Guess Paper 2026 — 1st Year Math

Chapter 4: Matrices and Determinants

Study chapter →

Short questions

• Adjoint and inverse of a 2×2 and 3×3 matrix
• Cramer\u{2019}s rule for two and three equations
• Properties of determinants (any two proofs)

Long questions

• Find the inverse of a 3×3 matrix using adjoint method
• Solve a system of 3 linear equations by Cramer\u{2019}s rule

Chapter 6: Sequences and Series

Study chapter →

Short questions

• nth term and sum of AP/GP
• Arithmetic, geometric and harmonic means
• Sigma notation expansions

Long questions

• Word problem on AP or GP (business/loan style)
• Prove a series sum using sigma notation

Chapter 10: Trigonometric Identities

Study chapter →

Short questions

• Prove: sin(A+B), cos(A−B) identities
• Double-angle and half-angle formulas
• Convert sum to product and back

Long questions

• Prove a compound identity (LHS = RHS) using sum/difference formulas

Chapter 3: Theory of Quadratic Functions

Study chapter →

Short questions

• Nature of roots via discriminant
• Sum and product of roots
• Vertex and axis of symmetry

Long questions

• Discuss the nature of roots and sketch the parabola
• Form a quadratic with given roots/conditions

Chapter 12: Limit and Continuity

Study chapter →

Short questions

• Evaluate limits by factorisation/rationalisation
• One-sided limits
• Check continuity at a point

Long questions

• Evaluate a 0/0 limit using algebraic techniques
• Discuss continuity of a piecewise function

Chapter 8: Mathematical Induction and Binomial Theorem

Study chapter →

Short questions

• Binomial general term and middle term
• Binomial approximations

Long questions

• Prove a statement by mathematical induction (divisibility or inequality)
• Find a specified term in a binomial expansion

Chapter 7: Permutations and Combinations

Study chapter →

Short questions

• nPr and nCr evaluations
• Word problems: committees, arrangements

Long questions

• Counting problem combining permutations and combinations

Chapter 9: Division of Polynomials

Study chapter →

Short questions

• Remainder theorem applications
• Factor theorem: show (x−a) is a factor

Long questions

• Divide polynomials and find quotient/remainder
• Use factor theorem to factorise a cubic