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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. Is Written as ab or a^b






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






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






4. b = b






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






6. 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.






7. An operation of arity k is called a






8. 1 - which preserves numbers: a^1 = a






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






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






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






12. A






13. (a






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






15. If a < b and c < d






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






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






18. Is called the codomain of the operation






19. 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'.






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






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






22. Is an equation involving derivatives.






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






24. 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)






25. k-ary operation is a






26. 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






27. Together with geometry - analysis - topology - combinatorics - and number theory - algebra is one of the main branches of






28. The squaring operation only produces






29. 1 - which preserves numbers: a






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






31. Elementary algebraic techniques are used to rewrite a given equation in the above way before arriving at the solution. then - by subtracting 1 from both sides of the equation - and then dividing both sides by 3 we obtain






32. A + b = b + a






33. Can be defined axiomatically up to an isomorphism






34. Logarithm (Log)






35. () 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.






36. Applies abstract algebra to the problems of geometry






37. Are called the domains of the operation






38. May not be defined for every possible value.






39. The operation of multiplication means _______________: a






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






41. Not associative






42. Include composition and convolution






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






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






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






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






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






48. The inner product operation on two vectors produces a






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






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