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






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






3. May not be defined for every possible value.






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






5. If a < b and c > 0






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 involving derivatives.






8. In which the specific properties of vector spaces are studied (including matrices)






9. Division ( / )






10. Not commutative a^b?b^a






11. Letters from the beginning of the alphabet like a - b - c... often denote






12. The value produced is called






13. 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.






14. The operation of multiplication means _______________: a






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






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






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






18. Parenthesis and other grouping symbols including brackets - absolute value symbols - and the fraction bar - exponents and roots - multiplication and division - addition and subtraction






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






20. 1 - which preserves numbers: a






21. Can be written in terms of n-th roots: a^m/n = (nva)^m and thus even roots of negative numbers do not exist in the real number system - has the property: a^ba^c = a^b+c - has the property: (a^b)^c = a^bc - In general a^b ? b^a and (a^b)^c ? a^(b^c)






22. 0 - which preserves numbers: a + 0 = a






23. 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)






24. Referring to the finite number of arguments (the value k)






25. If a < b and c < d






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






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






28. Are denoted by letters at the end of the alphabet - x - y - z - w - ...






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






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






31. (a






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






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






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






36. 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'.






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






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






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






40. 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.






41. 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






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






43. A unary operation






44. Is an equation involving integrals.






45. k-ary operation is a






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






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






48. The squaring operation only produces






49. 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.






50. 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.