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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 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






2. Non-Euclidean geometries abide by some - but not all of Euclid's five postulates.






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






4. 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 -






5. 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






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






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






8. If a is any whole number - then a






9. An important part of problem solving is identifying






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






11. 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.






12. 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.






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






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






15. A






16. A · 1/a = 1/a · a = 1






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






18. A + b = b + a






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






20. The fundamental theorem of arithmetic says that






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






22. 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






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






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






25. Negative






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






27. Multiplication is equivalent to






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






29. 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






30. 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.






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

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32. Division by zero is undefined. Each of the expressions 6






33. Positive integers are






34. Instruments produce notes that have a fundamental frequency in combination with multiples of that frequency known as partials or overtones






35. 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






36. The surface of a standard 'donut shape'.






37. Points in two-dimensional space require two numbers to specify them completely. The Cartesian plane is a good way to envision two-dimensional space.






38. If a = b then






39. An arrangement where order matters.






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






41. (a · b) · c = a · (b · c)






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






43. Has no factors other than 1 and itself






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






45. The study of shape from an external perspective.






46. 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.






47. 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






48. 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.'






49. 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






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