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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 binary operation






2. 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






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






4. 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)






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






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






7. The operation of multiplication means _______________: a






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






9. If a < b and c < 0






10. 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).






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






12. Is Written as ab or a^b






13. often express relationships between given quantities - the knowns - and quantities yet to be determined - the unknowns.






14. Is Written as a






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






16. The inner product operation on two vectors produces a






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






19. The value produced is called






20. If a = b then b = a






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






22. 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.






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






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






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






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






27. Some equations are true for all values of the involved variables (such as a + b = b + a); such equations are called






28. The squaring operation only produces






29. There are two common types of operations:






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






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






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






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






34. Operations can have fewer or more than






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






36. If a < b and c > 0






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






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






39. k-ary operation is a






40. Can be combined using logic operations - such as and - or - and not.






41. (a






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






43. 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






44. A






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






46. 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)






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






48. 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






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






50. Is Written as a + b