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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 · 1 = 1 · a = a






2. 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.






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






4. 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






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






6. When comparing two whole numbers a and b - only one of three possibilities is true: a < b or a = b or a > b.






7. Solving Equations






8. 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






9. Mathematical statement that equates two mathematical expressions.






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. An important part of problem solving is identifying






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






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






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






15. 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.






16. N = {1 - 2 - 3 - 4 - 5 - . . .}.






17. 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.






18. 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






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






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






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






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






23. A · b = b · a






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






25. 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.'






26. Is a path that visits every node in a graph and ends where it began.






27. 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






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






29. 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.






30. 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






31. A number is divisible by 2






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






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






34. (a · b) · c = a · (b · c)






35. 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.






36. If a represents any whole number - then a






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

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38. 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






39. 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).






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






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






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






43. Perform all additions and subtractions in the order presented






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






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






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






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






48. Does not change the solution set. That is - if a = b - then dividing both sides of the equation by c produces the equivalent equation a/c = b/c - provided c = 0.






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






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