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Math Tools for Class 11

A curated resource for mastering key mathematical concepts for the JEE exam.

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1. Trigonometry

Trigonometry deals with angles, triangles, and their ratios. It’s a fundamental part of JEE.

📌 Common Formula in Trigonometry:

Col 1	Col 2	Col 3
sin²θ + cos²θ = 1	1 + cot²θ = cosec²θ	1 + tan²θ = sec²θ
sin (90 + θ) = cos θ	sin (180 - θ) = sin θ	sin (90 - θ) = cos θ
cos (90 + θ) = - sin θ	cos (180 - θ) = - cos θ	cos (90 - θ) = sin θ

✅ Example:

Q: If sinθ = 3/5 and θ is in the first quadrant, find cosθ and tanθ.

Solution:

• sinθ = 3/5 ⇒ Opposite = 3, Hypotenuse = 5
• Adjacent = √(5² - 3²) = √16 = 4
• cosθ = 4/5, tanθ = 3/4

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2. Straight Lines

Straight lines are part of coordinate geometry and deal with equations of lines in a plane.

📌 Forms of Line:

• Slope-intercept form: y = mx + c
• Point-slope form: y - y₁ = m(x - x₁)
• General form: Ax + By + C = 0

✅ Example:

Q: Find the equation of the line passing through (2, 3) with slope 4.

Solution:

Use point-slope form:

y - 3 = 4(x - 2)
⇒ y = 4x - 5

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3. Differentiation

Differentiation is the rate of change of a function. It’s essential for calculus-based problems in JEE.

📌 Basic Derivatives:

• d/dx(xⁿ) = nxⁿ⁻¹
• d/dx(sin x) = cos x
• d/dx(eˣ) = eˣ
• d/dx(ln x) = 1/x

✅ Example:

Q: Differentiate f(x) = x³ + 2x² - 5x + 1

Solution:

f'(x) = 3x² + 4x - 5

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4. Integration

Integration is the reverse of differentiation. It’s used to calculate area, displacement, and more.

📌 Basic Integrals:

• ∫xⁿ dx = xⁿ⁺¹ / (n+1) + C, n ≠ -1
• ∫1/x dx = ln|x| + C
• ∫eˣ dx = eˣ + C
• ∫cos x dx = sin x + C

✅ Example:

Q: Find ∫(3x² + 2x - 1) dx

Solution:

∫(3x² + 2x - 1) dx = x³ + x² - x + C

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📎 Note:

Practice these concepts regularly with mock papers and past year questions. Tricky problems often require blending concepts across these topics.

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