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






2. Is an action or procedure which produces a new value from one or more input values.






3. Is called the type or arity of the operation






4. 1 - which preserves numbers: a^1 = a






5. The value produced is called






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






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






8. Is algebraic equation of degree one






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






10. 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






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






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






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






14. The operation of multiplication means _______________: a






15. 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'.






16. Not associative






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






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






20. 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)






21. 1 - which preserves numbers: a






22. Not commutative a^b?b^a






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






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






25. Can be defined axiomatically up to an isomorphism






26. Is called the codomain of the operation






27. Is Written as ab or a^b






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






29. 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)






30. 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






31. Can be added and subtracted.






32. 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.






33. () 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.






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






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






36. b = b






37. Is an equation involving integrals.






38. Take two values - and include addition - subtraction - multiplication - division - and exponentiation.






39. Are called the domains of the operation






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. There are two common types of operations:






42. 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).






43. The inner product operation on two vectors produces a






44. If a < b and c > 0






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






46. k-ary operation is a






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






48. Is an equation involving derivatives.






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






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