For most people, the culmination of their math career will be a standardized test of some sort, such as the SAT, ACT, GED, ASVAB, FE, GRE, etc. I've taken many standardized and did well on all of them, including a perfect score on the ASVAB. So I have a pretty good idea of what gets asked and thus how to get a good score. Most of those tests ask about 60 questions 2.5 hours, so test takers get about 2.5 minutes per question. It is important not just to get the right answer but also to get it quickly.
Most of the questions will be about arithmetic, algebra, and geometry. Most of the rest will be probability and statistics. The breakdown is below:
Arithmetic
1. addition with carrying
2. subtraction with borrowing
3. multiplication of numbers with two or more digits
4. long division and remainders
5. fractions (reciprocals, common denominators, reduction)
6. making a repeating decimal into a fraction
7. multiplication and division by powers of 10
8. negative numbers (rules for exponents and multiplication)
9. exponents and logarithms
10. radicals
11. factorization (primes, least common multiple, greatest common factor)
Algebra
12. order of operations (PEMDAS)
13. FOIL (first, outer, inner, last)
14. equation of a line (points, slopes, graphs)
15. solving a system of linear equations (elimination, substitution)
16. difference of squares
17. quadratic formula
18. inequalities
19. binomial theorem and Pascal's triangle
20. absolute value
21. functions (evaluation, composition, inverse)
22. piecewise functions, domain and range
23. the number line and intervals
24. properties of equality
25. exponential growth and decay (rule of 72, compound interest)
26. e and the natural logarithm
27. asymptotes, division by zero
28. complex numbers
29. ratios and proportionality
30. completing the square
31. percent change
32. unit conversion
33. roots of polynomials
Geometry
34. kinds of lines (intersecting, parallel, perpendicular, skew)
35. kinds of angles (vertical, transversal, complementary, supplementary)
36. sum of interior angles
37. perimeter
38. area
39. surface area
40. volume
41. graphs and equations of conic sections
42. Pythagorean theorem
43. Pythagorean triples
44. similar triangles
45. Heron's formula
46. distance formula
47. pi, radians, unit circle
48. basic trigonometry (sine, cosine, tangent and their inverses)
49. basic vectors
50. distance moved with constant acceleration
51. special right triangles
Other (probability, statistics, sequences, series)
52. arithmetic and geometric series
53. permutations and combinations
54. decimal vs binary
55. dice roll, coin flip probability
56. Venn/Euler diagrams and basic sets
57. kinds of graphs (bar, line, histogram, box and whisker)
58. percentiles and quartiles
59. mean, median, mode, and range
60. bell curve, standard deviation
There are other topics that could be studied and should be if time permits, but good knowledge of the above will ensure a superior score on the aforementioned exams. In my opinion, most of what gets taught in math classes is not essential for the important tests.
The way I see it, the point of studying math is not for everyday use, but to strengthen the mind and enjoy the resulting sense of accomplishment. Yes, it has practical applications, but mathematicians generally don't care what they are. In this way, math is more like poetry, music, or art. It is done for its own sake, and oddly enough, that has led to useful discoveries.
Doing math can be fun the way finishing a puzzle can be, but unfortunately, most students miss out on that as teachers try to cram as much knowledge into their heads as possible. The math teachers I liked the most treated their classes as kind of a playground for ideas, and I enjoyed that so much more than being given oodles of busy work by teachers seeking only to keep the class quiet.
No comments:
Post a Comment