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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. 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)






3. The operation of multiplication means _______________: a






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






5. 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)






6. If a < b and c < 0






7. 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)






8. 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






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






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






11. Is an equation in which a polynomial is set equal to another polynomial.






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






14. If a = b then b = a






15. Not associative






16. Is Written as a






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






18. A + b = b + a






19. May not be defined for every possible value.






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






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






22. Can be defined axiomatically up to an isomorphism






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






24. Is Written as ab or a^b






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






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






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






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






29. An operation of arity k is called a






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






31. A value that represents a quantity along a continuum - such as -5 (an integer) - 4/3 (a rational number that is not an integer) - 8.6 (a rational number given by a finite decimal representation) - v2 (the square root of two - an algebraic number that






32. 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.






33. Applies abstract algebra to the problems of geometry






34. Is an action or procedure which produces a new value from one or more input values.






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






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






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






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






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






40. Is an equation of the form X^m/n = a - for m - n integers - which has solution






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






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






43. There are two common types of operations:






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






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






46. 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).






47. Is algebraic equation of degree one






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






49. 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.






50. (a