JEE and CUET maths: formulas to know and exam strategy

Your CBSE formula sheets cover the board syllabus: Class 11 and Class 12. Learn those first; the lists below are the extra results worth knowing by heart.

Results worth knowing by heart

Algebra

• \(\alpha^2 + \beta^2 = (\alpha + \beta)^2 - 2\alpha\beta\) and \(\alpha^3 + \beta^3 = (\alpha + \beta)^3 - 3\alpha\beta(\alpha + \beta)\)
• Cube roots of unity: \(1 + \omega + \omega^2 = 0\), \(\omega^3 = 1\)
• Onto functions from an \(m\)-set to a 3-set: \(3^m - 3 \cdot 2^m + 3\)
• Number of terms of \((x + y + z)^n\): \(\binom{n + 2}{2}\)
• \(\binom{n}{0} + \binom{n}{2} + \dots = \binom{n}{1} + \binom{n}{3} + \dots = 2^{n-1}\)
• \(\sum k^3 = \left(\tfrac{n(n + 1)}{2}\right)^2\); \(\tfrac{1}{k(k + 1)} = \tfrac1k - \tfrac{1}{k + 1}\)

Matrices and determinants

• For an \(n \times n\) matrix: \(|kA| = k^n|A|\), \(|\operatorname{adj} A| = |A|^{n-1}\), \(\operatorname{adj}(kA) = k^{n-1}\operatorname{adj} A\)
• \(A(\operatorname{adj} A) = |A| I\)
• Three equations, zero determinant: infinitely many solutions or none, so check consistency

Trigonometry

• \(a\sin x + b\cos x\) lies between \(\pm\sqrt{a^2 + b^2}\)
• Principal ranges: \(\sin^{-1}, \tan^{-1}\): \([-\tfrac{\pi}{2}, \tfrac{\pi}{2}]\); \(\cos^{-1}\): \([0, \pi]\)
• \(\tan^{-1}a + \tan^{-1}b = \pi + \tan^{-1}\tfrac{a + b}{1 - ab}\) when \(a, b > 0\) and \(ab > 1\)

Coordinate geometry

• Distance between parallel lines \(ax + by + c_1 = 0\), \(ax + by + c_2 = 0\): \(\tfrac{|c_1 - c_2|}{\sqrt{a^2 + b^2}}\) (same \(a, b\) first)
• Ellipse \(b^2 = a^2(1 - e^2)\); hyperbola \(b^2 = a^2(e^2 - 1)\)
• Tangent to \(y^2 = 4ax\) with slope \(m\): \(y = mx + \tfrac{a}{m}\)

Calculus

• \(\lim_{x \to a}\tfrac{x^n - a^n}{x - a} = na^{n-1}\); \(\lim (1 + \tfrac{k}{x})^{x} = e^{k}\) as \(x \to \infty\)
• \(\sin x = x - \tfrac{x^3}{6} + \dots\), \(\tan x = x + \tfrac{x^3}{3} + \dots\) for limits
• \(\int_0^a f(x)\,dx = \int_0^a f(a - x)\,dx\) and \(\int_a^b f(x)\,dx = \int_a^b f(a + b - x)\,dx\)
• Odd function over \([-a, a]\): integral 0
• Area of an ellipse: \(\pi ab\)

Vectors, 3D and probability

• Coplanar vectors: scalar triple product 0
• Distance from \((x_1, y_1, z_1)\) to \(ax + by + cz + d = 0\): \(\tfrac{|ax_1 + by_1 + cz_1 + d|}{\sqrt{a^2 + b^2 + c^2}}\)
• Binomial distribution: mean \(np\), variance \(npq\); scaling data by \(k\) scales the variance by \(k^2\)

Strategy for the paper

1. Three passes. First pass: answer everything you can do in under a minute. Second pass: the questions you know how to start. Third pass: the rest, if time allows.
2. Use the options. In multiple choice, substitute a simple value (x = 0, x = 1, n = 1) to rule options out before solving in full.
3. Numerical-value questions have no options. Check the answer satisfies the question (and is the quantity asked for) before you type it.
4. Watch the clock, not the question. If a question passes two minutes with no clear route, mark it and move on.

Negative marking: when to guess

In 2026, JEE Main was marked +4 for a correct answer and −1 for a wrong one; CUET +5 and −1. With four options and those marks, the arithmetic is:

• A pure guess (all four options equally likely): JEE \(\tfrac14(4) - \tfrac34(1) = \tfrac14\) mark on average; CUET \(\tfrac14(5) - \tfrac34(1) = \tfrac12\). Small, and very uncertain over a few questions.
• After ruling out two options: JEE \(\tfrac12(4) - \tfrac12(1) = 1.5\) marks on average; CUET \(2\). Worth answering.
• Numerical-value questions: there are no options, so a guess is almost never right. Leave it blank unless you have worked it out.

Check the marking in the current information bulletin before the exam: if it changes, so does this arithmetic.

Arithmetic by hand

• Keep fractions and surds until the last line; most options are written that way.
• Know squares to 30, cubes to 12 and powers of 2 to \(2^{12}\).
• Remainders of large powers: find a power close to a multiple of the divisor, such as \(7^2 = 50 - 1\).

Practise with the chapter sets and the timed sets, and read the common traps. For the board paper, where every step earns marks, see the Class 12 exam strategy.

CBSE Math Revision is independent and not affiliated with NTA, the IITs or CBSE. Exam details marked to confirm are from the exam bodies' published documents but have not yet been re-checked against the current edition: always follow the official information bulletin.