What are the important formulas for NVS TGT Mathematics?

Dear Aspirants,

Greetings from Bansal Academy! Mastery of essential formulas is crucial for performing well in the NVS TGT Mathematics exam. Below, we have outlined some of the key formulas that you should be familiar with:

1. Algebra:
   • Quadratic Equations:
     • General Form: ax2+bx+c=0ax^2 + bx + c = 0ax2+bx+c=0
     • Roots: x=−b±b2−4ac2ax = \frac{-b \pm \sqrt{b^2 – 4ac}}{2a}x=2a−b±b2−4ac​​
   • Arithmetic Progression (AP):
     • nth Term: an=a+(n−1)da_n = a + (n-1)dan​=a+(n−1)d
     • Sum of n Terms: Sn=n2[2a+(n−1)d]S_n = \frac{n}{2} [2a + (n-1)d]Sn​=2n​[2a+(n−1)d]
   • Geometric Progression (GP):
     • nth Term: an=a⋅r(n−1)a_n = a \cdot r^{(n-1)}an​=a⋅r(n−1)
     • Sum of n Terms: Sn=arn−1r−1S_n = a \frac{r^n – 1}{r – 1}Sn​=ar−1rn−1​ (for r≠1r \neq 1r=1)
2. Coordinate Geometry:
   • Distance Formula:
     • Between Two Points: d=(x2−x1)2+(y2−y1)2d = \sqrt{(x_2 – x_1)^2 + (y_2 – y_1)^2}d=(x2​−x1​)2+(y2​−y1​)2​
   • Midpoint Formula:
     • Midpoint of a Line Segment: M=(x1+x22,y1+y22)M = \left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right)M=(2x1​+x2​​,2y1​+y2​​)
   • Equation of a Line:
     • Slope-Intercept Form: $y=mx+c$
     • Point-Slope Form: y−y1=m(x−x1)y – y_1 = m(x – x_1)y−y1​=m(x−x1​)
3. Geometry:
   • Triangles:
     • Pythagorean Theorem: a2+b2=c2a^2 + b^2 = c^2a2+b2=c2 (for a right-angled triangle)
     • Area of Triangle: Area=12×base×height\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}Area=21​×base×height
   • Circles:
     • Circumference: $C=2\pi r$
     • Area: A=πr2A = \pi r^2A=πr2
   • Quadrilaterals:
     • Area of a Rectangle: $A=l\times w$
     • Area of a Parallelogram: $A=\text{base}\times \text{height}$
     • Area of a Trapezium: A=12×(a+b)×hA = \frac{1}{2} \times (a + b) \times hA=21​×(a+b)×h
4. Trigonometry:
   • Trigonometric Ratios:
     • sin⁡(θ)=oppositehypotenuse\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}sin(θ)=hypotenuseopposite​
     • cos⁡(θ)=adjacenthypotenuse\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}cos(θ)=hypotenuseadjacent​
     • tan⁡(θ)=oppositeadjacent\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}tan(θ)=adjacentopposite​
   • Trigonometric Identities:
     • sin⁡2(θ)+cos⁡2(θ)=1\sin^2(\theta) + \cos^2(\theta) = 1sin2(θ)+cos2(θ)=1
     • tan⁡(θ)=sin⁡(θ)cos⁡(θ)\tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)}tan(θ)=cos(θ)sin(θ)​
   • Angle Sum and Difference Identities:
     • $\sin (A\pm B)=\sin A\cos B\pm \cos A\sin B$
     • $\cos (A\pm B)=\cos A\cos B\mp \sin A\sin B$
5. Calculus:
   • Differentiation:
     • Derivative of f(x)=xnf(x) = x^nf(x)=xn: ddx(xn)=nxn−1\frac{d}{dx} (x^n) = nx^{n-1}dxd​(xn)=nxn−1
   • Integration:
     • Integral of f(x)=xnf(x) = x^nf(x)=xn: ∫xn dx=xn+1n+1+C\int x^n \, dx = \frac{x^{n+1}}{n+1} + C∫xndx=n+1xn+1​+C
6. Statistics:
   • Mean:
     • Mean=∑xn\text{Mean} = \frac{\sum x}{n}Mean=n∑x​
   • Median:
     • For ungrouped data, arrange the data in ascending order and find the middle value.
   • Mode:
     • The value that appears most frequently in the data set.

These formulas are crucial for solving various problems in the NVS TGT Mathematics exam. Regular practice and application of these formulas will significantly boost your performance.

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