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






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






3. 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)






4. 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






5. May not be defined for every possible value.






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






7. Applies abstract algebra to the problems of geometry






8. The operation of multiplication means _______________: a






9. Is Written as a + b






10. There are two common types of operations:






11. Is called the type or arity of the operation






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






13. 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






14. 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)






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






16. Symbols that denote numbers - letters from the end of the alphabet - like ...x - y - z - are usually reserved for the






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






18. A unary operation






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






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






21. If a < b and c < d






22. Are true for only some values of the involved variables: x2 - 1 = 4.






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






24. Is an equation involving derivatives.






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






26. 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.






27. () 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.






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






29. Not commutative a^b?b^a






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






31. Take two values - and include addition - subtraction - multiplication - division - and exponentiation.






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






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






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






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






36. If a < b and c > 0






37. Subtraction ( - )






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






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






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






41. Algebra comes from Arabic al-jebr meaning '______________'. Studies the effects of adding and multiplying numbers - variables - and polynomials - along with their factorization and determining their roots. Works directly with numbers. Also covers sym






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






43. 1 - which preserves numbers: a^1 = a






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






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






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






47. Is an equation involving only algebraic expressions in the unknowns. These are further classified by degree.






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






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






50. 1 - which preserves numbers: a