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






2. 1 - which preserves numbers: a






3. 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






4. May not be defined for every possible value.






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






6. Is an equation involving integrals.






7. If a < b and c < d






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






9. A + b = b + a






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






11. (a






12. 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.






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






14. k-ary operation is a






15. Operations can have fewer or more than






16. 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)






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






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






19. Not associative






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






21. A unary operation






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






23. An equivalent for y can be deduced by using one of the two equations. Using the second equation: Subtracting 2x from each side of the equation: and multiplying by -1: Using this y value in the first equation in the original system: Adding 2 on each s






24. The process of expressing the unknowns in terms of the knowns is called






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






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






27. 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






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






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






30. Is algebraic equation of degree one






31. Subtraction ( - )






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






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






34. 0 - which preserves numbers: a + 0 = a






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






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






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






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






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






40. Is called the codomain of the operation






41. 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.

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42. If a < b and c > 0






43. Logarithm (Log)






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






45. A binary operation






46. b = b






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






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






49. 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.






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