CBSE Class 10 Maths: The 10-Minute Ultimate Formula Cheat Sheet (2026)

 

CBSE Class 10 Maths: The 10-Minute Ultimate Formula Cheat Sheet (2026)

It’s almost game time. You’ve done the hard work, solved the sample papers, and survived the pre-boards. Now, all you need is to keep these formulas at the top of your mind to avoid "blanking out" in the exam hall.

Here is every essential formula you need for the CBSE Class 10 Mathematics Exam 2026. Bookmark this page now!

1. Real Numbers & Algebra

Real Numbers

  • Circle Sector/Segment:

    • Area of Sector: $\frac{\theta}{360} \times \pi r^2$

    • Length of Arc: $\frac{\theta}{360} \times 2\pi r$

    5. Statistics & Probability

    • Mean $(\bar{x})$: $\frac{\sum f_ix_i}{\sum f_i}$

    • Mode: $l + \left( \frac{f_1 - f_0}{2f_1 - f_0 - f_2} \right) \times h$

    • Empirical Formula: $3 \text{ Median} = \text{ Mode} + 2 \text{ Mean}$

    • Probability $P(E)$: $\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$

    • $0 \le P(E) \le 1$

    Final Pro-Tips for Tomorrow:

    1. Read the Question Twice: Especially in Case Studies.

    2. Units Matter: Ensure all dimensions are in the same unit (cm, m, etc.) before calculating.

    3. Step Marking: Write the formula even if you can't finish the calculation. CBSE gives marks for it!

    4. Diagrams: Use a sharp pencil for geometry and heights/distances.

    You’ve got this! Go crush that paperFundamental Theorem: $HCF(a, b) \times LCM(a, b) = a \times b$

Polynomials

For a quadratic polynomial $ax^2 + bx + c$:

  • Sum of zeroes $(\alpha + \beta)$: $-\frac{b}{a}$

  • Product of zeroes $(\alpha\beta)$: $\frac{c}{a}$

  • Forming a polynomial: $x^2 - (\text{Sum})x + (\text{Product})$

Linear Equations

Conditions for $a_1x + b_1y + c_1 = 0$ and $a_2x + b_2y + c_2 = 0$:

  1. Unique Solution: $\frac{a_1}{a_2} \neq \frac{b_1}{b_2}$ (Intersecting lines)

  2. No Solution: $\frac{a_1}{a_2} = \frac{b_1}{b_2} \neq \frac{c_1}{c_2}$ (Parallel lines)

  3. Infinite Solutions: $\frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2}$ (Coincident lines)

Quadratic Equations

  • Quadratic Formula: $x = \frac{-b \pm \sqrt{D}}{2a}$

  • Discriminant $(D)$: $b^2 - 4ac$

  • Nature of Roots:

    • $D > 0$: Two distinct real roots.

    • $D = 0$: Two equal real roots.

    • $D < 0$: No real roots.

Arithmetic Progression (AP)

  • $n^{th}$ term $(a_n)$: $a + (n-1)d$

  • Sum of $n$ terms $(S_n)$: $\frac{n}{2}[2a + (n-1)d]$ or $\frac{n}{2}[a + l]$

2. Geometry & Coordinate Geometry

Coordinate Geometry
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  • Distance Formula: $\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$

  • Section Formula: $P(x, y) = \left( \frac{m_1x_2 + m_2x_1}{m_1+m_2}, \frac{m_1y_2 + m_2y_1}{m_1+m_2} \right)$

  • Mid-point Formula: $\left( \frac{x_1+x_2}{2}, \frac{y_1+y_2}{2} \right)$

Triangles & Circles

  • BPT (Thales Theorem): If $DE \parallel BC$, then $\frac{AD}{DB} = \frac{AE}{EC}$

  • Circle Tangent: Tangent at any point is $\perp$ to the radius through the point of contact ($90^\circ$).

  • Tangent Lengths: Tangents drawn from an external point to a circle are equal.

3. Trigonometry (The Scoring Zone)

Ratios & Identities

  • $\sin\theta = \frac{P}{H}, \cos\theta = \frac{B}{H}, \tan\theta = \frac{P}{B}$

  • Identity 1: $\sin^2\theta + \cos^2\theta = 1$

  • Identity 2: $1 + \tan^2\theta = \sec^2\theta$

  • Identity 3: $1 + \cot^2\theta = \text{cosec}^2\theta$

4. Mensuration (Surface Area & Volume)
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Explore

ShapeCurved Surface Area (CSA)Total Surface Area (TSA)Volume
Cylinder$2\pi rh$$2\pi r(h+r)$$\pi r^2h$
Cone$\pi rl$ (where $l = \sqrt{r^2+h^2}$)$\pi r(l+r)$$\frac{1}{3}\pi r^2h$
Sphere$4\pi r^2$$4\pi r^2$$\frac{4}{3}\pi r^3$
Hemisphere$2\pi r^2$$3\pi r^2$$\frac{2}{3}\pi r^3$

Circle Sector/Segment:

  • Area of Sector: $\frac{\theta}{360} \times \pi r^2$

  • Length of Arc: $\frac{\theta}{360} \times 2\pi r$

5. Statistics & Probability

  • Mean $(\bar{x})$: $\frac{\sum f_ix_i}{\sum f_i}$

  • Mode: $l + \left( \frac{f_1 - f_0}{2f_1 - f_0 - f_2} \right) \times h$

  • Empirical Formula: $3 \text{ Median} = \text{ Mode} + 2 \text{ Mean}$

  • Probability $P(E)$: $\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$

  • $0 \le P(E) \le 1$

Final Pro-Tips for Tomorrow:

  1. Read the Question Twice: Especially in Case Studies.

  2. Units Matter: Ensure all dimensions are in the same unit (cm, m, etc.) before calculating.

  3. Step Marking: Write the formula even if you can't finish the calculation. CBSE gives marks for it!

  4. Diagrams: Use a sharp pencil for geometry and heights/distances.

You’ve got this! Go crush that paper.

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