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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. If an equation in algebra is known to be true - the following operations may be used to produce another true equation:






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






3. In which abstract algebraic methods are used to study combinatorial questions.






4. May not be defined for every possible value.






5. 1 - which preserves numbers: a






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






7. 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






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






9. An example of solving a system of linear equations is by using the elimination method: Multiplying the terms in the second equation by 2: Adding the two equations together to get: which simplifies to Since the fact that x = 2 is known - it is then po






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






11. 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






12. (a






13. 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






14. Is called the type or arity of the operation






15. Subtraction ( - )






16. k-ary operation is a






17. Operations can have fewer or more than






18. Are called the domains of the operation






19. In an equation with a single unknown - a value of that unknown for which the equation is true is called






20. The codomain is the set of real numbers but the range is the






21. Is an equation involving derivatives.






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






23. A + b = b + a






24. An operation of arity k is called a






25. 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)






26. 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.






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






28. 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).






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






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






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






32. If a < b and c < 0






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






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






35. 1 - which preserves numbers: a^1 = a






36. 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)






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






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






39. In which the specific properties of vector spaces are studied (including matrices)






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






41. 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'.






42. The values combined are called






43. 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).






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






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






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






47. 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.






48. 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)






49. Can be added and subtracted.






50. Can be defined axiomatically up to an isomorphism