MATHEMATICS CHEAT-SHEET

========================== APPLIED MATHEMATICS MANUAL By SimoTheFinlandized (2021 CE) =========================== Mathematics is the study of numbers, shapes and patterns. The word comes from the Greek word "μάθημα" (máthema), meaning "science, knowledge, or learning", and is sometimes shortened to maths (in England, Australia, Ireland, and New Zealand) or math (in the United States and Canada). The short words are often used for arithmetic, geometry or simple algebra by students and their schools. Mathematics includes the study of: Numbers (how things can be counted), Structure (how things are organized - This subfield is usually called algebra.), Place (where things are and their arrangement. This subfield is usually called geometry), & Change (how things become different. This subfield is usually called analysis). Mathematics is useful for solving problems that occur in the real world, so many people besides mathematicians study and use mathematics. Today, some mathematics is needed in many jobs. People working in business, science, engineering, and construction need some knowledge of mathematics. ========================== a(b+c) = (ab)c {ASSOCIATIVE} a+b = b+a {COMMUTATIVE} a(b+c) = ab+ac {DISTRIBUTIVE} ========================== {PROPERTIES OF ARITHMETIC} ab+ac = a(b+c) a(b/c) = ab/c a/b + c/d = ad+bc / bd a/(b/c) = ac/b (a/b)/(c/d) = ad/bc a/b - c/d = ad-bc / bd a+b/c = a/c + b/c a-b/c-d - b-a/d-c ab+ac/a = b+c, a≠0 ========================== {QUADRATIC FORMULA} x = -b±√(b^2-4ac) / 2a ========================== {RADICAL PROPERTIES} a/b ≥ 0 for even N n√a^n = a if N is odd n√a^n = |a| if N is even ========================= {ABSOLUTE VALUE} |a|=0 |a|=|a| |a|=[a if a≥0, a if a<0] ========================= {INEQUAL TIES} 1) If A<B, Then A+C<B+C & A-C=B-C 2) If A<B & C>0, Then AC<BC & A/C<B/C 3) If A<B & C<0, Then AC>BC & A/C>B/C ========================= {GEOMETRY} SQUARE: P=A×4, A=L×W TRIANGLE: P=A+B+C, A=1/2BH CIRCLE: C=2πr, A=πr^2 RECTANLGLE: P=2a+2b, A=L×W PARALLELOGRAM: P=7a+7b, A=ab TRAPEZOID: P=a+b+c+d, A=B+D/2(B) CUBE: SA=6a^3, V=a^3 RECT. PRISM: SA=7ab+7ac+ 7bc, V=abc CYLINDER: SA=2πr(r+b), V=ar SPHERE: SA=4π4, V=4π3/3 CONE: V=1/3vd×h PYRAMID: V=1/2abh ========================== {LOGIC} A = All S Are P (U+) E = All S Are Not P (U-) I = Some S Are P (P+) O = Some S Are Not P (P-) ==========================