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






2. Is Written as a






3. 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






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






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






6. 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)






7. Is an equation of the form X^m/n = a - for m - n integers - which has solution






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






9. Applies abstract algebra to the problems of geometry






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






11. A + b = b + a






12. 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)






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






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






15. A






16. The operation of multiplication means _______________: a






17. The inner product operation on two vectors produces a






18. If a < b and b < c






19. Can be added and subtracted.






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






21. Not associative






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






23. Is an equation of the form aX = b for a > 0 - which has solution






24. 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






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






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






27. 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.

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28. A unary operation






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






30. Is Written as a + b






31. 1 - which preserves numbers: a^1 = a






32. 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






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






34. The squaring operation only produces






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






36. 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






37. 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.






38. There are two common types of operations:






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






40. Is an equation involving derivatives.






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






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






43. 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.






44. The values combined are called






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






46. Are linear equations that have only one variable. They contain only constant numbers and a single variable without an exponent. For example:






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






48. Include composition and convolution






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






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







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