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# Math 101 (Onko 101)

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When it comes to coolness math really should be up there with new techniques, insights and methods. Often people actually think that it’s cool to not be able to do math! As part of 10 Minute School's mission to make math cool, we have tried to pull the best math shortcuts and interesting insights in our first release of 'Math Hacks". We will release updated versions of 'Math Hacks' and more cheat-books of this sort in the coming days. Enjoy and do share them with your peers. Math needs all the PR it can get!

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### Math 101 (Onko 101)

1. 1. SCHOOL MINUTE 10 Math101
2. 2. #ONKO101 20% 20:10020/100 PERCENTAGE FRACTION RATIO= = THESE ARE NOT DIFFERENT MATH PROBLEMS THEY REPRESENT THE SAME THING IN DIFFERENT WAYS
3. 3. #ONKO101 FACING DIFFICULTIES IN DIVIDING NUMBERS! TRY MAKING THE DENOMINATOR 10 OR 100 AND VOILA 7/5 14/10 1.4 7/25 28/100 .28 = = = =
4. 4. #ONKO101 PERCENTAGE IS NOT A MATH TYPE IT IS BASICALLY A 2 IN 1 INFORMATION % OUT OF 100 MEANS 20% 20 OUT OF 100 MEANS % SIGN IN MULTIPLY BY 100 % SIGN OUT DIVIDE BY 100 A SIMPLE RULE TO FOLLOW
5. 5. #ONKO101 I THOUGHT I UNDERSTOOD PERCENTAGE BEFORE SEEING THIS 1 1/2 1500 50% 100% 150000% = = =
6. 6. #ONKO101 INEQUALITY SERVES LIKE EQUALITY EXCEPT FOR 2 DISTINCT CASES WHEN MULTIPLIED BY NEGATIVE NUMBER CASE 1 2 < 4 Or, -2 > -4 WHEN RECIPROCALS ARE TAKEN CASE 2 2 < 4 Or, 1/2 > 1/4
7. 7. #ONKO101 PEOPLE DON’T UNDERSTAND FRACTIONS! HOPE YOU GOT THE MISTAKE
8. 8. #ONKO101 WHAT ARE MULTIPLES! LET’S TAKE A NUMBER (12) AND KEEP MULTIPLYING 3612 24 48 60 ×1 ×2 ×3 ×4 ×5 HOW TO FIND L.C.M MULTIPLES OF 12 72 ×6 3612 24 18 36 54 36 IS THE LOWEST COMMON MULTIPLE (LCM) THESE NUMBERS ARE MULTIPLES OF 12 MULTIPLES OF 18
9. 9. #ONKO101 HOW TO FIND H.C.F FACTORS OF 12 412 6 18 9 6 6 IS THE HIGHEST COMMON FACTOR (HCF) FACTORS OF 18 WHAT ARE FACTORS! LET’S TAKE A NUMBER (12) AND TRY TO DIVIDE IT 412 6 3 2 1 THESE NUMBERS ARE FACTORS OF 12
10. 10. #ONKO101 WE ALL KNOW ABOUT L.C.M BUT WHY DON’T WE CALCULATE H.C.M! INFINITY BECAUSE THE HIGHEST COMMON MULTIPLE (H.C.M) IS ALWAYS GOING TO BE
11. 11. #ONKO101 WE ALL KNOW ABOUT H.C.F BUT WHY DON’T WE CALCULATE L.C.F! ONE BECAUSE THE LOWEST COMMON FACTOR (L.C.F) IS ALWAYS GOING TO BE
12. 12. #ONKO101 ‘0’ EVENIS 1 3-1-3 2 40-2-4 EVEN LOOK AT THE NUMBER LINE BELOW
13. 13. #ONKO101 ‘0’ NEGATIVE IS 0 NON-NEGATIVE LOOK AT THE NUMBER LINE NON POSITIVE >< NEGATIVE
14. 14. #ONKO101 0 to 1 ARE THE ONLY NUMBERS WHICH GET SMALLER AFTER TAKING A SQUARE OR CUBE OF THAT NUMBER 0 1 0<X<1 x²<x
15. 15. #ONKO101 WHAT IS A PRIME NUMBER! A NUMBER WHICH HAS EXACTLY 2 FACTORS 1 2 IS NOT A PRIME NUMBER BECAUSE IT HAS ONLY 1 FACTOR IS THE ONLY EVEN PRIME NUMBER BECAUSE IT HAS ONLY 2 FACTORS
16. 16. #ONKO101 PRIME NUMBER SEQUENCE A NUMBER WHICH HAS EXACTLY 2 FACTORS IS A PRIME 4 4 2 2 3 2 2 3 2 1 2 11 23 31 41 53 61 71 83 97 3 13 29 37 43 59 67 73 89 5 17 47 79 7 19
17. 17. #ONKO101 0 IS NOT A PRIME NUMBER IT’S DIVISIBLE BY ALL THE NUMBERS IS AN EVEN NUMBER BECAUSE IT IS DIVISIBLE BY 2 IS NEITHER POSITIVE NOR NEGATIVE IT IS A NON NEGATIVE NUMBER 0 0 THEMYSTERIOUSNUMBER‘0’
18. 18. #ONKO101 1 1 1 THEMYSTERIOUSNUMBER‘1’ IS NOT A PRIME NUMBER IT HAS ONLY ONE FACTOR IS THE LOWEST COMMON FACTOR BECAUSE EVERY NUMBER IS DIVIDED BY ‘1’ IS SQUARE AND ROOT PROOF IT REMAINS SAME AFTER THESE OPERATIONS
19. 19. #ONKO101 SPEED=X SPEED=Y AVERAGE SPEED 2XY X+Y IF SOMEONE COVERS THE SAME DISTANCE IN DIFFERENT SPEED =
20. 20. #ONKO101 S1+S2 S1±S2 L1+L2 T = S1-S2 S1 S1 S2 S2
21. 21. #ONKO101 DOWNSTREAM UPSTREAM ROWING SPEED THE CURRENT FLOWS IN THIS DIRECTION SPEED = X+Y SPEED = X-Y CURRENT SPEED X Y = =
22. 22. #ONKO101 KPH M/S×5/18 UNIT CONVERSIONS M/S KPH×18/5 METER FEET×3 MILE YARD×1760 QUART PINTS×2
23. 23. #ONKO101 THIS IS MR. A HE FINISHES A JOB IN ‘a’ DAYS THIS IS MR. B HE FINISHES A JOB IN ‘b’ DAYS WHEN BOTH WORK TOGETHER ON THAT WORK REQUIRED TIME a × b a + b =
24. 24. #ONKO101 THIS IS MR. B HE FINISHES A JOB IN ‘b’ DAYS THIS IS MR. C HE FINISHES A JOB IN ‘c’ DAYS WHEN 3 OF THEM WORK TOGETHER ON THAT WORK REQUIRED TIME a × b × c ab + bc + ca = THIS IS MR. A HE FINISHES A JOB IN ‘a’ DAYS
25. 25. #ONKO101 C1 MIXTURE 1 MIXTURE SHORTCUT C2 Q1 Q2 C MIXTURE 2 MIXTURE (1+2) Q1+Q2 C = C1 Q1 C2 Q2+× × Q1 Q2+
26. 26. #ONKO101 C1 MIXTURE 1 MIXTURE SHORTCUT C2 Q1 Q2 C : MIXTURE 2
27. 27. #ONKO101 PROBABILITY RANGES BETWEEN 0 - 1 1 THE EVENT IS CERTAIN TO HAPPEN 0 THE EVENT IS CERTAIN TO NOT HAPPEN PROBABILITY OF AN EVENT NUMBER OF FAVORABLE OUTCOMES NUMBER OF TOTAL OUTCOMES =
28. 28. #ONKO101 PERMUTATION WHEN ARRANGEMENT MATTERS COMBINATION WHEN ARRANGMENT DOESN’T MATTER Q. SELECTING 3 PLAYERS’ BATTING LINE UP FROM 5 PLAYRES Q. SELECTING 3 PLAYERS’ TEAM FROM 5 PLAYRES n rP = n! (n-r)! 5 3P = 5! (5-3)! 5 3P = n r C = n! (n-r)! 5 3 C = 5! (5-3)! 5 3 C = r! 3! 60 10
29. 29. #ONKO101 n(B)n(A) n(A B) U n(A) n(B)n(A B)U n(A B) U = + -
30. 30. #ONKO101 WE ALL KNOW HOW TO DRAW ANGLES…ITS EASY BUT WE GET CONFUSED WHILE DRAWING O° OR 360° INTERIOR ANGLE 0° THESE 2 LINES HAVE CREATED 2 ANGLES EXTERIOR ANGLE 360°
31. 31. #ONKO101 ANGLES IN A NUTSHELL ACUTE ANGLE RIGHT ANGLE OBTUSE ANGLE STRAIGHT ANGLE REFLEX ANGLE
32. 32. PARALLELOGRAM RECTANGLE SQUARERHOMBUS THESE ARE ALL PARALLELOGRAMS BECAUSE ALL THESE HAVE PARALLEL OPPOSITE HANDS STANDARD PARALLELOGRAM RIGHT ANGLE PARALLELOGRAM EQUAL HANDS PARALLELOGRAM RIGHT ANGLE, EQUAL HANDS PARALLELOGRAM #ONKO101 AREA(FOR ALL) = BASE × HEIGHT
33. 33. #ONKO101 RATIO FOR THE SPECIAL TRIANGLES 90°45° 45° √2xx x 90°30° 60° 2xx √3x 120°30° 30° √3xx x
34. 34. #ONKO101 CIRCLE IS LIKE JUST ANOTHER POLYGON THE ONLY DIFFERENCE IS THAT IT HAS INFINITE NUMBER OF LINES
35. 35. #ONKO101 SOLID GEOMETRY IN A NUTSHELL CUBE VOLUME a³ SURFACE AREA 6a² LONGEST DIAGONAL √3a a a a
36. 36. #ONKO101 SOLID GEOMETRY IN A NUTSHELL CYLINDER VOLUME πr²h SURFACE AREA 2πr (r + h) r h
37. 37. #ONKO101 SOLID GEOMETRY IN A NUTSHELL RECTANGULAR SOLID VOLUME abc SURFACE AREA 2(ab + bc + ca) LONGEST DIAGONAL √(a² + b² + c²) a bc
38. 38. #ONKO101 TRICKY MATH #1 WHAT IS THE PROBABILITY OF WINNING A CHESS GAME 1/3 BECAUSE A CHESS GAME HAS 3 OUTCOMES IS THE ANSWER YOU CAN WIN YOU CAN LOSE YOU CAN DRAW
39. 39. #ONKO101 TRICKY MATH #2 AFTER CROSSING THE 2ND PERSON WHAT’S 2ND BECAUSE NOW YOU ARE IN THE 2ND POSITION IS THE ANSWER AND THE GUY WHO WAS IN THE FIRST POSITION IS STILL RUNNING IN THE FIRST POSITION YOUR POSITION IN A RUNNING RACE
40. 40. #ONKO101 TRICKY MATH #3 IF YOU JUST LOSE A SINGLE MATCH THEN 0 BECAUSE YOU HAVE ALREADY LOST A MATCH IS THE ANSWER THERE IS NO WAY THAT YOU CAN WIN ALL THE MATCHES AND SECURE A PERFECT SCORE WHAT’S THE PROBABILITY OF HAVING A PERFECT SCORE
41. 41. #ONKO101 TRICKY MATH #4 FIND OUT THE PERIMETER OF THE REGION Y Y Y Y X+4 X+3 X+2 X+1 36 48 168 IT’S BASICALLY 2*(36+48) NO NEED FOR EQUATIONS IS THE ANSWER
42. 42. #ONKO101 TRICKY MATH #5 WHAT IS THE PRODUCT OF ALL NUMBERS 0 BECAUSE IT WILL BE MULTIPLIED BY ‘ZERO’ IS THE ANSWER FROM -50 TO 50 INCLUSIVE
43. 43. SCHOOL MINUTE 10 CHEATBOOK