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






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






3. 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.






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






5. 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.






6. If a < b and c < d






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






8. Logarithm (Log)






9. Is Written as a






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






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






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






13. May not be defined for every possible value.






14. Division ( / )






15. 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






16. 1 - which preserves numbers: a^1 = a






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






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






19. The operation of multiplication means _______________: a






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






21. Subtraction ( - )






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






23. Is Written as a + b






24. In which the properties of numbers are studied through algebraic systems. Number theory inspired much of the original abstraction in algebra.






25. A binary operation






26. b = b






27. Not associative






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






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






30. 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






31. Is called the codomain of the operation






32. k-ary operation is a






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






34. 1 - which preserves numbers: a






35. Operations can have fewer or more than






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






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






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






39. The relation of equality (=) is...reflexive: b = b; symmetric: if a = b then b = a; transitive: if a = b and b = c then a = c.






40. Are called the domains of the operation






41. Is called the type or arity of the operation






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






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






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






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






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. Is an equation involving derivatives.






48. 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)






49. 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






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