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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 + b = b + a






2. The inner product operation on two vectors produces a






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






4. 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.






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






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 b = c then a = c






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






9. There are two common types of operations:






10. Is an equation involving derivatives.






11. k-ary operation is a






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






13. Is an equation involving integrals.






14. 1 - which preserves numbers: a^1 = a






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






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






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






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






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






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






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






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






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






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






25. The squaring operation only produces






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






27. Is Written as ab or a^b






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






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. Will have two solutions in the complex number system - but need not have any in the real number system.






31. Include composition and convolution






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






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






34. 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






35. Is Written as a + b






36. Can be defined axiomatically up to an isomorphism






37. Logarithm (Log)






38. A






39. 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'.






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






41. 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).






42. Subtraction ( - )






43. 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






44. If a < b and c > 0






45. 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)






46. Is an equation of the form aX = b for a > 0 - which has solution






47. Is called the codomain of the operation






48. Is called the type or arity of the operation






49. If a < b and c < 0






50. The values of the variables which make the equation true are the solutions of the equation and can be found through