English mathematics mnemonics

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Here are some English mnemonics related to mathematics.

Multiplying positives and negatives

  • When a good thing happens to a good person, that's good. (A positive times a positive is positive.)
  • When a good thing happens to a bad person, that's bad. (A positive times a negative is negative.)
  • When a bad thing happens to a good person, that's bad. (A negative times a positive is negative.)
  • When a bad thing happens to a bad person, that's good. (A negative times a negative is positive.)
  • The friends of my friends are my friends. (A positive times a positive is positive.)
  • The friends of my enemies are my enemies. (A positive times a negative is negative.)
  • The enemies of my friends are my enemies. (A negative times a positive is negative.)
  • The enemies of my enemies are my friends. (A negative times a negative is positive.)
  • It is good when I like something that is good for me. (e.g. Liking healthy food.) (A positive times a positive is positive.)
  • It is bad when I like something that is bad for me. (e.g. Liking unhealthy food.) (A positive times a negative is negative.)
  • It is bad when I dislike something that is good for me. (e.g. Not liking healthy food.) (A negative times a positive is negative.)
  • It is good when I dislike something that is bad for me. (e.g. Not liking unhealthy food.) (A negative times a negative is positive.)

Metric system

The order of prefixes in the metric system, for every power of ten from 3 to -3, is Kilometer, Hectometer, Decameter, Meter, Decimeter, Centimeter, Millimeter:

  • Kids Hate Doing Math During Class on Mondays
  • King Hector's Daffy Mother Drinks Chocolate Milk
  • King Henry Drinks Much Dark Chocolate Milk
  • King Henry's Daughter Makes Delicious Chocolate Muffins
  • King Henry's Dirty Underwear Does Contain Mold
  • King Henry Died! Mother Didn't Care Much
  • King Hector Dector Makes Delicious Chocolate Milk
  • Kings Have Diamonds. Most Diamonds Cost Money.
  • King Henry Died Monday During Christmas Mass.
  • King Henry Died of Miserable Disease Called Malaria
  • Kangaroos Hopping Down the Mountain Drinking Chocolate Milk
  • Kangaroos Hop Down Mountains During Cold Months
  • King Henry Drank My Delicious Chocolate Milk
  • King Hector Died Saturday Drinking Chocolate Milk (Saturday stands for the standard metric like gram or meter)

== ''King henry died monday drinking chocolate milk ==whats good This variant is for the prefixes Kilo-, Hecto-, Deca-, then the Base unit (such as metre, gram, litre), then the prefixes Deci-, Centi-, Milli-:

  • Kings Have Diamonds But Diamonds Cost Money
  • Kill Him Dead But Don't Cry Murder
  • King Henry Died But Didn't Call Mom

Another version refers to the base unit as "Standard":

  • Kids Hate Detention So Don't Cut Math

Some other versions refer to the base unit as "Original":

  • King Henry Danced Once Drinking Chocalate Milk
  • Kids Have Dropped Over Dead Converting Metrics

The prefixes for powers of ten from 18 to -18 using increments of 3 are Exa- (18), Peta- (15), Tera- (12), Giga- (9), Mega- (6), Kilo- (3), unit (0), Milli- (-3), Micro- (-6), Nano- (-9), Pico- (-12), Femto- (-15), Atto- (-18):

  • Exacting Petals, Terribly Gigantic Megaphones Killed 1 Million Microscopic Nasturtiums Picked Freshly by Attorneys.

A subset for powers of ten from 15 to -18 using increments of 3 are Peta- (15), Tera- (12), Giga- (9), Mega- (6), Kilo- (3), unit (0), Milli- (-3), Micro- (-6), Nano- (-9), Pico- (-12), Femto- (-15), Atto- (-18):

  • Power Turns Gigantic Motors Killing Milking Moos, Never Pausing, Femtously Aware.

A subset of the prefixes is Tera- (12), Giga- (9), Mega- (6), Micro- (-6), Nano- (-9), Pico- (-12), Femto- (-15), Atto- (-18):

  • The Gooey Monster May Not Pick Five Apples.

The prefixes for powers of ten from 24 to -24 using increments of 3 from 24 to 3 and increments of 1 from 3 to 1 are Yotta- (24),Zetta- (21),Exa- (18), Peta- (15), Tera- (12), Giga- (9), Mega- (6), kilo- (3), hecto- (2), da (deca)- (1), unit (0), deci- (-1), centi- (-2), milli- (-3), mc (micro)- (-6), nano- (-9), pico- (-12), femto- (-15), atto- (-18), zepto- (-21), yocto- (-24):

  • Yellow Zits Engulf People That Go Mad.
  • Killer Horses Dance 1 Dryly Crying Madly.
  • McCain Needs People For A Zealous Yes.

Long division

The steps for long division are Divide, Multiply, Subtract, Bring Down:

  • Dad Mom Sister Brother
  • Dead Monkeys Smell Bad
  • Dracula Must Suck Blood



You may replace "Divide" by "Guess".

An editor writes: I learned this in 4th Grade, my teacher was Miss Selway at Frazer School in Canton, Ohio

Mnemonic Word
Great

Michael

Stanley

Band

Guess

Multiply

Subtract

Bring down

Great Michael Stanley Band GMSB Guess Multiply Subtract Bring down

Order of operations

The correct order of operations is Parentheses, Exponents, Multiplication, Division, Addition, Subtraction:

  • Please Egg My Dad And Sister.
  • Please Excuse My Dear Aunt Sally.
  • Please Excuse My Dear Aunt Selma.
  • Pink Elephants March Down A Street.
  • Please Eat My Dear Angus Steak.
  • Pee Every Morning During A Shower.

from brainpop[purple eggs meander during august seventh]

These acronyms give the correct order of operations:

  • Brackets Exponentiation Division Multiplication Addition Subtraction: BEDMAS
  • Brackets Indices Division Multiplication Addition Subtraction: BIDMAS
  • Brackets Operations Division Multiplication Addition Subtraction: BODMAS
  • Brackets Of Division Multiplication Addition Subtraction: BODMAS
  • Parentheses Exponents Division Multiplication Addition Subtraction: PEDMAS
  • Parentheses Exponents Multiplication Division Addition Subtraction: PEMDAS
  • Grouping Symbols Exponents Multiply/Divide Add/Subtract GEMA
  • Grouping Symbols Exponents Multiply/Divide Subtract/Add GEMS


This acronym explains how to multiply binomials such as (2x+4)(2x+4):

  • First Outer Inner Last: FOIL or
  • First Outside Inside Last: FOIL

e

e = 2.718281828459045

  • United States President Andrew Jackson served 2 terms in office. He was the 7th president and was elected in 1828.
  • Split up E by groups. 2.7 is easy to remember. Then, 1828 — twice. Finally, a 45-90-45 triangle. Thus e is 2.7 1828 1828 45-90-45
  • By Jupiter! I remember my mnemonic! gives e=2.71828

Pi

pi (π) = 3.1415926535897932384626433832795028841971693993......................

Piphilology is the practice of writing such that the number of letters in each word corresponds to a digit of pi. Words of at least eleven letters correspond to two digits of pi. Some examples of piphilology are:

  • How I want (or: need) a drink, alcoholic in nature (or: of course), after the heavy lectures involving quantum mechanics!
    Isaac Asimov
  • Pie. I wish I could determine pi. "Eureka!" cried the great inventor. "Christmas pudding, Christmas pie, is the problem's very center!" (Also found starting with "How I wish I could recollect pi."
  • For a girl I loved contrived; by nature tough, her heart survived.
  • Can I find a trick recalling pi easily?
  • Can I have a large container of coffee?
  • Can I have a large container of orange juice? (Some variants of this add "now please?" at the end, but this rounds the tenth digit, which is a 5 not a 6)
  • How I wish I could calculate pi faster.
  • But I must a while endeavour to reckon right the ratio.
  • Now I, even I, would celebrate
    in rhymes unapt, the great
    immortal syracusan, rivaled nevermore,
    who in his wondrous lore,
    passed on before,
    left men his guidance,
    how to circles mensurate.
  • Man, I can't, I shant
    formulate an anthem where the words comprise mnemonics
    dreaded mnemonics for pi
    The numerals just bother me, always
    even the dry anterior
    try to request something lower (zero)
    in numerary aptitude, even I, pantaloon gallant
    I cannot actualize the requested mnemonics
    the leading fifty, I...
    Songs To Wear Pants To
  • Poe, E.: Near a Raven
    Midnights so dreary, tired and weary,
    Silently pondering volumes extolling all by-now obsolete lore.
    During my rather long nap - the weirdest tap!
    An ominous vibrating sound disturbing my chamber's antedoor.
    "This," I whispered quietly, "I ignore."
    Poe, E.: Near a Raven, part of the Cadaeic Cadenza
  • Sir, I send a rhyme excelling
    In sacred truth and rigid spelling
    Numerical sprites elucidate
    For me the lexicon's dull weight.
    If nature gain, who can complain,
    Tho' Dr. Johnson fulminate.
  • See! I have a rhyme assisting my feeble brain, its task ofttimes resisting.
  • See, I have a charm assisting my feeble brain its task sometime resisting.
  • How I wish I could recollect of circle round the exact relation Hipparcus found(ed)
  • It's a fact -- I smoke marijuana in church every day while fondling choirboy's genitals.
  • How I wish I could assuredly go onward,
    Learn any truly valuable knowledge,
    Uncover seemingly all of the theorems
    Dear nature so kindly lays for our pleasure,
    And as rewards, profusely given.
    NightWolf

Got bored one day and spent about an hour creating this. Give it a try yourself (the word NOTHING represents a 0):

  • Yes, I seem a Godly construct to people. Peers see every cowardly attempted masking presented. For if you secretly hide things to define your lie you actually can be Godlike. Obviously, doing NOTHING is entirely defining. When I represent Godhood I always defiantly and passively succeed, yet visibly still a NOTHING.
    FVLindsey@hotmail.com

Trigonometry

The formulas for right-triangle trigonometric functions are:

  • Sine = Opposite / Hypotenuse
  • Cosine = Adjacent / Hypotenuse
  • Tangent = Opposite / Adjacent

Mnemonics for those formulas are:

  • SOH-CAH-TOA - Sounds like a Hawaiian volcano.
  • Saddle Our Horses, Canter Away Happily Toward Other Adventures
  • Saints On High Can Always Have Tea Or Alcohol
  • Sally Can Tell: Oscar Had A Hard On Always
  • Sam's Old Horse Carries A Heavy Truck Of Apples
  • Sex On Holiday Can Add Highlights To Our Adventures
  • Sex On Hard Concrete Always Hurts The Others Ass
  • Sex On Hard Concrete Always Hurts The Orgasmic Areas
  • Sex On Holidays Can Always Have The Odd Advantage
  • Sex On Holidays Can Always Help Teachers Overcome Anxiety
  • Sex On Horseback Can Always Happen To Our Amazement
  • Signs Of Happiness Come After Having Tankards Of Ale
  • Silly Old Hag Chased After Him Till Ordered Away
  • Sir Oliver's Horse Came Ambling Home To Oliver's Aunt
  • Silly Old Hag Cracked All Her Teeth On Apples
  • Silly Old Harry Carried A Horse To Our Apartment
  • Silly Old Harry Caught A Herring Tralling Off America
  • Silly Old Harry Couldn't Answer His Test On Algebra
  • Silly Old Harry Tripped Over A Cat And Howled
  • Silly Old Hens Can't Always Have Their Own Acorns
  • Silly Old Hitler Couldn't Advance His Troops Over Africa
  • Silly Old Hitler Climbed A Hill To Overthrow Austria
  • Six Overweight Heffalumps Came And Heavily Trod On Arthur
  • Sleeping On Hills Can Actually Harm Trees Or Armadillos
  • Snogging On Holiday, Causes A Headache, Take One Aspirin
  • SOHCAHTOA (soh-cah-toa)
  • Some Officers Have Curly Auburn Hair Til Old Age
  • Some Old Houses Creak And Heave Through Old Age
  • Some Officers Have Coaches And Horses To Order About
  • Some Old Hags Can Always Hide Their Old Age
  • Some Of Her Chickens Are Healthy The Others Aren't
  • Some Old Hippie Caught Another Hippie Tripping On Acid
  • Some Old Hippies Crave Acid Hourly To Operate Automobiles
  • Some Old Horse Came A-Hoppin' Through Our Apartment
  • Some Old Horses Can Always Hear Their Owners Approaching
  • Some Old Horse Caught Another Horse Taking Oats Away
  • Some Old Horses Catch A Horrible Type Of Ailment
  • Some Old wHore Caught Another wHore Tapping Old Ass
  • Spend On Holidays Cause All Holidays Tip Over Asses
  • Ten Old Angels, Sitting On Heaven, Carrying A Harp
  • Two Old Angels, Sitting On High, Chatting About Heaven
  • Students On Heroin, Chemistry Always High Teachers On Acid
  • The Cat Sat On An Orange And Howled Horribly (In this mnemonic, the words "tangent", "cosine" and "sine" were placed in front, followed by the formulae respectively)
  • The Old Aunt Sat On Her Chair At Home (or Chair And Hyperventilated)

These mnemonics for Opposite / Hypotenuse, Adjacent / Hypotenuse, Opposite / Adjacent require one to remember the order Sine, Cosine, Tangent:

  • Oh Heck, Another Hour Of Algebra
  • One Hopes, And Hopes, On America
  • Oscar Had A Hold On Arthur
    credited to Saxon Math
  • Oscar Had A Heap Of Apples
  • Oscar Had A Hand Of Ass
  • Old Hippies Are High On Acid
  • Oscar Humped A Hoe On Acid
  • Oh! A Hoae! (Hoe)

Another version of the formulas is:

  • Sine = Perpendicular / Hypotenuse
  • Cosine = Base / Hypotenuse
  • Tangent = Perpendicular / Base

Mnemonics for those formulas are:

  • Some People Have, Curly Brown Hair, They Perform Best
  • Some People Have, Curly Black Hair, Through Proper Brushing (from high schools of India)
  • Some People Have, Curly Brown Hair, Till Painted Black
  • Some People Have, Curly Brown Hair, Turned Permanently Black

Following can help two-way - for sin, cos, tan and also for the cosine, cosec, cot Read column wise : for sin first column, for cos second column, for tan third column. for example sin = Pundit/Hari and for cosec = Hari/Pundit

  Pundit Badri Prasad
  Hari   Hari  Bol 

The four quadrants, counterclockwise like a capital C, are I, II, III, and IV. In quadrant I, All trig functions are postiive; in quadrant II, Sine and its reciprocal are positive; in quadrant III, Tangent and its reciprocal are positive; in quadrant IV, Cosine and its reciprocal are positive. Mnemonics for All, Sine, Tangent, Cosine:

  • After Sex Through Condom
  • Always Study Trig Carefully
  • All Studs Take Calculus
  • After School Than College
  • All Students Try Cheating
  • All Students Take Calculus
  • All Scalpers Take Cash
  • All Students Take Crack
  • All Smurfs Take Cocaine
  • A Sexy Traffic Cone
  • Add Sugar To Coffee
  • All Silver Tea Cups
  • All Silly Tom Cats
  • All Silly Teachers Cry
  • All School Teachers are Crap
  • A Smart Trig Class
  • All Stations To Central
  • All Sluts Take Cock
  • All Strippers Take Cash
  • All Seniors Turn Crazy
  • Anal Sex Takes Courage

This can also be thought of as the "CAST" rule, with CAST being a mnemonic for this rule if you start in Quadrant VI and proceed counter-clockwise. (Cosine, All, Sine, Tangent.)

Some expansions are:

  • sin(a+b) = sin a cos b + cos a sin b
  • cos(a+b) = cos a cos b - sin a sin b

The expansions correspond to:

  • Sine Cosine, Cosine Sine. Cosine Cosine minus Sine Sine.
  • SOH CAH TOA - CHO SHA CAO
  • Cosine is crazy. Sine is sane. - meaning that cosine switches the (plus/minus) operator: cos(a - b)=cos(a)cos(b) + sin(a)sin(b), whereas sine will keep the same operator: sin(a - b) = sin(a)cos(b) - cos(a)sin(b). (_JLB)