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






2. 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.'






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






5. 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 -






6. 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.






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






8. 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.'






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






10. 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.






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






12. Add and subtract






13. 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.






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






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






16. An object possessing continuous symmetries can remain invariant while one symmetry is turned into another. A circle is an example of an object with continuous symmetries.






17. If a = b then






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






19. The expression a^m means a multiplied by itself m times. The number a is called the base of the exponential expression and the number m is called the exponent. The exponent m tells us to repeat the base a as a factor m times.






20. 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.






21. Dimension is how mathematicians express the idea of degrees of freedom






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






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






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






25. Originally known as analysis situs






26. Also known as 'clock math -' incorporates 'wrap around' effects by having some number other than zero play the role of zero in addition - subtraction - multiplication - and division.






27. Means approximately equal.






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






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






30. 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






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

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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. The state of appearing unchanged.






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






35. (a






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






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






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






39. A factor tree is a way to visualize a number's






40. 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






41. The cardinality of sets that cannot be put into one-to-one correspondence with the counting numbers - such as the set of real numbers - is referred to as c. The designations A_0 and c are known as 'transfinite' cardinalities.






42. 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






43. Also known as gluing diagrams - are a convenient way to examine intrinsic topology.






44. 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.






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






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

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47. 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.






48. W = {0 - 1 - 2 - 3 - 4 - 5 - . . .} is called






49. Some favor repeatedly dividing by 2 until the result is no longer divisible by 2. Then try repeatedly dividing by the next prime until the result is no longer divisible by that prime. The process terminates when the last resulting quotient is equal t






50. Public key encryption allows two parties to communicate securely over an un-secured computer network using the properties of prime numbers and modular arithmetic. RSA is the modern standard for public key encryption.