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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. 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






2. 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)






3. Real numbers can be thought of as points on an infinitely long line where the points corresponding to integers are equally spaced called the






4. Include composition and convolution






5. Is called the codomain of the operation






6. Can be defined axiomatically up to an isomorphism






7. Is an equation where the unknowns are required to be integers.






8. Is a way of solving a functional equation of two polynomials for a number of unknown parameters. It relies on the fact that two polynomials are identical precisely when all corresponding coefficients are equal. The method is used to bring formulas in






9. Division ( / )






10. 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.






11. 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'.






12. Are called the domains of the operation






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






14. The operation of multiplication means _______________: a






15. If a < b and c < 0






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






17. (a + b) + c = a + (b + c)






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






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






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






21. There are two common types of operations:






22. If a < b and c < d






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






24. Is Written as ab or a^b






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






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






28. 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






29. Can be added and subtracted.






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






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






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






33. Operations can have fewer or more than






34. 1 - which preserves numbers: a






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






36. Is Written as a






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






38. 0 - which preserves numbers: a + 0 = a






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






40. 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.






41. A






42. An operation of arity k is called a






43. 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






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






45. A unary operation






46. The inner product operation on two vectors produces a






47. Is an equation involving derivatives.






48. 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






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






50. 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)







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