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CLEP College Algebra: Algebra Principles

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. Can be written in terms of n-th roots: a^m/n = (nva)^m and thus even roots of negative numbers do not exist in the real number system - has the property: a^ba^c = a^b+c - has the property: (a^b)^c = a^bc - In general a^b ? b^a and (a^b)^c ? a^(b^c)






2. Include the binary operations union and intersection and the unary operation of complementation.






3. Is to add - subtract - multiply - or divide both sides of the equation by the same number in order to isolate the variable on one side of the equation. Once the variable is isolated - the other side of the equation is the value of the variable.






4. Is the claim that two expressions have the same value and are equal.






5. The squaring operation only produces






6. If a = b and b = c then a = c






7. Are denoted by letters at the beginning - a - b - c - d - ...






8. 1 - which preserves numbers: a^1 = a






9. Can be combined using the function composition operation - performing the first rotation and then the second.






10. If a < b and c < 0






11. Is algebraic equation of degree one






12. In which properties common to all algebraic structures are studied






13. The set which contains the values produced is called the codomain - but the set of actual values attained by the operation is its






14. Is an equation of the form log`a^X = b for a > 0 - which has solution






15. An equivalent for y can be deduced by using one of the two equations. Using the second equation: Subtracting 2x from each side of the equation: and multiplying by -1: Using this y value in the first equation in the original system: Adding 2 on each s






16. In an equation with a single unknown - a value of that unknown for which the equation is true is called






17. The values for which an operation is defined form a set called its






18. Is an equation involving derivatives.






19. Is an assignment of values to all the unknowns so that all of the equations are true. also called set simultaneous equations.






20. A + b = b + a






21. May contain numbers - variables and arithmetical operations. These are conventionally written with 'higher-power' terms on the left






22. Sometimes also called modern algebra - in which algebraic structures such as groups - rings and fields are axiomatically defined and investigated.






23. Parenthesis and other grouping symbols including brackets - absolute value symbols - and the fraction bar - exponents and roots - multiplication and division - addition and subtraction






24. A value that represents a quantity along a continuum - such as -5 (an integer) - 4/3 (a rational number that is not an integer) - 8.6 (a rational number given by a finite decimal representation) - v2 (the square root of two - an algebraic number that






25. If a < b and b < c






26. Subtraction ( - )






27. Operations can have fewer or more than






28. Is an algebraic 'sentence' containing an unknown quantity.






29. A vector can be multiplied by a scalar to form another vector






30. b = b






31. Is a basic technique used to simplify problems in which the original variables are replaced with new ones; the new and old variables being related in some specified way.






32. Not associative






33. If it holds for all a and b in X that if a is related to b then b is related to a.






34. Is an equation in which the unknowns are functions rather than simple quantities.






35. Real numbers can be thought of as points on an infinitely long line where the points corresponding to integers are equally spaced called the






36. That if a = b and c = d then a + c = b + d and ac = bd;that if a = b then a + c = b + c; that if two symbols are equal - then one can be substituted for the other.






37. Introduces the concept of variables representing numbers. Statements based on these variables are manipulated using the rules of operations that apply to numbers - such as addition. This can be done for a variety of reasons - including equation solvi






38. The values of the variables which make the equation true are the solutions of the equation and can be found through






39. Is Written as a + b






40. Involve only one value - such as negation and trigonometric functions.






41. Is a way of solving a functional equation of two polynomials for a number of unknown parameters. It relies on the fact that two polynomials are identical precisely when all corresponding coefficients are equal. The method is used to bring formulas in






42. In which abstract algebraic methods are used to study combinatorial questions.






43. k-ary operation is a






44. Is an equation involving a transcendental function of one of its variables.






45. A distinction is made between the equality sign ( = ) for an equation and the equivalence symbol () for an






46. Not commutative a^b?b^a






47. Transivity: if a < b and b < c then a < c; that if a < b and c < d then a + c < b + d; that if a < b and c > 0 then ac < bc; that if a < b and c < 0 then bc < ac.






48. Is an equation where the unknowns are required to be integers.






49. Reflexive: b = b; symmetric: if a = b then b = a; transitive: if a = b and b = c then a = c.






50. An operation of arity k is called a







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