Formulas

SEBA Class X Mathematics – Formula Sheet

1. Real Numbers

$a = bq + r,\; 0 \le r < b$

$\text{HCF} \times \text{LCM} = a \times b$

2. Polynomials

$\text{Dividend} = \text{Divisor} \times \text{Quotient} + \text{Remainder}$

$\text{Sum of zeroes} = -\frac{b}{a}$

$\text{Product of zeroes} = \frac{c}{a}$

3. Pair of Linear Equations

$a_1x + b_1y + c_1 = 0$

$a_2x + b_2y + c_2 = 0$

$\frac{a_1}{a_2} \ne \frac{b_1}{b_2}$ → Unique solution

$\frac{a_1}{a_2} = \frac{b_1}{b_2} \ne \frac{c_1}{c_2}$ → No solution

$\frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2}$ → Infinite solutions

4. Quadratic Equations

$ax^2 + bx + c = 0$

$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

$D = b^2 - 4ac$

5. Arithmetic Progression

$a_n = a + (n - 1)d$

$S_n = \frac{n}{2}[2a + (n - 1)d]$

$S_n = \frac{n}{2}(a + l)$

6. Coordinate Geometry

$\text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

$\text{Section Formula} = \left(\frac{mx_2 + nx_1}{m+n}, \frac{my_2 + ny_1}{m+n}\right)$

$\text{Area} = \frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|$

7. Trigonometry

$\sin\theta = \frac{\text{Perpendicular}}{\text{Hypotenuse}}$

$\cos\theta = \frac{\text{Base}}{\text{Hypotenuse}}$

$\tan\theta = \frac{\text{Perpendicular}}{\text{Base}}$

$\sin^2\theta + \cos^2\theta = 1$

$1 + \tan^2\theta = \sec^2\theta$

$1 + \cot^2\theta = \cosec^2\theta$

8. Areas Related to Circles

$\text{Circumference} = 2\pi r$

$\text{Area} = \pi r^2$

$\text{Sector Area} = \frac{\theta}{360}\pi r^2$

$\text{Arc Length} = \frac{\theta}{360}2\pi r$

9. Surface Areas & Volumes

$\text{Cuboid} = lbh$

$\text{Cylinder} = \pi r^2h$

$\text{Cone} = \frac{1}{3}\pi r^2h$

$\text{Sphere} = \frac{4}{3}\pi r^3$

10. Statistics

$\text{Mean} = \frac{\sum fx}{\sum f}$

$\text{Mean} = a + \frac{\sum fd}{\sum f}$

$\text{Mean} = a + \frac{\sum fu}{\sum f} \times h$

11. Probability

$P(E) = \frac{\text{Favourable Outcomes}}{\text{Total Outcomes}}$

$0 \le P(E) \le 1$