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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. 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)






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






3. 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)






4. 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.






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






6. Not associative






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






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






9. May not be defined for every possible value.






10. The codomain is the set of real numbers but the range is the






11. 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






12. 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






13. 1 - which preserves numbers: a






14. Applies abstract algebra to the problems of geometry






15. Can be defined axiomatically up to an isomorphism






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






17. Logarithm (Log)






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






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






20. Is called the codomain of the operation






21. Is Written as a + b






22. b = b






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






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






26. 1 - which preserves numbers: a^1 = a






27. 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






28. Division ( / )






29. 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)






30. Is an equation involving derivatives.






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






32. 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






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






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






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. 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. A binary operation






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






39. Subtraction ( - )






40. The inner product operation on two vectors produces a






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






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






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






45. If a = b then b = a






46. 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






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






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






49. Can be added and subtracted.






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







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