NUST NET ENGINEERING PREP
Mathematics Quick-Reference Cheat Sheet
Essential Formulas, Shortcuts, and Core Conic & Calculus Relations
1. ALGEBRA & FUNCTIONS
Quadratic Equations
For ax² + bx + c = 0:
• Roots: x = (-b ± √(b² - 4ac)) / 2a
• Sum of Roots (α + β) = -b/a
• Product (αβ) = c/a
• Discriminant (Δ = b² - 4ac)
Sequences & Series
• AP n-th Term: a_n = a₁ + (n-1)d
• AP Sum: S_n = (n/2)[2a₁ + (n-1)d]
• GP n-th Term: a_n = a₁r^(n-1)
• Infinite GP Sum: S_∞ = a₁ / (1 - r) where |r| < 1
2. TRIGONOMETRY & IDENTITIES
Fundamental Identities
• sin²θ + cos²θ = 1
• 1 + tan²θ = sec²θ
• 1 + cot²θ = csc²θ
Double & Half Angle
• sin(2θ) = 2sinθcosθ
• cos(2θ) = cos²θ - sin²θ = 2cos²θ - 1
• sin²θ = (1 - cos(2θ)) / 2
• cos²θ = (1 + cos(2θ)) / 2
3. COORDINATE GEOMETRY & CONIC SECTIONS
Conic Section Standard Equation Key Metrics / Eccentricity (e)
Circle (x - h)² + (y - k)² = r² e = 0, Center at (h, k)
Parabola y² = 4ax e = 1, Focus at (a, 0), Directrix: x = -a
Ellipse x²/a² + y²/b² = 1 e < 1, b² = a²(1 - e²)
Hyperbola x²/a² - y²/b² = 1 e > 1, b² = a²(e² - 1)
4. DIFFERENTIAL & INTEGRAL CALCULUS
Core Derivatives
• d/dx(x^n) = n x^(n-1)
• d/dx(ln x) = 1/x
• d/dx(sin x) = cos x
• d/dx(cos x) = -sin x
• d/dx(tan x) = sec²x
Core Integrals
• ∫ x^n dx = (x^(n+1))/(n+1) + C
• ∫ (1/x) dx = ln|x| + C
• ∫ sin x dx = -cos x + C
• ∫ cos x dx = sin x + C
• ∫ sec²x dx = tan x + C
NUST NET Prep | Mathematics
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