Maths Cheat Sheet - Summary Foundational Studies in Mathematics PDF

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CHEAT SHEET...

Description

Circumference C = 2πr Area of a Sector (Degrees) = θ◦ 360◦ × π × r2

First Principles

Integration SL(1) ≤ A ≤ SR(1)

Trapezoidal Rule f ( a ) + 2 f ( a+h )+2 f ( a+2 h) +…+2 f ( a+ ( n−1 ) h ) +f (b) = h ¿ 2

Where h =

Product Rule Stationary Points Quotient Rule

b− a 2

Index Laws am × an = am+n am ÷ an = am-n (am)n = amn 1 = a-m m a 1 n

(a) y = 2-x (Blue) (b) y = −2-x (Red) (c) y = 2x (Yellow) (d) y = −2x (Green)

(a) y = 2x (Blue) (b) y = x (Red) (c) y = log2 (x) (Yellow)

√

n

Difference of two squares a2 – b2 = (a + b)(a − b) x=

−b ± √ b 2−4 ac 2a

Gradient Formula y 2− y 1 m= x 2−x 1

N(t) = N(0) × bkt

The point gradient formula y − y1 = m(x − x1) General Form ax + by + c = 0 Midpoint x 1+ x 2 y 1+ y 2 ) , M= ( 2 2 Distance between two points d = √ ( x 2−x 1 )2+( y 2− y 1)2 A function is a relation with the special property that each input has one output at most A function f is called even if for every x in the domain f(−x) = f(x). A function f is called odd if for every x in the domain f(−x) = −f(x).

Log Rules logb(x) = y and x = by logb (1) = 0 logb (b) = 1 logb(x) + logb(y) = logb(xy), x, y > 0 x ), x, y > 0 logb(x) – logb(y) = logb ( y n logb( x ) = nlogb(x), x > 0 ln(x ) logb(x) = ln(b)

1. sin(θ) = cos(90◦ − θ) 2. sin2(θ) + cos2(θ) = 1 sin(θ) 3. tan(θ) = cos(θ) 4. sin(2θ) = 2 sin(θ) cos(θ) 5. cos(2θ) = cos2(θ) – sin2(θ) 6. cos(2θ) = 2 cos2(θ) − 1 7. cos(2θ) = 1 − 2 sin2(θ) 2 tan(θ) 8. tan(2θ) = 2 1−tan (θ) 9. sin(−θ) = − sin(θ) 10. cos(−θ) = cos(θ) 11. tan(−θ) = − tan(θ) 12. sin(a + b) = sin(a) cos(b) + cos(a) sin(b) 13. sin(a − b) = sin(a) cos(b) − cos(a) sin(b) 14. cos(a + b) = cos(a) cos(b) − sin(a) sin(b) 15. cos(a − b) = cos(a) cos(b) + sin(a) sin(b) Cosine Rule a2 = b2 + c2 − 2bc cos(θ)...