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






2. The squaring operation only produces






3. An operation of arity k is called a






4. If a < b and c < d






5. A unary operation






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






7. Operations can have fewer or more than






8. 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.






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






10. Logarithm (Log)






11. 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)






12. May not be defined for every possible value.






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






14. If a < b and c > 0






15. Is an equation involving derivatives.






16. 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'.






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






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






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






20. Can be combined using logic operations - such as and - or - and not.






21. 1 - which preserves numbers: a






22. () 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.






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






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






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






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






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






28. The values combined are called






29. Letters from the beginning of the alphabet like a - b - c... often denote






30. 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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31. 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)






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






33. Is to add - subtract - multiply - or divide both sides of the equation by the same number in order to isolate the variable on one side of the equation. Once the variable is isolated - the other side of the equation is the value of the variable.






34. 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.






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






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






37. 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






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






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






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






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






42. Can be added and subtracted.






43. Can be defined axiomatically up to an isomorphism






44. b = b






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






46. 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






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






48. 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)






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






50. 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.