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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 added and subtracted.






3. There are two common types of operations:






4. Applies abstract algebra to the problems of geometry






5. The squaring operation only produces






6. Some equations are true for all values of the involved variables (such as a + b = b + a); such equations are called






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






8. If a < b and c > 0






9. Can be defined axiomatically up to an isomorphism






10. 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.


11. Subtraction ( - )






12. 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






13. () 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.






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






15. 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)






16. In which the specific properties of vector spaces are studied (including matrices)






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






18. If a < b and c < 0






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






20. 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.






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






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






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






24. Is an equation involving derivatives.






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






26. If a = b then b = a






27. 0 - which preserves numbers: a + 0 = a






28. 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.






29. A + b = b + a






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






31. 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'.






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






33. 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






34. Division ( / )






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






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






37. Is called the type or arity of the operation






38. Can be combined using logic operations - such as and - or - and not.






39. Are called the domains of the operation






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






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






42. Not associative






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






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






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






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






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






48. The operation of multiplication means _______________: a






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






50. k-ary operation is a