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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. Are denoted by letters at the end of the alphabet - x - y - z - w - ...






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






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






4. Is an action or procedure which produces a new value from one or more input values.






5. May not be defined for every possible value.






6. Is an equation in which a polynomial is set equal to another polynomial.






7. Is an equation of the form X^m/n = a - for m - n integers - which has solution






8. If a < b and c < 0






9. Elementary algebra - Abstract algebra - Linear algebra - Universal algebra - Algebraic number theory - Algebraic geometry - Algebraic combinatorics






10. 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)






11. Letters from the beginning of the alphabet like a - b - c... often denote






12. b = b






13. Symbols that denote numbers - is to allow the making of generalizations in mathematics






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






15. 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.






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






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






18. Elementary algebraic techniques are used to rewrite a given equation in the above way before arriving at the solution. then - by subtracting 1 from both sides of the equation - and then dividing both sides by 3 we obtain






19. Is a function of the form ? : V ? Y - where V ? X1






20. Referring to the finite number of arguments (the value k)






21. 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






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






23. () is the branch of mathematics concerning the study of the rules of operations and relations - and the constructions and concepts arising from them - including terms - polynomials - equations and algebraic structures.






24. Logarithm (Log)






25. Can be added and subtracted.






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






27. Is a squared (multiplied by itself) number subtracted from another squared number. It refers to the identity






28. Is algebraic equation of degree one






29. An operation of arity zero is simply an element of the codomain Y - called a






30. If a < b and c < d






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






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






33. using factorization (the reverse process of which is expansion - but for two linear terms is sometimes denoted foiling).






34. Two equations in two variables - it is often possible to find the solutions of both variables that satisfy both equations.






35. The value produced is called






36. A mathematical statement that asserts the equality of two expressions - this is written by placing the expressions on either side of an equals sign (=).






37. Is Written as a






38. Will have two solutions in the complex number system - but need not have any in the real number system.






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






40. In which the properties of numbers are studied through algebraic systems. Number theory inspired much of the original abstraction in algebra.






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






42. Operations can have fewer or more than






43. Together with geometry - analysis - topology - combinatorics - and number theory - algebra is one of the main branches of






44. Is a binary relation on a set for which every element is related to itself - i.e. - a relation ~ on S where x~x holds true for every x in S. For example - ~ could be 'is equal to'.






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






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






47. An operation of arity k is called a






48. Is called the codomain of the operation






49. 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






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