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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 unary operation






2. Is called the type or arity of the operation






3. Subtraction ( - )






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






5. (a






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






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






8. () 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.






9. 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).






10. Division ( / )






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






12. If a < b and b < c






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






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






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






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






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. If a = b and b = c then a = c






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






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






22. 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)






23. 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.






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






25. Are called the domains of the operation






26. 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






27. If a < b and c < d






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






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






30. 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)






31. 1 - which preserves numbers: a






32. 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






33. The inner product operation on two vectors produces a






34. May not be defined for every possible value.






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






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






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






38. 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






39. An operation of arity k is called a






40. Not commutative a^b?b^a






41. The squaring operation only produces






42. Can be added and subtracted.






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






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






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






46. The operation of multiplication means _______________: a






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






48. b = b






49. 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.






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