AE = 1 cm, find EC.
- Evaluate: (cos 45°)/(sec 30° + cosec 30°).
- Two coins are tossed together. Find the probability of getting at least one head.
Section III — 8 × 4 = 32 marks
- Prove that √3 is irrational.
- The sum of a two-digit number and the number formed by reversing its digits is 66. The digits differ by 2. Find the number.
- Find the sum of all two-digit numbers divisible by 3.
- Prove that the lengths of the tangents drawn from an external point to a circle are equal.
- Prove: (1 + cot A − cosec A)(1 + tan A + sec A) = 2.
- Find the area of the minor segment of a circle of radius 14 cm when the angle of the sector is 60° (π = 22/7, √3 = 1.73).
- A cone of height 24 cm and radius 6 cm is made of clay. It is reshaped into a sphere. Find the radius of the sphere.
- A card is drawn from a well-shuffled deck of 52 cards. Find the probability of getting (i) a red king (ii) a face card (iii) a spade (iv) not an ace.
Section IV — 5 × 8 = 40 marks (answer one from each pair)
-
(a) Solve graphically: x − y + 1 = 0 and 3x + 2y − 12 = 0. Shade the triangle formed by these lines and the x-axis. OR (b) A boat goes 30 km upstream and 44 km downstream in 10 hours. In 13 hours it goes 40 km upstream and 55 km downstream. Find the speed of the stream and of the boat in still water.
-
(a) A motorboat with a speed of 18 km/h in still water takes 1 hour more to go 24 km upstream than to return. Find the speed of the stream. OR (b) The 17th term of an AP exceeds its 10th term by 7. Its 5th term is 12. Find the sum of its first 20 terms.
-
(a) State and prove the Basic Proportionality Theorem. OR (b) Prove that the ratio of the areas of two similar triangles equals the square of the ratio of their corresponding sides.
-
(a) The angles of elevation of the top of a tower from two points at 4 m and 9 m from its base, in the same straight line, are complementary. Prove that the height of the tower is 6 m. OR (b) From the top of a 60 m building, the angles of depression of the top and bottom of a tower are 30° and 60°. Find the height of the tower.
-
(a) Find the mean, median and mode of the following data:
| Class | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 |
|---|---|---|---|---|---|---|
| f | 4 | 6 | 10 | 12 | 5 | 3 |
OR (b) A solid is a cylinder with a hemisphere at each end. The total length is 19 cm and the diameter of the cylinder is 7 cm. Find the volume and the total surface area of the solid.
Maths Solutions
Section I
| Q | Answer |
|---|---|
| 1 | 2² × 3 × 13 |
| 2 | 4 − 2k + 6 = 0, so k = 5 |
| 3 | a₁/a₂ ≠ b₁/b₂ |
| 4 | D = 4 − 4(3)(1/3) = 0 |
| 5 | 3 + (n − 1)5 = 78, so n = 16 (16th term) |
| 6 | √(4 + 4) = 2√2 |
| 7 | 4 : 9 |
| 8 | 1 |
| 9 | 45° |
| 10 | πr + 2r = 22 + 14 = 36 cm |
| 11 | Mode = l + [(f₁ − f₀)/(2f₁ − f₀ − f₂)] × h |
| 12 | 2/6 = 1/3 |
Section II
13. 336 = 2⁴ × 3 × 7 and 54 = 2 × 3³. HCF = 2 × 3 = 6.
14. 6x² − 7x − 3 = (3x + 1)(2x − 3). Zeroes: −1/3 and 3/2.
15. Since y = 5 − x: 2x − 15 + 3x = 4, so x = 19/5 and y = 6/5.
16. 2x² − 6x − x + 3 = (2x − 1)(x − 3). Roots: 1/2 and 3.
17. x = (3 × 8 + 1 × 4)/4 = 7. y = (3 × 5 + 1 × (−3))/4 = 3. Point = (7, 3).
18. AD/DB = AE/EC, so 1.5/3 = 1/EC, giving EC = 2 cm.
19. (1/√2)/(2/√3 + 2) = (1/√2) × √3/(2(1 + √3)) = √3/(2√2(1 + √3)). Rationalising: (3√2 − √6)/8.
20. P(at least one head) = 1 − P(no head) = 1 − 1/4 = 3/4.
Section III
21. Assume √3 = a/b (co-prime). Then a² = 3b², so 3 divides a. Let a = 3c, giving b² = 3c², so 3 divides b. This contradicts co-primeness, so √3 is irrational.
22. Let the digits be x and y. (10x + y) + (10y + x) = 66 gives x + y = 6, and x − y = ±2. So (x, y) = (4, 2) or (2, 4). The number is 42 or 24.
23. Two-digit multiples of 3 run from 12 to 99, with d = 3. n = (99 − 12)/3 + 1 = 30. Sum = 30/2 × (12 + 99) = 1665.
24. Let PA and PB be tangents from P, with centre O. In right triangles OAP and OBP: OA = OB (radii), OP is common, and ∠OAP = ∠OBP = 90°. So △OAP ≅ △OBP (RHS), and PA = PB.
25.
- First bracket: (sin A + cos A − 1)/sin A
- Second bracket: (cos A + sin A + 1)/cos A
- Product = [(sin A + cos A)² − 1]/(sin A cos A) = 2 sin A cos A/(sin A cos A) = 2
26.
- Sector area = (60/360) × (22/7) × 196 = 102.67 cm²
- Equilateral triangle area = (√3/4) × 196 = 84.77 cm²
- Minor segment ≈ 17.9 cm²
27. (1/3)π(36)(24) = (4/3)πr³, so 288 = (4/3)r³, giving r³ = 216 and r = 6 cm.
28. (i) 2/52 = 1/26 (ii) 12/52 = 3/13 (iii) 13/52 = 1/4 (iv) 48/52 = 12/13
Section IV (one option each)
29(a). Points for x − y + 1 = 0: (0, 1), (−1, 0), (2, 3). Points for 3x + 2y = 12: (0, 6), (4, 0), (2, 3). The lines meet at (2, 3). The triangle has vertices (−1, 0), (4, 0) and (2, 3). Area = ½ × 5 × 3 = 7.5 sq units.
30(a). Let the stream speed be x. 24/(18 − x) − 24/(18 + x) = 1. This gives 48x = 324 − x², so x² + 48x − 324 = 0, or (x + 54)(x − 6) = 0. Stream speed = 6 km/h.
31(a). BPT statement and proof using area ratios (draw a figure, join BE and CD, and use ar(BDE) = ar(DEC)). See the full proof in any NCERT Chapter 6 solution. In the exam, write the given, to prove, construction and proof steps.
32(a). Let the height be h and the angles θ and (90° − θ). Then tan θ = h/4 and tan(90° − θ) = cot θ = h/9. Multiplying: tan θ × cot θ = h²/36 = 1, so h = 6 m.
33(a). Total f = 40. Midpoints are 5, 15, 25, 35, 45, 55, and Σfx = 20 + 90 + 250 + 420 + 225 + 165 = 1170.
- Mean = 1170/40 = 29.25
- Median: n/2 = 20 and cumulative frequencies are 4, 10, 20, 32, so the median class is 20-30 (cf = 10, f = 10). Median = 20 + (10/10) × 10 = 30
- Mode: the modal class is 30-40 (f₁ = 12, f₀ = 10, f₂ = 5). Mode = 30 + [2/(24 − 15)] × 10 = 30 + 2.22 = 32.2
Physical Science Practice Set — 50 Marks
| Section | Q | Question | Answer |
|---|---|---|---|
| I (1m) | 1 | Write the chemical formula of bleaching powder | CaOCl₂ |
| I | 2 | What is the pH of milk of magnesia — above or below 7? | Above 7 (basic) |
| I | 3 | Which metal is stored in kerosene? | Sodium (or potassium) |
| I | 4 | Name the first member of the alkyne series | Ethyne (C₂H₂) |
| I | 5 | What is the focal length of a plane mirror? | Infinity |
| I | 6 | Which colour of light deviates the most in a prism? | Violet |
| I | 7 | 1 kWh = ____ J | 3.6 × 10⁶ J |
| I | 8 | What does an electric motor convert? | Electrical energy → mechanical energy |
| II (2m) | 9 | Why is respiration called an exothermic reaction? | Glucose is oxidised and energy is released |
| II | 10 | Find the power of a lens with f = −25 cm | P = 1/(−0.25) = −4 D (concave) |
| II | 11 | Why is copper used for electric wiring? | Copper has very low resistivity, so little energy is lost as heat. It is also ductile, so it can be drawn into thin wires |
| III (4m) | 12 | An object 4 cm tall is 15 cm from a concave mirror (f = 10 cm). Find the image distance, size and nature | 1/v = 1/f − 1/u = −1/10 + 1/15 = −1/30, so v = −30 cm. m = −v/u = −2, so image height = −8 cm. Real, inverted, magnified |
| III | 13 | Explain the extraction of a metal low in the reactivity series (mercury from cinnabar) | 2HgS + 3O₂ → 2HgO + 2SO₂ (roasting), then 2HgO → 2Hg + O₂ (heating) |
| III | 14 | Three resistors of 4 Ω, 6 Ω and 12 Ω are in parallel across 12 V. Find the total current | 1/R = 1/4 + 1/6 + 1/12 = 1/2, so R = 2 Ω. I = 6 A |
| IV (8m) | 15 | Draw ray diagrams for a convex lens with the object (a) beyond 2F (b) between F and the optic centre. State the nature of each image | (a) Between F and 2F on the other side: real, inverted, diminished. (b) Same side as the object: virtual, erect, magnified |
| IV | 16 | Explain esterification, saponification and the cleansing action of soap | Acid + alcohol → ester (conc. H₂SO₄). Ester + NaOH → soap + alcohol. Micelle formation traps oily dirt |
| IV | 17 | State Fleming's left-hand rule. Draw and explain the working of an electric motor | Forefinger = field, middle finger = current, thumb = force. The coil rotates, and the split-ring commutator reverses the current every half turn |
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Biological Science Practice Set — 50 Marks
| Section | Q | Question | Answer |
|---|---|---|---|
| I (1m) | 1 | Site of complete digestion of food | Small intestine |
| I | 2 | Which blood vessel carries oxygenated blood from the heart to the body? | Aorta |
| I | 3 | Name the hormone secreted by the thyroid gland | Thyroxine |
| I | 4 | Gap between two neurons | Synapse |
| I | 5 | Mode of reproduction in yeast | Budding |
| I | 6 | Male reproductive part of a flower | Stamen |
| I | 7 | Mendel's F₂ phenotypic ratio in a dihybrid cross | 9 : 3 : 3 : 1 |
| I | 8 | Example of a biodegradable substance | Vegetable peels / paper |
| II (2m) | 9 | Why do arteries have thick walls? | Blood flows at high pressure from the heart |
| II | 10 | What is the role of the stomata? | Gas exchange (CO₂ in, O₂ out) and transpiration |
| II | 11 | Why is the father responsible for the sex of a child? | The father contributes X or Y. Y gives a boy (XY), X gives a girl (XX) |
| III (4m) | 12 | Describe how urine is formed in a nephron | Glomerular filtration → selective reabsorption in the tubule → urine collects in the collecting duct |
| III | 13 | Explain the role of auxin in phototropism | Auxin moves to the shaded side, so cells there elongate more and the shoot bends toward light |
| III | 14 | Explain the 10% law of energy transfer with a food chain | Only about 10% of energy passes to the next level. Example: grass → deer → tiger |
| IV (8m) | 15 | Draw a labelled diagram of the human digestive system and explain digestion in the stomach and small intestine | Stomach: HCl, pepsin, mucus. Small intestine: bile, pancreatic juice (trypsin, lipase, amylase), villi absorb food |
| IV | 16 | Draw the structure of a neuron. Explain a reflex arc with an example | Dendrite → cell body → axon. Receptor → sensory neuron → spinal cord → motor neuron → effector (e.g. pulling the hand from a hot object) |
| IV | 17 | Draw a L.S. of a flower. Explain pollination and fertilisation | Self vs cross pollination. The pollen tube enters the ovule, the male gamete fuses with the egg to form the zygote, and the ovary becomes the fruit |
Social Studies Practice Set (With Answer Points)
| # | Question | Marks | Answer Points |
|---|---|---|---|
| 1 | Who wrote "Vande Mataram"? | 1 | Bankim Chandra Chattopadhyay |
| 2 | Which is the largest multipurpose project on the Godavari in AP? | 1 | Polavaram project |
| 3 | What is meant by "community government" in Belgium? | 2 | A government elected by people of one language community (Dutch, French, German), handling cultural, educational and language matters |
| 4 | Distinguish between public and private sectors | 2 | Public: owned by the government, service motive. Private: owned by individuals, profit motive |
| 5 | Explain any four causes of the Non-Cooperation Movement | 4 | Rowlatt Act, Jallianwala Bagh massacre, Khilafat issue, wartime economic hardship |
| 6 | Explain the importance of the tertiary sector in India | 4 | Basic services, transport and trade support, rising incomes, IT and new services |
| 7 | Describe the features of the Indian Constitution that make it federal. Explain decentralisation | 8 | Three lists, written constitution, rigid amendment, independent judiciary, financial sources. 73rd/74th amendments: one-third seats for women, State Election Commission, panchayats |
| 8 | Map: locate Visakhapatnam port, Polavaram dam, Sriharikota, Bhilai steel plant and Dandi | 4 | Practise on a blank India outline map |
How to Use This Model Paper
| Step | Action |
|---|---|
| 1 | Use the 15-minute reading time to choose your Section IV options |
| 2 | Section I: about 15 min. Section II: about 25 min. Section III: about 60 min. Section IV: about 80 min |
| 3 | Leave 10 minutes to check |
| 4 | Mark your answers against the solutions and list every lost mark |
| 5 | Revise those chapters, then solve the official BSEAP model paper |
Frequently Asked Questions
Where can I download the official AP SSC 2027 model papers?
BSEAP publishes model papers and blueprints for all subjects on bse.ap.gov.in, in both English and Telugu medium. They are usually released in the second half of the year. This practice paper is a supplement to the official papers.
How many questions are in the AP SSC Maths paper?
The 100-mark Maths paper has 33 questions in four sections: 12 one-mark, 8 two-mark, 8 four-mark and 5 eight-mark questions. Section IV usually offers internal choice. Confirm with the 2027 blueprint.
Are Physical Science and Biology separate papers?
Yes. General Science is written as two separate 50-mark papers: Physical Science and Biological Science. Each has 17 questions across four sections.
What is the AP SSC exam duration?
The 100-mark papers are 3 hours 15 minutes, including 15 minutes of reading time. The 50-mark Science papers are shorter. Check the 2027 hall ticket and time table for the exact timing.
Is AP SSC based on NCERT now?
Yes. AP has moved Class 10 to NCERT-based textbooks, so the Maths, Science and Social Studies chapters match the NCERT syllabus. Older guides that mention "Sets" or "Progressions (AP + GP)" chapters follow the previous state syllabus.
How many model papers should I solve?
Solve at least 3 papers per subject: the official BSEAP model paper, previous year papers, and this practice set. Time yourself for every paper.
Related Guides
AP SSC Chapter-Wise Weightage 2027 | AP SSC Important Questions | AP Board Class 10 Complete Guide | AP SSC Date Sheet 2027 | AP SSC vs Telangana SSC
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