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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. Can be defined axiomatically up to an isomorphism






2. If a < b and c < d






3. Is Written as a






4. 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.






5. Is called the codomain of the operation






6. Is called the type or arity of the operation






7. Not associative






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






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






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






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






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






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






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






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






16. Applies abstract algebra to the problems of geometry






17. A unary operation






18. 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'.






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






20. 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.






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






22. Is an equation involving derivatives.






23. 1 - which preserves numbers: a^1 = a






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






25. A distinction is made between the equality sign ( = ) for an equation and the equivalence symbol () for an






26. Subtraction ( - )






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






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






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






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






31. If a < b and c < 0






32. 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






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






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






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






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






37. 0 - which preserves numbers: a + 0 = a






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






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






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






41. A binary operation






42. The inner product operation on two vectors produces a






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






44. The operation of multiplication means _______________: a






45. 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)






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






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






48. 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).






49. If a = b then b = a






50. If a < b and b < c