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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. 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






2. Is called the type or arity of the operation






3. If a = b then b = a






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






5. Is called the codomain of the operation






6. 0 - which preserves numbers: a + 0 = a






7. Are called the domains of the operation






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






9. Is Written as a + b






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






11. 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).






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






13. Include composition and convolution






14. Two equations in two variables - it is often possible to find the solutions of both variables that satisfy both equations.






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






16. There are two common types of operations:






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






18. Take two values - and include addition - subtraction - multiplication - division - and exponentiation.






19. 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)






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






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






22. 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'.






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






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






25. Is Written as ab or a^b






26. Is algebraic equation of degree one






27. Not commutative a^b?b^a






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






29. Can be defined axiomatically up to an isomorphism






30. The inner product operation on two vectors produces a






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






32. 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






33. 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)






34. The squaring operation only produces






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






36. Can be added and subtracted.






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






38. The value produced is called






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






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






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






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






43. Algebra comes from Arabic al-jebr meaning '______________'. Studies the effects of adding and multiplying numbers - variables - and polynomials - along with their factorization and determining their roots. Works directly with numbers. Also covers sym






44. If a < b and c < 0






45. 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)






46. 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.






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






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






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






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