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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. A + b = b + a






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






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






4. 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)






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






6. (a






7. Subtraction ( - )






8. If a < b and c < d






9. 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






10. An operation of arity k is called a






11. 1 - which preserves numbers: a






12. 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.






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






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






15. If a = b then b = a






16. 1 - which preserves numbers: a^1 = a






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






18. The value produced is called






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






20. The inner product operation on two vectors produces a






21. If a < b and b < c






22. 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






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






24. Include composition and convolution






25. A binary operation






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






27. Operations can have fewer or more than






28. 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)






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






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






31. 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)






32. 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






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






34. A unary operation






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






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






37. 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'.






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






39. 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.






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






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






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






43. Is Written as a






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






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






46. 0 - which preserves numbers: a + 0 = a






47. Is algebraic equation of degree one






48. Division ( / )






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






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