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CLEP General Math: Number Sense - Patterns - Algebraic Thinking

Subjects : clep, math, algebra
Instructions:
  • Answer 50 questions in 15 minutes.
  • If you are not ready to take this test, you can study here.
  • Match each statement with the correct term.
  • Don't refresh. All questions and answers are randomly picked and ordered every time you load a test.

This is a study tool. The 3 wrong answers for each question are randomly chosen from answers to other questions. So, you might find at times the answers obvious, but you will see it re-enforces your understanding as you take the test each time.
1. The cardinality of sets that cannot be put into one-to-one correspondence with the counting numbers - such as the set of real numbers - is referred to as c. The designations A_0 and c are known as 'transfinite' cardinalities.






2. Is a symbol (usually a letter) that stands for a value that may vary.






3. Some numbers make geometric shapes when arranged as a collection of dots - for example - 16 makes a square - and 10 makes a triangle.






4. In any ratio of two whole numbers - expressed as a fraction - we can interpret the first (top) number to be the 'counter -' or numerator






5. A number is divisible by 2






6. We can think of the space between primes as 'prime deserts -' strings of consecutive numbers - none of which are prime.






7. The amount of displacement - as measured from the still surface line.






8. If a = b then a + c = b + c If a = b then a - c = b - c If a = b then a






9. When writing mathematical statements - follow the mantra:






10. In this type of geometry the angles of a triangle add up to more than 180 degrees. In such a system - one has to replace the parallel postulate with a version that admits no parallel lines as well as modify Euclid's first two postulates.






11. A way to extrinsically measure the curvature of a surface by looking at a given point and finding the contour line with the greatest curvature and the contour line with the least curvature.






12. The identification of a 'one-to-one' correspondence--enables us to enumerate a set that may be difficult to count in terms of another set that is more easily counted.






13. The fundamental theorem of arithmetic says that






14. The whole number zero is called the additive identity. If a is any whole number - then a + 0 = a.






15. This method can create a flat map from a curved surface while preserving all angles in any features present.






16. If we start with a number x and subtract a number a - then adding a to the result will return us to the original number x. In symbols - x - a + a = x. So -






17. Dimension is how mathematicians express the idea of degrees of freedom






18. GThe mathematical study of space. The geometry of a space goes hand in hand with how one defines the shortest distance between two points in that space.






19. Cantor called the cardinality of all the sets that can be put into one-to-one correspondence with the counting numbers - or 'Aleph Null.'






20. Codifies the 'average behavior' of a random event and is a key concept in the application of probability.






21. A '___________' infinite set is one that can be put into one-to-one correspondence with the set of natural numbers.






22. An arrangement where order matters.






23. Einstein's famous theory - relates gravity to the curvature of spacetime.






24. In this type of geometry the angles of a triangle add up to less than 180 degrees. In such a system - one has to replace the parallel postulate with a version that admits many parallel lines.






25. Used to display measurements. The measurement was taken is placed on the horizontal axis - and the height of each bar equals the amount during that year.






26. Use parentheses - brackets - or curly braces to delimit the part of an expression you want evaluated first.






27. (a + b) + c = a + (b + c)






28. Mathematical statement that equates two mathematical expressions.






29. A whole number (other than 1) is a _____________ if its only factors (divisors) are 1 and itself. Equivalently - a number is prime if and only if it has exactly two factors (divisors).






30. The answer to the question of why the primes occur where they do on the number line has eluded mathematicians for centuries. Gauss's Prime Number Theorem is perhaps one of the most famous attempts to find the 'pattern behind the primes.'






31. 1. Find the prime factorizations of each number.






32. Positive integers are






33. A way to measure how far away a given individual result is from the average result.






34. In some ways - the opposite of a multitude is a magnitude - which is ___________. In other words - there are no well defined partitions.






35. A point in three-dimensional space requires three numbers to fix its location.






36. All integers are thus divided into three classes:






37. A point in four-space - also known as 4-D space - requires four numbers to fix its position. Four-space has a fourth independent direction - described by 'ana' and 'kata.'






38. Determines the likelihood of events that are not independent of one another.






39. If we start with a number x and add a number a - then subtracting a from the result will return us to the original number x. x + a - a = x. so -






40. Aka The Osculating Circle - a way to measure the curvature of a line.






41. Negative






42. If a whole number is not a prime number - then it is called a...






43. This important result says that every natural number greater than one can be expressed as a product of primes in exactly one way.






44. Every solution to a word problem must include a carefully crafted equation that accurately describes the constraints in the problem statement.






45. Every whole number can be uniquely factored as a product of primes. This result guarantees that if the prime factors are ordered from smallest to largest - everyone will get the same result when breaking a number into a product of prime factors.






46. This ubiquitous result describes the outcomes of many trials of events from a wide array of contexts. It says that most results cluster around the average with few results far above or far below average.






47. You must always solve the equation set up in the previous step.






48. A way to analyze sequences of events where the outcomes of prior events affect the probability of outcomes of subsequent events.






49. W = {0 - 1 - 2 - 3 - 4 - 5 - . . .} is called






50. This famous - as yet unproven - result relates to the distribution of prime numbers on the number line.







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