Algebra, Geometry, Trigonometry & Calculus Formulas

Key Algebra, Geometry,
Trigonometry & Calculus
Formulas
ALGEBRA FORMULAS (15 Main Formulas)

1. (a + b)² = a² + 2ab + b²


2. (a - b)² = a² - 2ab + b²


3. a² - b² = (a + b)(a - b)


4. (x + a)(x + b) = x² + (a + b)x + ab


5. a^n × a^m = a^(n+m)


6. (a^m)^n = a^(mn)


7. a^0 = 1 (a ≠ 0)


8. a^(-n) = 1 / a^n


9. y = mx + b (slope-intercept form)


10. m = (y2 - y1) / (x2 - x1)


11. Quadratic formula: x = [-b ± √(b² - 4ac)] / 2a


12. Vertex form: y = a(x - h)² + k

, 13. Factoring by grouping: ax + ay + bx + by = a(x + y) + b(x + y) = (a + b)(x + y)


14. log(ab) = log a + log b


15. log(a^n) = n log a




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GEOMETRY FORMULAS (15 Main Formulas)

1. Area of triangle = (1/2) × base × height


2. Area of square = side²


3. Perimeter of square = 4 × side


4. Area of rectangle = length × width


5. Perimeter of rectangle = 2(length + width)


6. Area of circle = πr²


7. Circumference of circle = 2πr


8. Area of trapezoid = (1/2)(base1 + base2) × height


9. Surface area of cube = 6a²