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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 + b = b + a






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

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3. If the sum of its digits is divisible by 3 (ex: 3591 is divisible by 3 since 3 + 5 + 9 + 1 = 18 is divisible by 3).






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






5. 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.






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






7. Solving Equations






8. Writing Mathematical equations - arrange your work one equation






9. 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.






10. Requirements for Word Problem Solutions.






11. × - ( )( ) - · - 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






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






13. An equation is a numerical value that satisfies the equation. That is - when the variable in the equation is replaced by the solution - a true statement results.






14. A point in three-dimensional space requires three numbers to fix its location.






15. A number is divisible by 2






16. If a = b then






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






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






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






20. In this type of geometry the angles of a triangle add up to less than 180 degrees. In such a system - one has to replace the parallel postulate with a version that admits many parallel lines.






21. Mathematical statement that equates two mathematical expressions.






22. 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






23. If a is any whole number - then a






24. 1. Any two points can be joined by a straight line. 2. Any straight line segment can be extended indefinitely in a straight line. 3. Given any straight line segment - a circle can be drawn having the segment as radius and one endpoint as center. 4. A

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25. If a represents any whole number - then a






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






27. 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






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






29. Says that when a random process - such as dropping marbles through a Galton board - is repeated many times - the frequencies of the observed outcomes get increasingly closer to the theoretical probabilities.






30. 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






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






32. A + (-a) = (-a) + a = 0






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






34. 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






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






36. 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.






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






38. The fundamental theorem of arithmetic says that






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






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






41. 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.






42. 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






43. A · 1/a = 1/a · a = 1






44. 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






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






46. 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






47. The expression a/b means






48. Every solution to a word problem must include a carefully crafted equation that accurately describes the constraints in the problem statement.






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






50. This result relates conserved physical quantities - like conservation of energy - to continuous symmetries of spacetime.

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