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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. 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






2. b = b






3. A + b = b + a






4. A mathematical statement that asserts the equality of two expressions - this is written by placing the expressions on either side of an equals sign (=).






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






6. 1 - which preserves numbers: a^1 = a






7. 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)






8. Is algebraic equation of degree one






9. Is the claim that two expressions have the same value and are equal.






10. Operations can have fewer or more than






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






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






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






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






15. Applies abstract algebra to the problems of geometry






16. 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).






17. An operation of arity k is called a






18. 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






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






20. 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'.






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






22. If a < b and c > 0






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






24. The values combined are called






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






26. There are two common types of operations:






27. 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)






28. If a < b and c < d






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






30. Not commutative a^b?b^a






31. If a < b and c < 0






32. Is an equation involving integrals.






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






34. 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.






35. 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.






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






37. Subtraction ( - )






38. The value produced is called






39. 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.






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






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






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






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






44. 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).






45. 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






46. Is Written as a






47. Logarithm (Log)






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






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






50. 0 - which preserves numbers: a + 0 = a