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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. 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.






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






3. The four-dimensional analog of the cube - square - and line segment. A hypercube is formed by taking a 3-D cube - pushing a copy of it into the fourth dimension - and connecting it with cubes. Envisioning this object in lower dimensions requires that






4. Non-Euclidean geometries abide by some - but not all of Euclid's five postulates.






5. If the sum of its digits is divisible by 9 (ex: 3591 is divisible by 9 since 3 + 5 + 9 + 1 = 18 is divisible by 9).






6. 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).






7. Perform all additions and subtractions in the order presented






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






9. A + 0 = 0 + a = a






10. A sphere can be thought of as a stack of circular discs of increasing - then decreasing - radii. The process of slicing is one way to visualize higher-dimensional objects via level curves and surfaces. A hypersphere can be thought of as a 'stack' of






11. Topological objects are categorized by their _______ (number of holes). The genus of a surface is a feature of its global topology.






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






13. 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






14. A number is divisible by 2






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






16. If a = b then






17. 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






18. A · 1 = 1 · a = a






19. 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.






20. Arise from the attempt to measure all quantities with a common unit of measure.






21. A topological object that can be used to study the allowable states of a given system.






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






23. A point in one dimension requires only one number to define it. The number line is a good example of a one-dimensional space.






24. Rules for Rounding - To round a number to a particular place - follow these steps:






25. A graph in which every node is connected to every other node is called a complete graph.






26. 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.






27. A






28. An algebraic 'sentence' containing an unknown quantity.






29. 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.'






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






31. × - ( )( ) - · - 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






32. 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.






33. Original Balance minus River Tam's Withdrawal is Current Balance






34. An arrangement where order matters.






35. 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.






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






37. A(b + c) = a · b + a · c a(b - c) = a · b - a · c






38. This means that for any two magnitudes - one should always be able to find a fundamental unit that fits some whole number of times into each of them (i.e. - a unit whose magnitude is a whole number factor of each of the original magnitudes)






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






40. 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






41. 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.'






42. You must let your readers know what each variable in your problem represents. This can be accomplished in a number of ways: Statements such as 'Let P represent the perimeter of the rectangle.' - Labeling unknown values with variables in a table - Lab






43. 4 more than a certain number is 12






44. An important part of problem solving is identifying






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






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






47. (a






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






49. 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.






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