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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. Can be defined axiomatically up to an isomorphism






2. 1 - which preserves numbers: a^1 = a






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






5. May not be defined for every possible value.






6. 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.






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






8. b = b






9. Is called the type or arity of the operation






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






11. Is Written as ab or a^b






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






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






14. The operation of multiplication means _______________: a






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






16. Not associative






17. A






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






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






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






21. 0 - which preserves numbers: a + 0 = a






22. 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






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






24. A binary operation






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






26. Is synonymous with function - map and mapping - that is - a relation - for which each element of the domain (input set) is associated with exactly one element of the codomain (set of possible outputs).






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






28. Is Written as a






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






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






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






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






33. 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.






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






35. An operation of arity k is called a






36. 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.






37. 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






38. The value produced is called






39. Applies abstract algebra to the problems of geometry






40. 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'.






41. 1 - which preserves numbers: a






42. A + b = b + a






43. Subtraction ( - )






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






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






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. Are called the domains of the operation






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






49. Is an equation involving integrals.






50. 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)