Math Topics

Integrating ln x gives x ln x − x + C. See why integration by parts works, three worked examples, a quick check by differentiating, a table of related integrals and JEE-style questions.

Geometric sequence formulas made clear: the nth term, the sum of n terms and the sum to infinity, a quick ratio test, the link to SAT exponential functions, common mistakes and JEE-style practice.

Compound interest is interest on interest; simple interest is on the start amount only. Learn both formulas, see a 5-year AED table where they split, find the rate or time, and link it to SAT exponential growth.

The surface area of the cone is πr² + πrl: the base plus the curved side. Find the slant height from the height, see why the side is πrl, and tell open cones from closed ones.

The area circle formula is A = πr²: square the radius, then multiply by π. See why it works, find the radius from the area, work out sectors and rings, and avoid the mistakes that cost marks.

The formula of volume of cylinder is V = πr²h: the circle area times the height. Find volume, height or radius, change cm³ to litres, and work out hollow pipes, with the mistakes that cost marks.

Completing the square rewrites x² + bx + c as (x + b/2)² plus a number. See why it works with an area picture, how to handle a ≠ 1, find a turning point and solve SAT-style circle questions.

All the trigonometry formulas in 8 groups, each with when to use it. Learn three core formulas, sin²θ + cos²θ = 1, sin(A + B) and cos(A + B), and build the rest from them.

The unit circle has radius 1, so the point at angle θ is (cos θ, sin θ). Build the exact values at 30°, 45° and 60° from two triangles, then use the quadrant signs.

Calculus basics in plain words: rate of change and area, shown with one Dubai Metro train, a ready-for-calculus checklist, 4 beginner mistakes, and where calculus sits in JEE Main and the SAT.