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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. Implies that the domain of the function is a power of the codomain (i.e. the Cartesian product of one or more copies of the codomain)






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






3. The relation of equality (=) is...reflexive: b = b; symmetric: if a = b then b = a; transitive: if a = b and b = c then a = c.






4. () 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.






5. Is Written as a






6. Can be defined axiomatically up to an isomorphism






7. 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)






8. Not associative






9. If a < b and b < c






10. If an equation in algebra is known to be true - the following operations may be used to produce another true equation:






11. Are linear equations that have only one variable. They contain only constant numbers and a single variable without an exponent. For example:






12. Applies abstract algebra to the problems of geometry






13. Means repeated addition of ones: a + n = a + 1 + 1 +...+ 1 (n number of times) - has an inverse operation called subtraction: (a + b) - b = a - which is the same as adding a negative number - a - b = a + (-b)






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






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






16. Subtraction ( - )






17. Include composition and convolution






18. Is an equation involving integrals.






19. Division ( / )






20. Operations can have fewer or more than






21. Is an equation of the form aX = b for a > 0 - which has solution






22. 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'.






23. Is Written as ab or a^b






24. b = b






25. Is called the codomain of the operation






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






27. often express relationships between given quantities - the knowns - and quantities yet to be determined - the unknowns.






28. A + b = b + a






29. The inner product operation on two vectors produces a






30. An example of solving a system of linear equations is by using the elimination method: Multiplying the terms in the second equation by 2: Adding the two equations together to get: which simplifies to Since the fact that x = 2 is known - it is then po






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






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






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






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






35. 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.






36. 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.






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






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






39. The operation of exponentiation means ________________: a^n = a






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






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






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






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






44. Is Written as a + b






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






46. Is algebraic equation of degree one






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






48. 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






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






50. An operation of arity k is called a