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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 binary operation






2. If a < b and c < 0






3. 0 - which preserves numbers: a + 0 = a






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






5. If a = b then b = a






6. 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






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






8. The inner product operation on two vectors produces a






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






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






11. () is the branch of mathematics concerning the study of the rules of operations and relations - and the constructions and concepts arising from them - including terms - polynomials - equations and algebraic structures.






12. There are two common types of operations:






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






14. Not commutative a^b?b^a






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






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






17. 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






18. 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.






19. Division ( / )






20. Is called the type or arity of the operation






21. An operation of arity k is called a






22. Is an equation involving derivatives.






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






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






25. If a < b and c > 0






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






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






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






29. 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






30. Are called the domains of the operation






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. The operation of multiplication means _______________: a






33. Include composition and convolution






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






35. 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






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






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






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






39. 1 - which preserves numbers: a^1 = a






40. Applies abstract algebra to the problems of geometry






41. 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.






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






43. Is Written as a + b






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






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






46. Is a function of the form ? : V ? Y - where V ? X1






47. (a






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






49. Is Written as a






50. Symbols that denote numbers - is to allow the making of generalizations in mathematics