What the board asks

We went through the ISC board papers, question by question, and matched each question to a topic. Here is what was asked, how often, and what was never asked.

Mathematics: 309 topics in the 2027 syllabus, across 11 units. The board has asked 255 of them at least once. 54 were never asked in the papers we checked.

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M6 Calculus: Application of Integrals

All the topics in Mathematics: Calculus: Application of Integrals

Asked topics first, the most asked at the top. Tap a topic to see what to write, the result, the years, and the real board questions.

14 topics shown

#	Topic	Type	Marks	Times asked	Last asked	Status
1	Area between a parabola and a lineSketch both, solve for the intersection points, decide which is on top (or on the right), write area = integral of (upper - lower) between the intersections, integrate, evaluate, and give sq units.	Sum	5	5 papers	Specimen 2027	Asked
2	Sketch simple curves and find their intersection pointsDraw clean axes, sketch each curve with its vertex, centre or intercepts labelled, solve the equations together for the points of intersection, mark them, and shade the required region.	Graph	1	5 papers	2025	Asked
3	Area of a parabola cut off by line x=kSketch y^2 = 4ax and the line x = k, write area = 2 x integral from 0 to k of sqrt(4ax) dx using symmetry about the x-axis, integrate x^(1/2), and simplify.	Sum	3	2 papers	2024	Asked
4	Area between two parabolasSketch both parabolas, solve together for the intersection points, write area = integral of (upper - lower) dx or (right - left) dy, integrate the square-root and square terms, and evaluate.	Sum	5	2 papers	2024	Asked
5	Choose the integral that gives a shaded area (MCQ)Read the boundaries from the figure, write each boundary as y in terms of x (or x in terms of y), decide the limits and which curve is on top, and pick or write the matching integral.	Give reason	1	1 paper	Specimen 2027	Asked
6	Case study: find the curve first, then the areaFind the missing equation (tangent at a point from the derivative, or a parabola through given intercepts), mark the region on the given diagram, then set up and evaluate the area integral.	Sum	3	1 paper	Specimen 2027	Asked
7	Area of a circle, ellipse or part by integrationSketch the circle or ellipse, write y = sqrt(a^2 - x^2) (or (b/a) sqrt(a^2 - x^2)), use symmetry to take one quadrant, integrate with the standard result, substitute limits, and multiply back.	Sum	3	1 paper	2026	Asked
8	Area under a curve between the x-axis and two ordinatesSketch the curve, write area = integral from a to b of y dx, integrate, substitute the limits, and write the answer in square units; use symmetry when the region is symmetric about the y-axis.	Sum	2	1 paper	2025	Asked
9	Area between a curve and the y-axis, integrating in ySketch the region, rewrite each boundary as x in terms of y, write area = integral from c to d of x dy (or right minus left), integrate and evaluate; split the region if the right boundary changes.	Sum	3	1 paper	2025 improvement	Asked
10	Word problem: area of a field bounded by three linesFind the three vertices by solving the lines in pairs, sketch the triangle, split it at the middle vertex, write each part as integral of (upper line - lower line), evaluate and add.	Sum	5	1 paper	2025	Asked
11	Area under a modulus function between two linesSketch the V-shaped graph, split the interval at the vertex, write y without modulus on each piece, integrate each piece and add.	Sum	3	1 paper	2018	Asked
12	Area under an exponential or logarithmic curveSketch y = e^x or y = log x with its intercept, set up the integral with the correct limits (from x = 1 for log x), integrate (by parts for log x), and evaluate.	Sum	2	never		Never asked
13	Area when the curve crosses the x-axis: split and addFind where the curve cuts the x-axis, sketch, integrate separately over each sub-interval, take the absolute value of each negative part, and add.	Sum	3	never		Never asked
14	Area between circle or ellipse and line or parabolaSketch, find the intersection points, write the integral of (upper - lower), use the sqrt(a^2 - x^2) standard result for the circle part, split the integral where a boundary changes, and simplify.	Sum	5	never		Never asked

This list was made from the 2027 syllabus and checked with 10 board papers, including the 2027 specimen paper. It is not yet checked with the textbook.

The 10 topics Mathematics papers ask most

Counted on the board papers from 2018 to the 2027 specimen paper, which every unit has been checked against.

1.Formulate an LPP from a word problemM10 Linear Programming · asked 7 times since 2018
2.Scalar and vector projection of one vector on anotherM8 Vector Algebra · asked 6 times since 2018
3.Mean (expected value) of a random variableM11 Probability · asked 6 times since 2018
4.Find the inverse of an invertible algebraic function and verifyM1 Relations and Functions · asked 5 times since 2018
5.Principal value of expressions and nested inverse trigM1 Relations and Functions · asked 5 times since 2018
6.Evaluate or show zero without expanding, using propertiesM2 Algebra: Matrices and Determinants · asked 5 times since 2018
7.Prove a determinant equals a factorised expression using propertiesM2 Algebra: Matrices and Determinants · asked 5 times since 2018
8.Definite integral of a modulus functionM5 Calculus: Integrals · asked 5 times since 2018
9.Case study or linked parts on lines and planesM9 Three-Dimensional Geometry · asked 5 times since 2018
10.Equations solved with the complementary identitiesM1 Relations and Functions · asked 4 times since 2018

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