AP Inter 1st Year Maths Answer Key 2026 (OUT)AP Inter 1st Year Maths Exam 2026 : Board of Intermediate Education, Andhra Pradesh, has successfully conducted the AP Inter 1st Year Maths Exam 2026 on March 2, 2026. The exam was held from 9 AM to 12 PM. As per the student reviews, the exam was not easy. Some found it Moderate, while others found it Moderate to Difficult. Students found solving the merged paper of 1A and 1B Maths very challenging. Our Mathematics subject expert, Mahima Gupta, has solved the question paper after the exam, and an unofficial answer key has been provided here for the students. Detailed solutions for 4-mark and 8-mark questions can also be checked here, along with answers for 1-mark and 2-mark questions.
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AP Inter 1st Year Maths Answer Key 2026 (Unofficial)
Here is the unofficial AP Inter 1st Year Maths Answer Key 2026:Q. No. | Question | Answer |
|---|---|---|
Section A, 1 | The domain of the function 1/root (x^2−25) is: | (3) (−∞,−5)∪(5,∞) |
Section A, 2 | The value of root(−25) x root(−9) is: | (2) −15 |
Section A, 3 | If ^12C_s+1 = ^12C_2s−5, then the value of s is: | (4) 6 |
Section A, 4 | The coefficient of x^8y^10 in the expansion of (x+y)^18 is: | (1) 18^C_8 |
Section A, 5 | XOZ-plane divides the line joining the points (2,3,1) and (6,7,1) in the ratio: | (3) −3:7 |
Section A, 6 | If P(A)=0.5, P(B)=0.3 (given A and B are mutually exclusive), then P(A′∩B′)= | (4) 0.2 |
Section A, 7 | List all the elements of the set C={x:x is an integer, x^2≤4}. | C={−2,−1,0,1,2} |
Section A, 8 | Find the value of sin(−11π/3). | root 3/ 2 |
Section A, 9 | Find the sum to infinity in Geometric Progression 1, 1/3, 1/9… | 3/2 |
Section A, 10 | Find the equation of the line passing through (−4,3) with slope -1/2. | x−2y+10=0 |
Section A, 11 | Find the length of the transverse axis of the hyperbola x^2−4y^2=4. | 4 units |
Section A, 12 | Find the derivative of x^2−2 at x=10. | 20 |
Section B, 13 | Let A={1,2,{3,4},5}. Is the statement {3,4}∈A incorrect? And why? | No, it is correct. {3,4} is an element of set A. |
Section B, 14 | If P={a,b,c} and Q={r}, form P×Q and Q×P. Are these two products equal? | P×Q={(a,r),(b,r),(c,r)}; Q×P={(r,a),(r,b),(r,c)}. No. |
Section B, 15 | A wheel makes 360 revolutions in one minute. Through how many radians does it turn in one second? | 12π radians |
Section B, 16 | Express the complex number (1/5+3i)^3 in the form a+ib. | −674/125−108/5i |
Section B, 17 | How many 4-digit numbers can be formed by using the digits 1 to 9 if repetition of digits is not allowed? | 3024 |
Section B, 18 | Expand (x/3+1/x)^5 | x^5/243+ 5x^3/81 + 10^x/27 + 10/9x + 5/3x^3 + 1/x^5 |
Section B, 19 | Find the equation of the parabola with vertex (0,0) and passing through (2,3), and the axis is along the x-axis. | y^2=4.5x (or 2y^2=9x) |
Section B, 20 | Find 'x' if the distance between (5,−1,7) and (x,5,1) is 9 units. | x=2 or x=8 |
Section B, 21 | Evaluate limx→0x1+x−1. | 21 |
Section B, 22 | Find the mean deviation about the mean for the following data: 4, 7, 8, 9, 10, 12, 13, 17. | 3 |
Section B, 23 | U={1,2,3,4,5,6},A={2,3},B={3,4,5}. Find A′,B′,A′∩B′. | A′={1,4,5,6},B′={1,2,6},A′∩B′={1,6} |
Section B, 26 | A solution is to be kept between 68∘F and 77∘F. What is the range in Celsius (∘C) if F=59C+32? | 20∘C<C<25∘C |
Section B, 30 | Find coordinates of the foci, vertices, length of major axis, minor axis, and eccentricity of ellipse 100x2+400y2=1. | Vertices: (0,±20); Foci: (0,±103); Major Axis: 40; Minor Axis: 20; Eccentricity: 23 |
Section B, 32 | P(A)=0.54,P(B)=0.69,P(A∩B)=0.35. Find P(A∪B). | 0.88 |
AP Inter 1st Year Maths Exam 2026: Quick Facts
Below are some of the quick facts related to AP Inter First Year Maths Exam 2026:
Particulars | Details |
|---|---|
Name of the Exam | Andhra Pradesh Intermediate First Year Board Examination |
Conducting Body | Board of Intermediate Education, Andhra Pradesh (BIEAP) |
Exam Date | March 2, 2026 (As per official BIEAP Time Table) |
Exam Time | 9 AM to 12 PM |
Exam Mode | Offline (Pen-and-Paper) |
Maximum Marks | 100 Marks (Total weightage of paper is 136 Marks, including choices) |
Total Number of Questions | 39 Questions (Estimated based on marks distribution) |
Question Paper Sections |
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Section-wise Marks Allotted |
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Negative Marking | No Negative Marking |
What Next After AP Inter 1st Year Maths Exam 2026?
Now that the AP Inter 1st Year Maths Exam 2026 has ended, students should start preparing for the Biology exam. As per the AP Inter 1st Year time table, regular students have Biology Paper 1 on March 5, 2026, while backlog students have Mathematics Paper 1B and Zoology Paper 1A. Going through AP Inter 1st Year Botany Marks Weightage 2026 , Chapter-Wise with Detailed Blueprint, will help students prepare beforehand and understand the nature and pattern of the questions. They can invest more time in studying and revising high-weightage topics. Chapters such as Respiration in Plants, Anatomy of Flowering Plants and Morphology of Flowering Plants have the most weightage with 9 marks, 8 marks and 8 marks each.Stay tuned to the LIVE Blog for more updates on AP Inter 1st Year Maths Exam 2026.
AP Inter 1st Year Maths Exam 2026 LIVE
03 15 PM IST - 02 Mar'26
Section D, Question 40: (a) Probability of Math (40%), Bio (30%), Both (10%). Find P(Math or Bio).(b) 4 men, 6 women. Prob of selecting a woman.
Correct Answer:
(a) Use P(M∪B)=P(M)+P(B)−P(M∩B)P(M∪B)=0.40+0.30−0.10=0.60
(b) Total members = 4+6=10. Number of women = 6P(Woman)=106=0.6
(a) Probability = 0.6 (or 60%) (b) Probability = 0.6 (or 3/5)
03 00 PM IST - 02 Mar'26
Section D, Question 38: For what integers m and n do both limx→0f(x) and limx→1f(x) exist?
Correct Answer:
1. At x=0: LHL = limx→0−(mx2+n)=n; RHL = limx→0+(nx+m)=m. For a limit to exist, n=m
2. At x=1: LHL = limx→1−(nx+m)=n+m; RHL = limx→1+(nx3+m)=n+m.
3. The limit at x=1 exists for any values of m and n since LHL = RHL.
The limit at x=0 exists if m=n. Limit at x=1 exists for any integers m,n.
02 50 PM IST - 02 Mar'26
Section D, Question 36: Line through Q(2,3) at angle 43π with negative X-axis. Intersects x+y−7=0 at P. Find PQ.
Correct Answer:
1. Angle with positive X-axis (θ) = π−43π=4π (or 45∘)
2. Parametric coordinates of P at distance r from Q: x=2+rcos45∘, y=3+rsin45∘
3. x=2+2r, y=3+2r
4. Substitute into x+y−7=0: (2+2r)+(3+2r)−7=05. 22r−2=0⟹r2=2⟹r=2
Distance PQ=2 units
02 40 PM IST - 02 Mar'26
Section D, Question 35: Deposit = ₹10,000 at 5% simple interest. Find amount in 15th year and total after 20 years.
Correct Answer:
1. Interest per year: 10,000×0.05=₹500
2. Amount in 15th year: This is the Principal + Interest for 14 full years. 10,000+(14×500)=10,000+7,000=17,000
3. Total after 20 years: Principal + Interest for 20 years. 10,000+(20×500)=10,000+10,000=20,000
Amount in 15th year: ₹17,000, Total after 20 years: ₹20,000
02 30 PM IST - 02 Mar'26
Section D, Question 33: Given f(x)=2x−1 and g(x)=x2, find specific function operations.
Correct Answer:
(i) (3f−2g)(x)=3(2x−1)−2(x2)=−2x2+6x−3
(ii) (fg)(x)=(2x−1)(x2)=2x3−x2
(iii) (f/g)(x)=x22x−1
(iv) (f+g+2)(x)=(2x−1)+x2+2=x2+2x+1
(v) 2f(3)=2[2(3)−1]=2(5)=10
(vi) 2+f(x)=2+(2x−1)=2x+1
02 15 PM IST - 02 Mar'26
Section C, Section 32: P(A)=0.54, P(B)=0.69, P(A∩B)=0.35.
Correct Answer:
1. P(A∪B)=0.54+0.69−0.35=0.88.
2. P(A′∩B′)=1−P(A∪B)=1−0.88.
3. P(A∩B′)=P(A)−P(A∩B)=0.54−0.35.
4. P(B∩A′)=P(B)−P(A∩B)=0.69−0.35.
(i) 0.88 (ii) 0.12(iii) 0.19 (iv) 0.34
02 10 PM IST - 02 Mar'26
Section C, Section 31: Differentiate sin2x using first principle.
Correct Answer:
1. f′(x)=limh→0hsin2(x+h)−sin2x.
2. Use sinC−sinD=2cos2C+Dsin2C−D.
3. f′(x)=limh→0h2cos(2x+h)sinh.
4. Since limh→0hsinh=1.
f′(x)=2cos2x
02 05 PM IST - 02 Mar'26
Section C, Question 29: Line through (3,−5) and (−6,1). Find eq. of lines through (1,3) parallel and perp.
Correct Answer:
1. Slope m=−6−31−(−5)=−96=−32.
2. Parallel: mp=−2/3. Eq: y−3=−32(x−1).
3. Perp: m⊥=3/2. Eq: y−3=23(x−1).
Ans: (i) 2x+3y−11=0 (ii) 3x−2y+3=0
02 00 PM IST - 02 Mar'26
Section C, Question 26: CombinationsProve: (rn−3)+3(r−1n−3)+3(r−2n−3)+(r−3n−3)=(rn).
Correct Answer:
1. Group terms: [(rn−3)+(r−1n−3)]+2[(r−1n−3)+(r−2n−3)]+[(r−2n−3)+(r−3n−3)].
2. Apply Pascal’s Rule ((rn)+(r−1n)=(rn+1)):(rn−2)+2(r−1n−2)+(r−2n−2).
3. Repeat grouping to get (rn−1)+(r−1n−1).
LHS = RHS (rn)
01 50 PM IST - 02 Mar'26
Section C, Question 25: Show that the four points in the Argand plane represented by the complex number 2+i, 4+3i, 2+5i, 3i are the vertices of a square
Correct Answer:
1. Coordinates: A(2,1),B(4,3),C(2,5),D(0,3).
2. Sides: AB=22+22=8; BC=(−2)2+22=8.
3. All sides equal 8.
4. Diagonals: AC=02+42=4; BD=(−4)2+02=4.
Since Sides are equal and Diagonals are equal, it is a Square.
01 45 PM IST - 02 Mar'26
Section C, Question 24: Let A = {1, 2, 3, 4, 5, 6}. Define a relation R from A to A by R = {(x, y): y = x + 1}. (i) Depict this relation using an arrow diagram. (ii) Write down the domain, codomain and range of R.
Correct Answer:
1. List pairs: (1,2),(2,3),(3,4),(4,5),(5,6). (Note: (6,7) is excluded because 7∈/A).
2. Domain: Set of all first elements.
3. Range: Set of all second elements.
4. Codomain: The entire set A.
Domain: {1,2,3,4,5}, Range: {2,3,4,5,6}, Codomain: {1,2,3,4,5,6}01 20 PM IST - 02 Mar'26
Section C, Question 23: U={1,2,3,4,5,6}, A={2,3} and B={3,4,5}. Find A′, B′, A′∩B′, A∪B and hence show that (A∪B)′=A′∩B′.
Answer: 1. Find A′: The complement A' consists of all elements in U that are not in A.
A' = U-A = {1,4,5,6}
2. Find B′: The complement B' consists of all elements in U that are not in B.
B′ = U-B = {1,2,6}
3. Find A′∩B′: The intersection consists of elements common to both A' and B'.
A′∩B′= {1,4,5,6} ∩ {1,2,6} = {1,6}
4.Find A∪ B: The union consists of all elements present in either A or B.
A∪B= {2,3,4,5}
5. Find (A ∪ B)': The complement of the union consists of elements in U not present in {2, 3, 4, 5}.
(A∪B)' = U- {2, 3, 4, 5} = {1,6}
6. Since (A ∪ B)' = {1,6} and A′∩B′ = {1,6}, it means (A ∪ B)' = A′∩B′.
This is also known as This is known as De Morgan's First Law.
12 40 PM IST - 02 Mar'26
Exam Review: Paper not easy; exam was time taking!
Merging 1A and 1B Maths into a single paper proved to be a challenge for students. Some found the paper moderate, while others found it difficult.
12 15 PM IST - 02 Mar'26
Answer key out!
The answer key of the exam is out! Our expert is still solving the question paper, and more questions are being added to the page. Keep refreshing to see more unsolved questions!
12 00 PM IST - 02 Mar'26
Exam ends, answer key soon
The exam has ended, and students are expected to come out of the exam hall at any moment now. Stay glued for the answer key and student reactions!
11 00 AM IST - 02 Mar'26
One Hour Left!
The exam is all set to end in the next 1 hour! Students are expected to come out of the exam hall around 12:10 PM. The answer key by experts and reviews from students will be shared here soon after the students start coming out of their centre.
10 30 AM IST - 02 Mar'26
32-Page Answer Booklet Provided
Students have been given a 32-page answer booklet in the examination hall and are required to write all their answers in it.
This is the first time that Maths 1A and 1B have been combined into a single paper, and many students are concerned about whether the 32-page booklet will be sufficient or not.
10 00 AM IST - 02 Mar'26
Exam underway; answer key soon
AP Inter 1st Year Maths Exam 2026 is underway. This 3-hour-long test is being held from 9 AM to 12 PM. The solved question paper or answer key and student reviews will be shared here a few minutes after the exam is over!
09 00 AM IST - 02 Mar'26
AP Intermediate 1st Year Mathematics Exam 2026: Exam Starts
The examination has started and will get over at 12 PM. Post-exam, the answer key and detailed analysis will be provided here.
08 00 AM IST - 02 Mar'26
Reporting Time
Students are reporting to the examination venue, and their admit cards and documents are being checked by the authorities at the entrance.
07 00 AM IST - 02 Mar'26
AP Intermediate 1st Year Mathematics Exam 2026: Short Note 30
Topic Short Note Key Detail Binomial Middle Term If n is even, middle term is (2n+1)th. If odd, two middle terms. 06 00 AM IST - 02 Mar'26
Short Note 29
Topic Short Note Key Detail P & C Permutation (nPr) Arrangement of n things taking r at a time. Order matters. 05 00 AM IST - 02 Mar'26
AP Intermediate 1st Year Mathematics Exam 2026: Short Note 28
Topic Short Note Key Detail Probability Independent Events Two events A,B are independent if P(A∩B)=P(A)⋅P(B). 04 00 AM IST - 02 Mar'26
Short Note 27
Topic Short Note Key Detail Probability Addition Theorem P(A∪B)=P(A)+P(B)−P(A∩B). 03 00 AM IST - 02 Mar'26
AP Intermediate 1st Year Mathematics Exam 2026: Short Note 26
Topic Short Note Key Detail Stats Variance Square of standard deviation: σ2=n∑(xi−xˉ)2. 02 00 AM IST - 02 Mar'26
Short Note 25
Topic Short Note Key Detail Stats Mean Deviation Average of absolute differences from the mean: M.D=n∑∣xi−xˉ∣. 01 00 AM IST - 02 Mar'26
AP Intermediate 1st Year Mathematics Exam 2026: Short Note 24
Topic Short Note Key Detail Calculus Chain Rule For y=f(u) and u=g(x), dxdy=dudy⋅dxdu. 12 00 AM IST - 02 Mar'26
Exam Today
Board of Intermediate Education, Andhra Pradesh will conduct AP Inter 1st Year Maths 2026 examination today, March 2, from 9 AM to 12 PM.
11 00 PM IST - 01 Mar'26
AP Inter First Year Mathematics Exam 2026: Short Note 23
Topic Short Note Key Detail Calculus First Principle f′(x)=limh→0hf(x+h)−f(x). Used for standard derivations. 10 45 PM IST - 01 Mar'26
Short Note 22
Topic Short Note Key Detail Calculus Continuity f(x) is continuous at a if limx→af(x)=f(a). 10 30 PM IST - 01 Mar'26
AP Inter First Year Mathematics Exam 2026: Short Note 21
Topic Short Note Key Detail 3D Geometry yz-plane ratio The yz-plane divides the line joining P1,P2 in ratio −x1:x2. 10 15 PM IST - 01 Mar'26
Short Note 20
Topic Short Note Key Detail Geometry Direction Cosines l=cosα,m=cosβ,n=cosγ, where l2+m2+n2=1. 10 00 PM IST - 01 Mar'26
AP Inter First Year Mathematics Exam 2026: Short Note 19
Topic Short Note Key Detail Geometry Circumcentre The point of intersection of perpendicular bisectors of sides. 09 45 PM IST - 01 Mar'26
Short Note 18
Topic Short Note Key Detail Geometry Orthocentre The point of intersection of the altitudes of a triangle. 09 30 PM IST - 01 Mar'26
AP Inter First Year Mathematics Exam 2026: Short Note 17
Topic Short Note Key Detail Geometry Locus The set of points satisfying a given geometric condition. 09 15 PM IST - 01 Mar'26
Short Note 16
Topic Short Note Key Detail Induction Inductive Step Assuming P(k) is true to prove P(k+1) is true. 09 00 PM IST - 01 Mar'26
AP Inter First Year Mathematics Exam 2026: Short Note 15
Topic Short Note Key Detail Induction Basis Step Verifying the statement P(n) is true for n=1. 08 45 PM IST - 01 Mar'26
Short Note 14
Topic Short Note Key Detail Hyperbolic Exponential Form sinhx=2ex−e−x and coshx=2ex+e−x. 08 30 PM IST - 01 Mar'26
AP Inter First Year Mathematics Exam 2026: Short Note 13
Topic Short Note Key Detail Trig General Solutions If sinθ=sinα, then θ=nπ+(−1)nα. 08 15 PM IST - 01 Mar'26
Short Note 12
Topic Short Note Key Detail Trig Periodicity Period of sin(ax+b) is ∣a∣2π, and for tan(ax+b) is ∣a∣π. 08 00 PM IST - 01 Mar'26
AP Inter 1st Year Mathematics Exam 2026: Short Note 11
Topic Short Note Key Detail Vectors Coplanar Vectors Four points are coplanar if their scalar triple product [a,b,c]=0. 07 45 PM IST - 01 Mar'26
Short Note 10
Topic Short Note Key Detail Vectors Unit Vector A vector with magnitude 1: a^=∣a∣a. 07 30 PM IST - 01 Mar'26
AP Inter 1st Year Mathematics Exam 2026: Short Note 9
Topic Short Note Key Detail Vectors Collinearity Points A,B,C are collinear if AB=λBC for scalar λ. 07 15 PM IST - 01 Mar'26
Short Note 8
Topic Short Note Key Detail Matrices Gauss-Jordan Method Solving equations by reducing augmented matrix $[A 07 00 PM IST - 01 Mar'26
AP Inter 1st Year Mathematics Exam 2026: Short Note 7
Topic Short Note Key Detail Matrices Skew-Symmetric A square matrix where AT=−A. 06 45 PM IST - 01 Mar'26
Short Note 6
Topic Short Note Key Detail Matrices Symmetric Matrix A square matrix where A=AT (Transpose is equal). 06 30 PM IST - 01 Mar'26
AP Inter 1st Year Mathematics Exam 2026: Short Note 5
Topic Short Note Key Detail Matrices Singular Matrix A square matrix A where det(A)=0. Inverse doesn't exist. 06 15 PM IST - 01 Mar'26
Short Note 4
Topic Short Note Key Detail Functions Composite Function (g∘f)(x)=g[f(x)]. Note: g∘f=f∘g usually. 06 00 PM IST - 01 Mar'26
AP Inter 1st Year Mathematics Exam 2026: Short Note 3
Topic Short Note Key Detail Functions Bijection A function that is both injective and surjective. 05 45 PM IST - 01 Mar'26
Short Note 2
Topic Short Note Key Detail Functions Surjection (Onto) Range of function = Co-domain (f(A)=B). 05 30 PM IST - 01 Mar'26
AP Inter 1st Year Mathematics Exam 2026: Short Note 1
Topic Short Note Key Detail Functions Injection (One-One) Every distinct element in A has a distinct image in B. 05 15 PM IST - 01 Mar'26
Important Formula from Combinations
Formula: (rn)=r!(n−r)!n!
Use Case: Selection-based problems05 00 PM IST - 01 Mar'26
Important Formula from General Term
Formula: Tr+1=(rn)an−rbr
Use Case: Finding specific terms04 45 PM IST - 01 Mar'26
AP Intermediate First Year Maths Exam 2026: Important Formula from Variance (Discrete)
Formula: σ2=n∑(xi−xˉ)2
Use Case: 8-Mark Statistics Qs04 30 PM IST - 01 Mar'26
Important Formula from Conditional
Formula: P(A∣B)=P(B)P(A∩B)
Use Case: Dependency problems04 15 PM IST - 01 Mar'26
AP Intermediate First Year Maths Exam 2026: Important Formula from Addition Theorem
Formula: P(A∪B)=P(A)+P(B)−P(A∩B)
Use Case: 4-Mark Probability Theorem04 00 PM IST - 01 Mar'26
Important Formula from Chain Rule
Formula: dxdy=dudy⋅dxdu
Use Case: Composite Functions03 45 PM IST - 01 Mar'26
AP Intermediate First Year Maths Exam 2026: Important Formula from Standard Limit
Formula: limθ→0θsinθ=1
Use Case: Solving Limit problems03 30 PM IST - 01 Mar'26
Important Formula from Product Rule
Formula: dxd(uv)=udxdv+vdxdu
Use Case: Standard Differentiation03 15 PM IST - 01 Mar'26
AP Intermediate First Year Maths Exam 2026: Important Formula from First Principle
Formula: f′(x)=limh→0hf(x+h)−f(x)
Use Case: 8-Mark Derivations03 00 PM IST - 01 Mar'26
Important Formula from Parabola (Standard)
Formula: y2=4ax
Use Case: Locus and Focal chord Qs02 45 PM IST - 01 Mar'26
AP Intermediate First Year Maths Exam 2026: Important Formula from Circle Equation
Formula: (x−h)2+(y−k)2=r2
Use Case: Standard 8-Mark Conic Qs02 30 PM IST - 01 Mar'26
Important Formula from Intercept Form
Formula: ax+by=1
Use Case: Straight Line SAQs02 15 PM IST - 01 Mar'26
AP Intermediate First Year Maths Exam 2026: Important Formula from Distance from Point
Formula: d=a2+b2∣ax1+by1+c∣
Use Case: Distance to a line02 00 PM IST - 01 Mar'26
Important Formula from Ex-radii (r1)
Formula: r1=s−aΔ=4Rsin2Acos2Bcos2C
Use Case: 8-Mark Properties of Triangles01 45 PM IST - 01 Mar'26
AP Intermediate 1st Year Maths Exam 2026: Important Formula from Sine Rule
Formula: sinAa=sinBb=sinCc=2R
Use Case: Side-Angle relationships01 30 PM IST - 01 Mar'26
Important Formula from Inverse Identity
Formula: sinh−1x=loge(x+x2+1)
Use Case: 2-Mark Hyperbolic VSAQs01 15 PM IST - 01 Mar'26
AP Intermediate 1st Year Maths Exam 2026: Important Formula from Triple Angle (sin)
Formula: sin3θ=3sinθ−4sin3θ
Use Case: VSAQs and Identities01 00 PM IST - 01 Mar'26
Important Formula from Double Angle (cos)
Formula: cos2θ=1−2sin2θ=2cos2θ−1
Use Case: Solving Trig Equations12 45 PM IST - 01 Mar'26
AP Intermediate 1st Year Maths Exam 2026: Important Formula from Transformations
Formula: sinC+sinD=2sin2C+Dcos2C−D
Use Case: 8-Mark Trig identities12 30 PM IST - 01 Mar'26
Important Formula from Vector (Cross) Product
Formula: ∣a×b∣=∣a∣∣b∣sinθ
Use Case: Area of Triangle/Parallel.12 15 PM IST - 01 Mar'26
AP Intermediate 1st Year Maths Exam 2026: Important Formula from Scalar (Dot) Product
Formula: a⋅b=∣a∣∣b∣cosθ
Use Case: Finding angle between vectors12 00 PM IST - 01 Mar'26
Important Formula from Determinant (3x3)
Formula: a(ei−fh)−b(di−fg)+c(dh−eg)
Use Case: Cramer's Rule / Volume11 45 AM IST - 01 Mar'26
AP Intermediate 1st Year Maths Exam 2026: Important Formula from Inverse Formula
Formula: A−1=det(A)adj(A)
Use Case: Matrix Inversion method11 30 AM IST - 01 Mar'26
Important Formula from Composition Inverse
Formula: (g∘f)−1=f−1∘g−1
Use Case: 8-Mark Bijection proofs11 15 AM IST - 01 Mar'26
AP Intermediate 1st Year Maths Exam 2026: Important Formula from Identity Property
Formula: f∘IA=IB∘f=f
Use Case: Identity function proofs11 00 AM IST - 01 Mar'26
Most Important Question 25
Question: If n(A)=5,n(B)=7,n(A∩B)=3, find n(A∪B).
Answer: n(A∪B)=5+7−3=9.10 45 AM IST - 01 Mar'26
Most Important Question 24
Question: Find variance of first n natural numbers.
Answer: Formula: σ2=12n2−1.10 30 AM IST - 01 Mar'26
Most Important Question 23
Question: Find number of terms in (2x+3y+z)7.
Answer: Formula 2(n+1)(n+2). Ans: 28×9=36 terms.10 15 AM IST - 01 Mar'26
AP Inter First Year Maths Exam 2026: Most Important Question 22
Question: Number of ways to arrange letters of word "INTER".
Answer: Total 5 distinct letters. Ans: 5!=120.10 00 AM IST - 01 Mar'26
AP Inter First Year Maths Exam 2026: Most Important Question 21
Question: Evaluate limx→0xe3x−1.
Answer: Use standard limit limx→0xeax−1=a. Ans: 3.09 45 AM IST - 01 Mar'26
Most Important Question 20
Question: Find ratio in which yz-plane divides (2,4,5) and (3,5,−4).
Answer: Ratio =−x1:x2=−2:3. (Externally 2:3).09 30 AM IST - 01 Mar'26
AP Inter First Year Maths Exam 2026: Most Important Question 19
Question: If sinhx=3, find x in terms of log.
Answer: x=sinh−1(3)=log(3+32+1)=log(3+10).09 15 AM IST - 01 Mar'26
Most Important Question 18
Question: Find the period of f(x)=cos(4x+9).
Answer: Period =∣a∣2π=42π=2π.09 00 AM IST - 01 Mar'26
AP Inter First Year Maths Exam 2026: Most Important Question 17
Question: Find domain of f(x)=x2−a21.
Answer: x2−a2>0. Ans: (−∞,−a)∪(a,∞).08 45 AM IST - 01 Mar'26
Most Important Question 16
Question: Find unit vector in direction of a=2i+3j+k.
Answer: a^=∣a∣a=142i+3j+k.08 30 AM IST - 01 Mar'26
AP Inter First Year Maths Exam 2026: Most Important Question 15
Question: If A=[2−5−43], find A+A′.
Answer: A′=[2−4−53]. Sum =[4−9−96].08 15 AM IST - 01 Mar'26
Most Important Question 14
Question: Find the area of parallelogram with diagonals 3i+j−2k and i−3j+4k.
Answer: Area =21∣d1×d2∣=21∣−2i−14j−10k∣=53.08 00 AM IST - 01 Mar'26
AP Inter First Year Maths Exam 2026: Most Important Question 13
Question: Find distance between parallel lines 3x+4y−3=0 and 6x+8y−1=0.
Answer: d=a2+b2∣c1−c2∣. Normalize: 10∣−6−(−1)∣=0.5.07 45 AM IST - 01 Mar'26
Most Important Question 12
Question: State and prove the Addition Theorem on Probability.
Answer: P(A∪B)=P(A)+P(B)−P(A∩B). Use n(A∪B) set formula.07 30 AM IST - 01 Mar'26
AP Inter 1st Year Maths Exam 2026: Most Important Question 11
Question: Resolve (x+2)(x2+1)x2−3 into partial fractions.
Answer: 5(x+2)1+5(x2+1)4x−8. Values: A=1/5,B=4/5,C=−8/5.07 15 AM IST - 01 Mar'26
Most Important Question 10
Question: Solve 3cosθ+sinθ=2.
Answer: cos(θ−30∘)=21⟹θ=n⋅360∘±45∘+30∘.07 00 AM IST - 01 Mar'26
AP Inter 1st Year Maths Exam 2026: Most Important Question 9
Question: Position vectors 2a+3b−c,a−2b+3c,3a+8b−5c are collinear.
Answer: Find AB=−a−5b+4c and AC=a+5b−4c. Show AB=−1(AC).06 45 AM IST - 01 Mar'26
Most Important Question 8
Question: Sum of distances from P to (0,2) and (0,−2) is 6. Find locus.
Answer: x2+(y−2)2+x2+(y+2)2=6⟹9x2+5y2=45.06 30 AM IST - 01 Mar'26
AP Inter 1st Year Maths Exam 2026: Most Important Question 7
Question: Show that r+r3+r1−r2=4RcosB.
Answer: Use r=4Rsin2Asin2Bsin2C and r1=4Rsin2Acos2Bcos2C.06 15 AM IST - 01 Mar'26
Most Important Question 6
Question: Find the derivative of tan2x from the first principle.
Answer: f′(x)=limh→0htan2(x+h)−tan2x. Result: 2sec22x.06 00 AM IST - 01 Mar'26
AP Inter 1st Year Maths Exam 2026: Most Important Question 5
Question: Find the orthocentre of triangle with vertices (5,−2),(−1,2),(1,4).
Answer: Find slopes of sides; find Eq. of altitudes; solve intersection. Ans: (1/5,2/5).05 45 AM IST - 01 Mar'26
Most Important Question 4
Question: If A+B+C=180∘, prove sin2A+sin2B+sin2C=4sinAsinBsinC.
Answer: Use 2sin(A+B)cos(A−B)+2sinCcosC. Subst. A+B=180−C.05 30 AM IST - 01 Mar'26
AP Inter 1st Year Maths Exam 2026: Most Important Question 3
Question: Solve 3x+4y+5z=18,2x−y+8z=13,5x−2y+7z=20 by Gauss-Jordan.
Answer: Reduce augmented matrix [A∣B] to [I∣X]. Ans: x=3,y=1,z=1.05 15 AM IST - 01 Mar'26
Most Important Question 2
Question: Show 12+(12+22)+⋯+n terms=12n(n+1)2(n+2).
Answer: Step 1: P(1) is true. Step 2: Assume P(k). Step 3: Sk+1=Sk+6(k+1)(k+2)(2k+3).05 00 AM IST - 01 Mar'26
AP Inter 1st Year Maths Exam 2026: Most Important Question 1
Question: If f:A→B and g:B→C are bijections, prove (g∘f)−1=f−1∘g−1.
Answer: Prove g∘f is a bijection, then show (g∘f)∘(f−1∘g−1)=IC.
