CBSE Class 10 Maths All Formulas Sheet 2026: Chapter-by-Chapter Quick Revision Guide

If you're gearing up for your Class 10 Mathematics board exam, having every essential formula on a single revision sheet saves hours of panic during pre-board preparation. Mathematics isn't about memorizing blindly—it's about knowing when and how to apply each formula under exam pressure.

1. Real Numbers & Polynomials

• Euclid's Division Lemma: $a=bq+r$, where $0\le r<b$.
• HCF and LCM Relationship: $\text{HCF}(a,b)\times \text{LCM}(a,b)=a\times b$.
• Quadratic Polynomial: If $\alpha$ and $\beta$ are zeroes of $a{x}^2+bx+c$:
  • Sum of zeroes: $\alpha +\beta =-\frac{b}{a}$
  • Product of zeroes: $\alpha \beta =\frac{c}{a}$

2. Quadratic Equations & Arithmetic Progressions

• Quadratic Formula: $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$
• Discriminant ($D$): $D=b^2-4ac$
  • If $D>0$: Two distinct real roots.
  • If $D=0$: Two equal real roots.
  • If $D<0$: No real roots.
• Arithmetic Progression ($n$-th term): $a_n=a+(n-1)d$
• Sum of First $n$ Terms ($S_n$): $S_n=\frac{n}{2}[2a+(n-1)d]=\frac{n}{2}(a+l)$

3. Surface Areas and Volumes Summary Table

Shape	Curved / Lateral Surface Area	Total Surface Area	Volume
Cylinder	$2\pi rh$	$2\pi r(r+h)$	$\pi r^{2}h$
Cone	$\pi rl$   $(l=\sqrt{r^2+h^2})$	$\pi r(r+l)$	$\frac{1}{3}\pi r^{2}h$
Sphere	$4\pi r^2$	$4\pi r^2$	$\frac{4}{3}\pi r^3$
Hemisphere	$2\pi r^2$	$3\pi r^2$	$\frac{2}{3}\pi r^3$

4. Trigonometric Identities

• ${\sin }^2\theta +{\cos }^2\theta =1$
• $1+{\tan }^2\theta ={\sec }^2\theta$
• $1+{\cot }^2\theta ={\csc }^2\theta$

Teacher's Advice for Exam Day

Pro Tip: Always write down the general formula at the start of any 3-mark or 5-mark numerical problem before substituting values. CBSE marking schemes assign dedicated step marks for writing the correct formula even if your final calculation contains a minor arithmetic error.