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






2. 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.






3. If a = b then






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

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5. 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)






6. 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






7. 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






8. 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.






9. When writing mathematical statements - follow the mantra:






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






11. The process of taking a complicated signal and breaking it into sine and cosine components.






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






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






14. 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.'






15. 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.






16. 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






17. If a = b then






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






19. 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 -






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






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






22. 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.'






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






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






25. Because of the associate property of addition - when presented with a sum of three numbers - whether you start by adding the first two numbers or the last two numbers - the resulting sum is






26. 1. Find the prime factorizations of each number. To find the prime factorization one method is a factor tree where you begin with any two factors and proceed by dividing the numbers until all the ends are prime factors. 2. Star factors which are shar






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






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






29. If a = b then a + c = b + c If a = b then a - c = b - c If a = b then a






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






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






32. 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).






33. The solutions to this gambling dilemma is traditionally held to be the start of modern probability theory.






34. 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.






35. To describe and extend a numerical pattern






36. The fundamental theorem of arithmetic says that






37. Perform all additions and subtractions in the order presented






38. 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.






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






40. The state of appearing unchanged.






41. 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






42. 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.






43. A · 1/a = 1/a · a = 1






44. Are the fundamental building blocks of arithmetic.






45. (a






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






47. 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.






48. Negative






49. In the expression 3






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