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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. If a < b and b < c






2. 1 - which preserves numbers: a






3. Can be defined axiomatically up to an isomorphism






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






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






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






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






8. b = b






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






10. A + b = b + a






11. An operation of arity k is called a






12. 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'.






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






14. The operation of multiplication means _______________: a






15. Are called the domains of the operation






16. Is called the type or arity of the operation






17. The inner product operation on two vectors produces a






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






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






20. 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






21. 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.






22. Is Written as a + b






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






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






25. Logarithm (Log)






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






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






28. If an equation in algebra is known to be true - the following operations may be used to produce another true equation:






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






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






31. 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.


32. 0 - which preserves numbers: a + 0 = a






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






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






35. If a < b and c < d






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






37. 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






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






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






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






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






42. May not be defined for every possible value.






43. 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






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






45. A






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






47. 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)






48. If a < b and c > 0






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






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