(#1-#50 of 100) STANDARD TASKS
(Every CITIZEN should be "put to the task" of such as these -- at least once.) (To see an0swer to given Task, click at eyelet. To dismiss answer, click at "OK".)

1. A pilot flies a square course: side 100 mi. W-E: average speed 100mph; N-S: 200mph; E-W: 300mph; S-N: 400. What is average speed for the entire course?
2. How do you calculate ABSOLUTE ERROR and RELATIVE ERROR for incorrect answers to problems such as in Task 1?
3. Define FACTOR OF A NUMBER; PROPER FACTOR; IMPROPER FACTOR; PRIME NUMBER; COMPOSITE NUMBER.
4. State THE PRIME NUMBER THEOREM.
5. 103 is a PRIME NUMBER. Prove this.
6. Of numbers 91, 111, 113, which is PRIME, which is COMPOSITE?
7. What is the difference between FACTORING A NUMBER and PARITIONING A NUMBER?
8. Given nine numbers: 3, 7, 12, 12, 17, 21, 21, 25, 31. Find their mode(s).
9. Find the RANGE of the above nine numbers.
10. Find the MEDIAN of the above nine numbers.
11. Find 1st, 2nd, 3rd, 4th QUARTILES of those nine numbers.
12. Find the 10 PERCENTILE and 90 PERCENTILE of these nine numbers.
13. Find the ARITHMETIC MEAN of the above nine numbers.
14. Find the VARIANCE of the above nine numbers.
15. Find the STANDARD DEVIATION of the above nine numbers.
16. Find the GEOMETRIC MEAN of the above nine numbers.
17. Find the HARMONIC MEAN of the above nine numbers.
18. Number n has a factor 2 if ____; factor 2x2=4 if ____; factor 2x2x2=8 if ____; factor 2x2x2x2=16 if ____.
19. Number n has a factor 5 if ____; factor 5x5=25 if ____; 5x5x5=125 if ____; 5x5x5x5 = 625 if ____.
20. Number n has factor 3 if ___; factor 9 if ___.
21. Number n has factor 11 if ___.
22. What is THE ALTERNATE SUM OF THE DIGITS of number 85297?
23. Given three 10-digit numbers: (a)1729306448; (b)1545906348; (c)1724906448. Determine WITHOUT DIVISION if A NUMBER HAS FACTOR 144; if not, why not.
24. Use the methods of Tasks 18, 19, 20, to factor 420. (This result and the result of Task 24 will be used in Task 25.)
25. Use the methods of Tasks 18, 19, 20, 21 to factor 990. (This result and the result of Task 23 will be used in Task 26.)
26. Use factoring to find the GREATEST COMMON DIVISOR (GCD) and LEAST COMMON MULTIPLE (lcm) of 420 & 990.
27. What is the PRINCIPLE OF INCLUSION AND EXCLUSION? Illustrate for 3 CLASSIFICATIONS.
28. A clerk at The Census Bureau received the following report from a Census-Taker, where "W" denotes "White"; "H" denotes "Hispanic"; "A",denotes "Asian-American"; "NR", denotes "nonresponding to 'race' question"; and "T", denotes "total censused": n(T) = 24; n(W) = 11; n(H) = 9; n(A) = 8; n(NR) = 3; n(W&H;) = 3; n(W&A;) = 3; n(H&A;) = 1; n(W&H;&A;) = 1. Use the PRINCIPLE OF INCLUSION-EXCLUSION to check this report for CONSISTENCY.
29. Given the four number sequence, 2, 4, 6, 8, what is the next or 5th number?
30. Given two CONSECUTIVE TERMS OF AN ARITHMETIC PROGRESSION -- 3, 9 -- continue it for 9 more TERMS.
31. Find the ARITHMETIC MEAN of the terms of the ARITHMETIC PROGRESSION in Task 28.
32. Without adding all the numbers, find the sum of the FIRST 736 COUNTING NUMBERS (1, 2, 3, ...).
33. Given the ARITHMETIC PROGRESSION obtained in Task 25, CREATE from it A HARMONIC PROGRESSION.
34. Find the HARMONIC MEAN (HM) of the HARMONIC PROGRESSION of Task 31.
35. Show that the solution to Task 1 is the HARMONIC MEAN of its data.
36. Given 2, 10 as two CONSECUTIVE TERMS OF A GEOMETRIC PROGRESSION, continue it for 9 more TERMS.
37. Find the GEOMETRIC MEAN (GM) of the GEOMETRIC PROGRESSION of Task 33.
38. Given decimal number 394.5807, the digits 394 to the left of the decimal point form the number's ____; the digits 5807 to the right of the decimal point form the number's ____.
39. A number in decimal form (as in 0.25) is RATIONAL (or IRRATIONAL) if____.
40. You know that 1/3 = 0.|3| (where the digit between verticals is repeated to right infinitely). You find this by dividing 1 by 3. Conversely, given 0.|3|, how can we DERIVE THE FRACTIONAL FORM, 1/3, FROM IT?
41. Given the decimal, 0.1695|737| -- where the digits between verticals repeat to the right infinitely. What is the FRACTIONAL FORM of this number? (Hint: Be guided by Prob. 30.)
42. What is the relation between a RATIONAL decimal number (with PERIOD) and a GEOMETRIC PROGRESSION?
43. We see in Task 39 that 1/7 = 0.|142857|. In the manner of Task 40, show that this is the SUM OF A GEOMETRIC PROGRESSION (GP).
44. Task 39 shows that 1/3 = 0.|3|, with a PERIOD of a SINGLE DIGIT, while 1/7 = 0.|142857|, with a PERIOD of SIX DIGITS. Is there a Principle involved here?
45. The EUCLIDEAN ALGORITHM (EA) is perhaps the most famous of algorithms. Computer scientists use it to test the processing speed of computers. Use EA to find the GREATEST COMMON DIVISOR (gcd) and LEAST COMMON MULTIPLE (lcm) of numbers 420& 990.
46. Given a classroom with 30 desks and 32 student, can each student be assigned a desk? What mathematical principles are involved?
47. Given 7 market-towns in your area, 5 malls in each town, 3 food-markets at each mall, how many CHOICES of marketing do you have? What principle is involved here?
48. What is THE EQUIVALENCE PRINCIPLE?
49. Given 5 cans of different colors for woodwork in a room, if CHOICE is INDEPENDENT (one color doesn't preclude another), how many CHOICES have you (including NONE or ALL). What principle is involved here?
50. Calculations of the sort in Task 47 can seem "huge". For n = 9, the number of CHOICES is vastly greater than a GOOGOL (1 followed by 100 zeros). Find an approximation for finding powers of 2 as powers of 10. Apply to n = 9.

To see Tasks #51-#100, click here.