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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 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.






2. 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).






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






4. In the expression 3






5. This step is easily overlooked. For example - the problem might ask for Jane's age - but your equation's solution gives the age of Jane's sister Liz. Make sure you answer the original question asked in the problem. Your solution should be written in






6. Negative






7. Original Balance minus River Tam's Withdrawal is Current Balance






8. A group is just a collection of objects (i.e. - elements in a set) that obey a few rules when combined or composed by an operation. In order for a set to be considered a group under a certain operation - each element must have an inverse - the set mu






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






10. 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






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






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






13. 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






14. Mathematical statement that equates two mathematical expressions.






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

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






17. Are the fundamental building blocks of arithmetic.






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






19. 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.'






20. If a = b then






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






22. 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






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






24. 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.






25. A






26. 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






27. If a is any whole number - then a






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






29. 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






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






31. 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.






32. A number is divisible by 2






33. 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 -






34. × - ( )( ) - · - 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






35. The study of shape from an external perspective.






36. A way to extrinsically measure the curvature of a surface by looking at a given point and finding the contour line with the greatest curvature and the contour line with the least curvature.






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






38. 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






39. The system that Euclid used in The Elements






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






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






42. 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






43. The study of shape from the perspective of being on the surface of the shape.






44. 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.






45. This ubiquitous result describes the outcomes of many trials of events from a wide array of contexts. It says that most results cluster around the average with few results far above or far below average.






46. The inverse of multiplication






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






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






49. 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.






50. 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.'