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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. Of central importance in Ramsey Theory - and in combinatorics in general - is the 'pigeonhole principle -' also known as Dirichlet's box. This principle simply states that we cannot fit n+1 pigeons into n pigeonholes in such a way that only one pigeo






2. An arrangement where order matters.






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






4. Reveals why we tend to find structure in seemingly random sets. Ramsey numbers indicate how big a set must be to guarantee the existence of certain minimal structures.






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






6. Mathematical statement that equates two mathematical expressions.






7. The multitude concept presented numbers as collections of discrete units - rather like indivisible atoms.






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






9. Requirements for Word Problem Solutions.






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






11. 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).






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






13. If a and b are any whole numbers - then a






14. If a - b - and c are any whole numbers - then a






15. 1. Any two points can be joined by a straight line. 2. Any straight line segment can be extended indefinitely in a straight line. 3. Given any straight line segment - a circle can be drawn having the segment as radius and one endpoint as center. 4. A

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16. Negative






17. Our standard notions of Pythagorean distance and angle via the inner product extend quite nicely from three-space.






18. Let a and b represent two whole numbers. Then - a + b = b + a.






19. A group is just a collection of objects (i.e. - elements in a set) that obey a few rules when combined or composed by an operation. In order for a set to be considered a group under a certain operation - each element must have an inverse - the set mu






20. Is the shortest string that contains all possible permutations of a particular length from a given set.






21. Three is the common property of the group of sets containing three members. This idea is called '__________ -' which is a synonym for 'size.' The set {a -b -c} is a representative set of the cardinal number 3.






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






23. If on a surface there is no meaningful way to tell an object's orientation (left or right handedness) - the surface is said to be non-orientable.






24. × - ( )( ) - · - 1. Multiply the numbers (ignoring the signs)2. The answer is positive if they have the same signs. 3. The answer is negative if they have different signs. 4. Alternatively - count the amount of negative numbers. If there are an even






25. TA model of a sequence of random events. Each marble that passes through the system represents a trial consisting of as many random events as there are rows in the system.






26. The system that Euclid used in The Elements






27. This area of mathematics relates symmetry to whether or not an equation has a 'simple' solution.






28. The surface of a standard 'donut shape'.






29. Is the length around an object. Used to calculate such things as fencing around a yard - trimming a piece of material - and the amount of baseboard needed for a room.It is not necessary to have a formula since it is always just calculated by adding t






30. The state of appearing unchanged.






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






32. If a = b then






33. Multiplication is equivalent to






34. Two equations if they have the same solution set.






35. Says that when a random process - such as dropping marbles through a Galton board - is repeated many times - the frequencies of the observed outcomes get increasingly closer to the theoretical probabilities.






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






37. Adding the same quantity to both sides of an equation - if a = b - then adding c to both sides of the equation produces the equivalent equation a + c = b + c.






38. This model is at the forefront of probability research. Mathematicians use it to model traffic patterns in an attempt to understand flow rates and gridlock - among other things.






39. It is important to note that this step does not imply that you should simply check your solution in your equation. After all - it's possible that your equation incorrectly models the problem's situation - so you could have a valid solution to an inco






40. An equation is a numerical value that satisfies the equation. That is - when the variable in the equation is replaced by the solution - a true statement results.






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






42. A topological invariant that relates a surface's vertices - edges - and faces.






43. All integers are thus divided into three classes:






44. 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.






45. Does not change the solution set. That is - if a = b - then multiplying both sides of the equation by c produces the equivalent equation a






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






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






48. When writing mathematical statements - follow the mantra:






49. In a mathematical sense - it is a transformation that leaves an object invariant. Symmetry is perhaps most familiar as an artistic or aesthetic concept. Designs are said to be symmetric if they exhibit specific kinds of balance - repetition - and/or






50. A · 1/a = 1/a · a = 1







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