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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. Subtraction ( - )






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






3. 1 - which preserves numbers: a






4. If a < b and b < c






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






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






7. 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






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






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






10. 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






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






12. A binary operation






13. Can be defined axiomatically up to an isomorphism






14. 0 - which preserves numbers: a + 0 = a






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






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






17. () 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.






18. Are called the domains of the operation






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






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






21. If a < b and c < d






22. Symbols that denote numbers - letters from the end of the alphabet - like ...x - y - z - are usually reserved for the






23. 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






24. k-ary operation is a






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






26. Not commutative a^b?b^a






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






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






29. 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)






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






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






32. If a < b and c < 0






33. Operations can have fewer or more than






34. 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)






35. A






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






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






38. 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)






39. 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).






40. 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.






41. A unary operation






42. Not associative






43. b = b






44. The inner product operation on two vectors produces a






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






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






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






48. Is Written as a + b






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






50. Is called the codomain of the operation