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






2. Is an equation involving integrals.






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






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






5. Reflexive: b = b; symmetric: if a = b then b = a; transitive: if a = b and b = c then a = c.






6. The inner product operation on two vectors produces a






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






8. Real numbers can be thought of as points on an infinitely long line where the points corresponding to integers are equally spaced called the






9. The value produced is called






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






11. 0 - which preserves numbers: a + 0 = a






12. Not associative






13. Is algebraic equation of degree one






14. The squaring operation only produces






15. 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






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






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






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






19. 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).






20. () 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.






21. 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)






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






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






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






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






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






27. 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






28. 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






29. The values combined are called






30. 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.






31. An operation of arity k is called a






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






33. Is Written as a + b






34. Is called the type or arity of the operation






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






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






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






39. A vector can be multiplied by a scalar to form another vector






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






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






42. Is an equation involving a transcendental function of one of its variables.






43. 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)






44. There are two common types of operations:






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






46. b = b






47. Division ( / )






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






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






50. 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.