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






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






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






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






5. Has no factors other than 1 and itself






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






7. (a · b) · c = a · (b · c)






8. 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.






9. If we start with a number x and multiply by a number a - then dividing the result by the number a returns us to the original number x. In symbols - a






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






11. ____________ theory enables us to use mathematics to characterize and predict the behavior of random events. By 'random' we mean 'unpredictable' in the sense that in a given specific situation - our knowledge of current conditions gives us no way to






12. At each level of the tree - break the current number into a product of two factors. The process is complete when all of the 'circled leaves' at the bottom of the tree are prime numbers. Arranging the factors in the 'circled leaves' in order. The fina






13. A · 1 = 1 · a = a






14. 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.






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






16. 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.'






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






18. An important part of problem solving is identifying






19. Let a - b - and c be any whole numbers. Then - a






20. Perform all additions and subtractions in the order presented






21. 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






22. 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.






23. When writing mathematical statements - follow the mantra:






24. 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.






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






26. 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.'






27. 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 -






28. Collection of objects. list all the objects in the set and enclosing the list in curly braces.






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






30. The inverse of multiplication






31. This result says that the symmetries of geometric objects can be expressed as groups of permutations.

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32. The fundamental theorem of arithmetic says that






33. 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)






34. 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






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






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






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






38. Originally known as analysis situs






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






40. This result relates conserved physical quantities - like conservation of energy - to continuous symmetries of spacetime.

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41. Add and subtract






42. If its final digit is a 0 or 5.






43. 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.






44. 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.






45. The distribution of averages of many trials is always normal - even if the distribution of each trial is not.






46. Multiplication is equivalent to






47. Objects are topologically equivalent if they can be continuously deformed into one another. Properties that are preserved during this process are called topological invariants.






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






49. 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.






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