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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. The operation of multiplication means _______________: a






2. (a + b) + c = a + (b + c)






3. Not associative






4. Include composition and convolution






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






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






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






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






9. The values combined are called






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






11. 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






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






13. 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)






14. There are two common types of operations:






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






16. using factorization (the reverse process of which is expansion - but for two linear terms is sometimes denoted foiling).






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






18. Logarithm (Log)






19. A






20. Is called the codomain of the operation






21. If a < b and c < d






22. An operation of arity k is called a






23. A unary operation






24. Operations can have fewer or more than






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






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






27. 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






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






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






30. 1 - which preserves numbers: a^1 = a






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






32. 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.






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






34. 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).






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






36. 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)






37. The value produced is called






38. Not commutative a^b?b^a






39. k-ary operation is a






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






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






43. 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'.






44. Is algebraic equation of degree one






45. 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.






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






47. The inner product operation on two vectors produces a






48. If a < b and c < 0






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






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