ICSE · Class 10 · Code 511

ICSE Class 10 Mathematics — Important Questions

Question types and patterns from official CISCE board papers 2023, 2024, and 2025. Every topic below has appeared in at least one recent board examination.

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Section A — Compulsory (Questions 1–3, 40 marks)

All questions in Section A must be attempted. Q1 is MCQ (15 marks). Q2 and Q3 are short answer (4 marks each part).

Quadratic Equations — Nature of Roots

Q1 MCQ every year

·Identify number of roots from discriminant b²−4ac
·Assertion-Reason on trigonometric identity and cos⁴A + cos²A

Banking / Recurring Deposit

Q1 MCQ + Q2 every year

·Calculate maturity value given P, n, r
·Find rate of interest given maturity value
·Compare deposits at different amounts same rate

Probability

Q1 MCQ every year

·Identify which value cannot be a probability
·Probability from number cards (1–30) — perfect squares, primes, multiples

Coordinate Geometry — Lines

Q1 MCQ every year

·Equation of line through origin parallel to given line
·Slope of parallel/perpendicular lines

Matrices

Q1 MCQ + Q3 every year

·Find A² given a 2×2 matrix
·Compute A+C, B(A+C), 5B, B(A+C)−5B

Circles — Chord/Angle Properties

Q1 MCQ every year

·Find angle given equal chords and a known angle
·Angle subtended at centre vs remaining arc

Factorisation / Polynomials

Q1 MCQ every year

·Find common factor of two polynomials
·Factor theorem — find value of k then factorise completely

Shares and Dividends

Q1 MCQ + Q8 every year

·Shares at premium — find market value, dividend %, number of shares
·Given return %, determine if shares at par/above/below par

GST

Q1 MCQ + Q7 every year

·Find price including CGST + SGST given marked price
·Check if bill total is correct — multiple items with different GST rates and discount

Similarity

Q1 MCQ + Q2 every year

·Find side length given similar triangles and a ratio
·Prove triangles similar, then find side lengths and scale factor

Mensuration — Spheres/Cylinders/Cones

Q1 MCQ + Q5 every year

·Ratio of radii given ratio of volumes
·Total surface area of capsule (cylinder + two hemispheres)

Statistics — Mean / Median

Q8 every year

·Find mean and median from ungrouped frequency table
·Read median class and lower-quartile from ogive

Constructions

Q3 every year

·Circumscribe a circle on triangle with given sides and angle
·Construct tangents from external point

Section B — Attempt any 4 of 7 (Questions 4–10, 40 marks)

Choose 4 questions. Each question has 2–3 parts worth 3, 3, and 4 marks.

Linear Inequations

Section B every year (Q4)

·Solve double inequation in R, show on number line
·Solve and write solution set for x ∈ Z

Arithmetic Progression (AP)

Section B every year (Q4/Q10)

·Given first term, last term, sum — find number of terms and common difference
·Find n given nth term of GP, then find sum

Trigonometric Identities — Prove

Section B every year (Q4)

·Prove (cosecA + tanA − 1)(sinA + cosA) = sinA·cosecA / sin³A + cos³A

Ratio and Proportion

Section B every year (Q5)

·Using componendo-dividendo, find x from a proportion
·Applying properties to simplify

Heights and Distances

Section B every year (Q6)

·Find height of tower and building given angles of depression from top of building (use trig tables)
·2-D problems with two right-angled triangles

Coordinate Geometry — Reflection, Graphs

Section B every year (Q6)

·Reflect points on x-axis, y-axis, origin; join to form a closed figure
·From graph of parallelogram — coordinates, midpoint, slope, equation of diagonal

Statistics — Histogram + Ogive

Section B every year (Q7)

·Draw histogram from frequency table, find mode
·Read upper quartile, lower quartile, median from ogive; calculate IQR

Circles — Tangent and Secant

Section B every year (Q10)

·Prove ΔPTR ~ ΔPST; prove PT² = PR × PS; find PT given PR and PS
·Find angles given tangent and chord with alternate segment theorem

Geometric Progression (GP)

Section B every year (Q10)

·Find n given Tn of a GP, then find Sn

Source: All patterns derived from official CISCE ICSE Class 10 board examination papers (2023, 2024, 2025) downloaded from cisce.org. For the actual question papers, view the Mathematics Previous Year Papers.