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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 an equation where the unknowns are required to be integers.






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






3. There are two common types of operations:






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






5. 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






6. 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)






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






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






9. 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.






10. Is an equation of the form log`a^X = b for a > 0 - which has solution






11. Include composition and convolution






12. An operation of arity k is called a






13. Is algebraic equation of degree one






14. 1 - which preserves numbers: a






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






16. Logarithm (Log)






17. 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.






18. Is an equation involving derivatives.






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






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






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






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






23. k-ary operation is a






24. A






25. Division ( / )






26. Is Written as a + b






27. 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)






28. If a < b and b < c






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






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






31. If a = b then b = a






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






33. using factorization (the reverse process of which is expansion - but for two linear terms is sometimes denoted foiling).






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






35. b = b






36. Is called the type or arity of the operation






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






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






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






40. 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).






41. 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






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






43. 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)






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






45. If a < b and c > 0






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






47. 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






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






49. Can be expressed in the form ax^2 + bx + c = 0 - where a is not zero (if it were zero - then the equation would not be quadratic but linear).






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