AP Inter 1st Year Maths Answer Key 2026 (OUT) Live Updates: Difficulty Level of Question Paper; Detailed Solutions
AP Inter 1st Year Maths Exam 2026 was successfully conducted on March 2, 2026. Through this live blog, students can check the unofficial answer key prepared by subject expert and detailed analysis of the difficulty level of question paper.
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 throughAP Inter 1st Year Botany Marks Weightage 2026, Chapter-Wise with Detailed Blueprint,will help students prepare beforehand and understandthe 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
Mar 02, 2026 03:15 PM IST
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)
Mar 02, 2026 03:00 PM IST
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.
Mar 02, 2026 02:50 PM IST
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
Mar 02, 2026 02:40 PM IST
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
Mar 02, 2026 02:30 PM IST
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
Mar 02, 2026 02:15 PM IST
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
Mar 02, 2026 02:10 PM IST
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
Mar 02, 2026 02:05 PM IST
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
Mar 02, 2026 02:00 PM IST
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)
Mar 02, 2026 01:50 PM IST
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.
Mar 02, 2026 01:45 PM IST
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}Mar 02, 2026 01:20 PM IST
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.
Mar 02, 2026 12:40 PM IST
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.
Mar 02, 2026 12:15 PM IST
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!
Mar 02, 2026 12:00 PM IST
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!
Mar 02, 2026 11:00 AM IST
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.
Mar 02, 2026 10:30 AM IST
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.
Mar 02, 2026 10:00 AM IST
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!
Mar 02, 2026 09:00 AM IST
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.
Mar 02, 2026 08:00 AM IST
Reporting Time
Students are reporting to the examination venue, and their admit cards and documents are being checked by the authorities at the entrance.
Mar 02, 2026 07:00 AM IST
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. Mar 02, 2026 06:00 AM IST
Short Note 29
Topic Short Note Key Detail P & C Permutation (nPr) Arrangement of n things taking r at a time. Order matters. Mar 02, 2026 05:00 AM IST
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). Mar 02, 2026 04:00 AM IST
Short Note 27
Topic Short Note Key Detail Probability Addition Theorem P(A∪B)=P(A)+P(B)−P(A∩B). Mar 02, 2026 03:00 AM IST
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. Mar 02, 2026 02:00 AM IST
Short Note 25
Topic Short Note Key Detail Stats Mean Deviation Average of absolute differences from the mean: M.D=n∑∣xi−xˉ∣. Mar 02, 2026 01:00 AM IST
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. Mar 02, 2026 12:00 AM IST
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.
Mar 01, 2026 11:00 PM IST
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. Mar 01, 2026 10:45 PM IST
Short Note 22
Topic Short Note Key Detail Calculus Continuity f(x) is continuous at a if limx→af(x)=f(a). Mar 01, 2026 10:30 PM IST
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. Mar 01, 2026 10:15 PM IST
Short Note 20
Topic Short Note Key Detail Geometry Direction Cosines l=cosα,m=cosβ,n=cosγ, where l2+m2+n2=1. Mar 01, 2026 10:00 PM IST
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. Mar 01, 2026 09:45 PM IST
Short Note 18
Topic Short Note Key Detail Geometry Orthocentre The point of intersection of the altitudes of a triangle. Mar 01, 2026 09:30 PM IST
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. Mar 01, 2026 09:15 PM IST
Short Note 16
Topic Short Note Key Detail Induction Inductive Step Assuming P(k) is true to prove P(k+1) is true. Mar 01, 2026 09:00 PM IST
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. Mar 01, 2026 08:45 PM IST
Short Note 14
Topic Short Note Key Detail Hyperbolic Exponential Form sinhx=2ex−e−x and coshx=2ex+e−x. Mar 01, 2026 08:30 PM IST
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. Mar 01, 2026 08:15 PM IST
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. Mar 01, 2026 08:00 PM IST
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. Mar 01, 2026 07:45 PM IST
Short Note 10
Topic Short Note Key Detail Vectors Unit Vector A vector with magnitude 1: a^=∣a∣a. Mar 01, 2026 07:30 PM IST
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. Mar 01, 2026 07:15 PM IST
Short Note 8
Topic Short Note Key Detail Matrices Gauss-Jordan Method Solving equations by reducing augmented matrix $[A Mar 01, 2026 07:00 PM IST
AP Inter 1st Year Mathematics Exam 2026: Short Note 7
Topic Short Note Key Detail Matrices Skew-Symmetric A square matrix where AT=−A. Mar 01, 2026 06:45 PM IST
Short Note 6
Topic Short Note Key Detail Matrices Symmetric Matrix A square matrix where A=AT (Transpose is equal). Mar 01, 2026 06:30 PM IST
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. Mar 01, 2026 06:15 PM IST
Short Note 4
Topic Short Note Key Detail Functions Composite Function (g∘f)(x)=g[f(x)]. Note: g∘f=f∘g usually. Mar 01, 2026 06:00 PM IST
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. Mar 01, 2026 05:45 PM IST
Short Note 2
Topic Short Note Key Detail Functions Surjection (Onto) Range of function = Co-domain (f(A)=B). Mar 01, 2026 05:30 PM IST
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. Mar 01, 2026 05:15 PM IST
Important Formula from Combinations
Formula: (rn)=r!(n−r)!n!
Use Case: Selection-based problemsMar 01, 2026 05:00 PM IST
Important Formula from General Term
Formula: Tr+1=(rn)an−rbr
Use Case: Finding specific termsMar 01, 2026 04:45 PM IST
AP Intermediate First Year Maths Exam 2026: Important Formula from Variance (Discrete)
Formula: σ2=n∑(xi−xˉ)2
Use Case: 8-Mark Statistics QsMar 01, 2026 04:30 PM IST
Important Formula from Conditional
Formula: P(A∣B)=P(B)P(A∩B)
Use Case: Dependency problemsMar 01, 2026 04:15 PM IST
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 TheoremMar 01, 2026 04:00 PM IST
Important Formula from Chain Rule
Formula: dxdy=dudy⋅dxdu
Use Case: Composite FunctionsMar 01, 2026 03:45 PM IST
AP Intermediate First Year Maths Exam 2026: Important Formula from Standard Limit
Formula: limθ→0θsinθ=1
Use Case: Solving Limit problemsMar 01, 2026 03:30 PM IST
Important Formula from Product Rule
Formula: dxd(uv)=udxdv+vdxdu
Use Case: Standard DifferentiationMar 01, 2026 03:15 PM IST
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 DerivationsMar 01, 2026 03:00 PM IST
Important Formula from Parabola (Standard)
Formula: y2=4ax
Use Case: Locus and Focal chord QsMar 01, 2026 02:45 PM IST
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 QsMar 01, 2026 02:30 PM IST
Important Formula from Intercept Form
Formula: ax+by=1
Use Case: Straight Line SAQsMar 01, 2026 02:15 PM IST
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 lineMar 01, 2026 02:00 PM IST
Important Formula from Ex-radii (r1)
Formula: r1=s−aΔ=4Rsin2Acos2Bcos2C
Use Case: 8-Mark Properties of TrianglesMar 01, 2026 01:45 PM IST
AP Intermediate 1st Year Maths Exam 2026: Important Formula from Sine Rule
Formula: sinAa=sinBb=sinCc=2R
Use Case: Side-Angle relationshipsMar 01, 2026 01:30 PM IST
Important Formula from Inverse Identity
Formula: sinh−1x=loge(x+x2+1)
Use Case: 2-Mark Hyperbolic VSAQsMar 01, 2026 01:15 PM IST
AP Intermediate 1st Year Maths Exam 2026: Important Formula from Triple Angle (sin)
Formula: sin3θ=3sinθ−4sin3θ
Use Case: VSAQs and IdentitiesMar 01, 2026 01:00 PM IST
Important Formula from Double Angle (cos)
Formula: cos2θ=1−2sin2θ=2cos2θ−1
Use Case: Solving Trig EquationsMar 01, 2026 12:45 PM IST
AP Intermediate 1st Year Maths Exam 2026: Important Formula from Transformations
Formula: sinC+sinD=2sin2C+Dcos2C−D
Use Case: 8-Mark Trig identitiesMar 01, 2026 12:30 PM IST
Important Formula from Vector (Cross) Product
Formula: ∣a×b∣=∣a∣∣b∣sinθ
Use Case: Area of Triangle/Parallel.Mar 01, 2026 12:15 PM IST
AP Intermediate 1st Year Maths Exam 2026: Important Formula from Scalar (Dot) Product
Formula: a⋅b=∣a∣∣b∣cosθ
Use Case: Finding angle between vectorsMar 01, 2026 12:00 PM IST
Important Formula from Determinant (3x3)
Formula: a(ei−fh)−b(di−fg)+c(dh−eg)
Use Case: Cramer's Rule / VolumeMar 01, 2026 11:45 AM IST
AP Intermediate 1st Year Maths Exam 2026: Important Formula from Inverse Formula
Formula: A−1=det(A)adj(A)
Use Case: Matrix Inversion methodMar 01, 2026 11:30 AM IST
Important Formula from Composition Inverse
Formula: (g∘f)−1=f−1∘g−1
Use Case: 8-Mark Bijection proofsMar 01, 2026 11:15 AM IST
AP Intermediate 1st Year Maths Exam 2026: Important Formula from Identity Property
Formula: f∘IA=IB∘f=f
Use Case: Identity function proofsMar 01, 2026 11:00 AM IST
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.Mar 01, 2026 10:45 AM IST
Most Important Question 24
Question: Find variance of first n natural numbers.
Answer: Formula: σ2=12n2−1.Mar 01, 2026 10:30 AM IST
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.Mar 01, 2026 10:15 AM IST
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.Mar 01, 2026 10:00 AM IST
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.Mar 01, 2026 09:45 AM IST
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).Mar 01, 2026 09:30 AM IST
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).Mar 01, 2026 09:15 AM IST
Most Important Question 18
Question: Find the period of f(x)=cos(4x+9).
Answer: Period =∣a∣2π=42π=2π.Mar 01, 2026 09:00 AM IST
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,∞).Mar 01, 2026 08:45 AM IST
Most Important Question 16
Question: Find unit vector in direction of a=2i+3j+k.
Answer: a^=∣a∣a=142i+3j+k.Mar 01, 2026 08:30 AM IST
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].Mar 01, 2026 08:15 AM IST
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.Mar 01, 2026 08:00 AM IST
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.Mar 01, 2026 07:45 AM IST
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.Mar 01, 2026 07:30 AM IST
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.Mar 01, 2026 07:15 AM IST
Most Important Question 10
Question: Solve 3cosθ+sinθ=2.
Answer: cos(θ−30∘)=21⟹θ=n⋅360∘±45∘+30∘.Mar 01, 2026 07:00 AM IST
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).Mar 01, 2026 06:45 AM IST
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.Mar 01, 2026 06:30 AM IST
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.Mar 01, 2026 06:15 AM IST
Most Important Question 6
Question: Find the derivative of tan2x from the first principle.
Answer: f′(x)=limh→0htan2(x+h)−tan2x. Result: 2sec22x.Mar 01, 2026 06:00 AM IST
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).Mar 01, 2026 05:45 AM IST
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.Mar 01, 2026 05:30 AM IST
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.Mar 01, 2026 05:15 AM IST
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).Mar 01, 2026 05:00 AM IST
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.