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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M10 Linear Programming

All the topics in Mathematics: Linear Programming

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.

13 topics shown

#	Topic	Type	Marks	Times asked	Last asked	Status
1	Formulate an LPP from a word problemName the decision variables in words with units, write the objective function with max or min, write one constraint for each limited resource, and add the non-negativity conditions.	Sum	2	8 papers	2026	Asked
2	Word problem: budget and capacity limits, maximise profit or countFormulate with one money or weight constraint and one capacity constraint, draw the region, evaluate Z at the corners, and state the numbers to buy, stock or place and the maximum value, checking the answer is sensible (whole items).	Sum	5	4 papers	2026	Asked
3	Draw the feasible region for up to three constraintsConvert each inequality to a line, find its two axis intercepts, test the origin to choose the side, shade the common region in the first quadrant, solve pairs of lines for every corner point and label all corners with coordinates.	Graph	2	3 papers	2023	Asked
4	Word problem: manufacturing with machine or labour hours, maximise profitTabulate hours per item on each machine, formulate (variables, objective, up to three constraints), draw the feasible region, evaluate profit at each corner, and state how many of each item to make and the maximum profit.	Sum	5	3 papers	2020	Asked
5	Solve a given LPP graphically: bounded region, maximiseDraw and label the feasible region, list every corner point, make a corner point table of Z values, and state the maximum (or minimum) value of Z and the point where it occurs.	Sum	3	2 papers	Specimen 2027	Asked
6	Two-statement or assertion-reason on existence of optimal solutionsJudge each statement using the corner point theorem: a bounded feasible region always has a maximum and a minimum at corner points, an unbounded one may have none, an empty region has no solution, and two optimal corners give infinitely many optimal points on the segment joining them; then pick the option.	Give reason	1	1 paper	Specimen 2027	Asked
7	Write the constraints from a given shaded feasible regionFind the equation of each boundary line from two marked points, test a point inside the shaded region to fix the inequality sign for each line, and list all constraints including any bound such as x >= 1.	Graph	1	1 paper	Specimen 2027	Asked
8	Bounded, unbounded or infeasible region; change a constraintSay whether the region is bounded, unbounded or empty, and state which constraint to reverse or alter (and how) to make it unbounded or infeasible, with a one-line reason from the graph.	Give reason	1	1 paper	Specimen 2027	Asked
9	Objective optimal at two points: find coefficients or valueEquate Z at the two optimal points to get a relation between a and b, combine it with the extra condition given, solve for a and b, and evaluate the optimal value.	Sum	1	1 paper	Specimen 2027	Asked
10	Minimise over an unbounded region with the half-plane checkDraw the unbounded region, evaluate Z at each corner, take the smallest value m, then draw ax + by < m and show it has no point in common with the region before stating the minimum.	Sum	3	1 paper	2017	Asked
11	Word problem: diet or mixture, minimise costFormulate with 'at least' nutrient constraints (>=), draw the unbounded region, evaluate cost at the corners, do the half-plane check for the minimum, and state the quantities and the minimum cost.	Sum	5	1 paper	2017	Asked
12	LP terminology, advantages, limitations and application areasDefine decision variables, constraints, non-negativity restrictions, objective function, feasible region, feasible solution and optimal solution in one line each, and list two advantages, two limitations and two application areas of linear programming.	Statement	1	never		Never asked
13	Word problem: transportation from two depotsLet x and y be the amounts sent from one depot to two destinations, write every other route in terms of x and y, write supply and demand constraints, form the total cost, solve graphically and give the full shipping table.	Sum	5	never		Not in syllabus

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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