Mathematics Learning Path
High School (11–12) Mathematics
Explore structured mathematics courses, solved problems, simulations and Python activities.
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The Corner Point Method
A profit that grows along a straight line must be largest at the edge of what is allowed. Use that idea to find the maximum or minimum of an objective function at the corner points. See why unbounded regions need an extra test, what happens when there is no feasible solution or many, and check each answer with scipy.
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Linear Programming Problems from Words
A workshop, a canteen and a delivery van all face the same question: what is the best plan with limited resources? Turn the story into variables, an objective and constraints, draw the region, find the best corner and say what it means in the units of the problem. Manufacturing, diet and transport problems, in the style of the board and CUET papers.
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Linear Inequalities and Feasible Regions
What does the region 3x + 2y at most 12 look like? Draw one inequality, then several together, and shade the points that satisfy them all. Learn to tell a bounded region from an unbounded one, and to find its corner points by solving pairs of boundary lines.
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Inverse Trigonometric Functions: Domains, Ranges and Graphs
Why can the sine not be undone until we cut its graph? Learn the cuts, called principal value branches, for the six inverse functions. Read their domains, ranges and graphs, and work out values such as where the angle lies outside the cut. It covers the first part of the Indian syllabus unit (NCERT, JEE Main) and the matching topics of A-Level, IB and AP.
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Properties and Identities of Inverse Trigonometric Functions
The inverse sine and inverse cosine of the same number add up to a right angle. Prove it, and meet its family: the reflection rules, the reciprocal rules, the sum and difference of two inverse tangents with the condition on their product, and the double angle forms. Use a right triangle to find expressions such as . It covers the Indian syllabus (NCERT, JEE Main) and the matching topics of A-Level, IB and AP.
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Simplifying Expressions and Solving Equations with Inverse Trigonometric Functions
An expression like looks hopeless until you put . Learn the substitutions that make such expressions collapse, solve equations that hide an angle inside, and avoid the traps of domain and range that give false roots. A graph on the computer checks each answer. It covers the Indian syllabus (NCERT, JEE Main) and the matching topics of A-Level, IB and AP.
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Centre and Spread of Data
A weather office reports the average temperature of a town, but a farmer also wants to know how much the temperature jumps from day to day. Start with the three averages: the mean, the median and the mode, for a short list, a frequency table and grouped data. Then measure the spread with the range, the mean deviation, the variance and the standard deviation. The shortcut and step-deviation methods save work on big tables. It covers the first part of the Indian syllabus unit (NCERT, JEE Main) and the matching topics of A-Level, IB and AP.
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Comparing and Combining Data
Which of two bowlers is more consistent, when one takes more wickets on average? Which batch of bulbs is steadier? The standard deviation alone cannot answer, because it depends on the size of the numbers. Use the coefficient of variation to compare. See what happens to the mean and the spread when every value changes, and how to combine two groups, or correct a wrong reading, without starting again. Finish with quartiles, box plots and the rule for outliers. It covers the second part of the Indian syllabus unit (NCERT, JEE Main) and the matching topics of A-Level, IB and AP.
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Correlation and Regression
Do students who sleep longer score higher? Does a hotter day sell more ice cream? A scatter plot shows the pattern, and the correlation coefficient puts a number on it. Then fit the line of best fit by least squares, in both directions, and use it to predict. You also learn when a prediction can be trusted, and the traps that catch many students: causation, outliers and going beyond the data. The Indian Class 11 and 12 mathematics books do not teach this topic. A-Level, IB, AP Statistics and the SAT do.
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Random Variables and the Binomial Distribution
A basketball player takes ten free throws. How many will she score? You cannot say, but you can say how likely each count is. A random variable turns outcomes into numbers, and its distribution lists the chances. Find the mean and the variance of a random variable, then study repeated independent trials and the binomial distribution that describes them. The chapter ends with the normal approximation that A-Level and IB use for large trials. It covers the third part of the Indian syllabus unit (NCERT, JEE Main) and the matching topics of A-Level, IB and AP.
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Conditional Probability and Independent Events
You roll a die behind a screen, and a friend peeks and says the number is even. What is the chance it is a six? The answer is no longer one in six. Learn to shrink the sample space with a condition, to multiply along the branches of a tree diagram, and to decide when two events do not affect each other at all. It covers the first part of the Indian syllabus unit (NCERT, JEE Main) and the matching topics of A-Level, IB and AP.
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Total Probability and Bayes' Theorem
A factory has three machines, and one faulty bolt is found in the box. Which machine made it? You know how often each machine makes a faulty bolt, and now you want to run the question backwards. Split the world into cases, add the cases with the law of total probability, and reverse a condition with Bayes' theorem. Then meet the traps that catch even careful readers, from screening tests to the game show with three doors. It covers the second part of the Indian syllabus unit (NCERT, JEE Main) and the matching topics of A-Level, IB and AP.
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