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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 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.






2. To describe and extend a numerical pattern






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






4. The fundamental theorem of arithmetic says that






5. Trigonometric functions - such as sine and cosine - are useful for modeling sound waves - because they oscillate between values






6. Assuming that the air is of uniform density and pressure to begin with - a region of high pressure will be balanced by a region of low pressure - called rarefaction - immediately following the compression






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






8. 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 -






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






10. Breaks a complicated signal into a combination of simple sine waves. Fourier synthesis does the opposite - constructing a complicated signal from simple sine waves.






11. × - ( )( ) - · - 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






12. An instrument's _____ - the sound it produces - is a complex mixture of waves of different frequencies.






13. 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).






14. 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






15. 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.'






16. The state of appearing unchanged.






17. An important part of problem solving is identifying






18. 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.






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






20. Mathematical statement that equates two mathematical expressions.






21. 4 more than a certain number is 12






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






23. 1. Parentheses (or any grouping symbol {braces} - [square brackets] - |absolute value|)

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24. Points in two-dimensional space require two numbers to specify them completely. The Cartesian plane is a good way to envision two-dimensional space.






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






26. A · 1/a = 1/a · a = 1






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






28. Whether or not we hear waves as sound has everything to do with their _____________ - or how many times every second the molecules switch from compression to rarefaction and back to compression again - and their intensity - or how much the air is com






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






30. An arrangement where order matters.






31. A + b = b + a






32. 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.






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






34. 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).






35. 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






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






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






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






39. Uses second derivatives to relate acceleration in space to acceleration in time.






40. 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 -






41. 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






42. In the expression 3






43. If a is any whole number - then a






44. The inverse of multiplication






45. A






46. 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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47. The expression a/b means






48. Let a and b be whole numbers. Then a is _______________ by b if and only if the remainder is zero when a is divided by b. In this case - we say that 'b is a divisor of a.'






49. Cannot be written as a ratio of natural numbers.






50. Are the fundamental building blocks of arithmetic.