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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. k-ary operation is a






2. Can be expressed in the form ax^2 + bx + c = 0 - where a is not zero (if it were zero - then the equation would not be quadratic but linear).






3. Is Written as ab or a^b






4. 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.






5. If a < b and b < c






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






7. If a < b and c < d






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






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






10. 0 - which preserves numbers: a + 0 = a






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






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






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






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






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






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






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






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






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






20. Division ( / )






21. Subtraction ( - )






22. 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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23. Applies abstract algebra to the problems of geometry






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






25. 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.






26. 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)






27. If a < b and c > 0






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






29. 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






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






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






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






34. May not be defined for every possible value.






35. Are called the domains of the operation






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






37. 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'.






38. 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






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






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






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






42. Is called the codomain of the operation






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






44. 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.






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






46. (a + b) + c = a + (b + c)






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






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






49. An operation of arity k is called a






50. 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