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






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






3. 1 - which preserves numbers: a






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






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






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






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






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






9. Can be defined axiomatically up to an isomorphism






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






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






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






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






14. The value produced is called






15. 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.






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






17. Is Written as a + b






18. 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






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






20. 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






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






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. In which properties common to all algebraic structures are studied






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






25. A unary operation






26. A + b = b + a






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






28. 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)






29. Subtraction ( - )






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






31. 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.






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






33. If a < b and c > 0






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






35. k-ary operation is a






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






37. Applies abstract algebra to the problems of geometry






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






39. Is an equation involving integrals.






40. If a < b and b < c






41. The operation of multiplication means _______________: a






42. An operation of arity k is called a






43. If a < b and c < 0






44. The values combined are called






45. 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.






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






47. 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)






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






49. May not be defined for every possible value.






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