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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. 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






2. Is a basic technique used to simplify problems in which the original variables are replaced with new ones; the new and old variables being related in some specified way.






3. Not associative






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






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






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






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 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






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






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






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






13. Operations can have fewer or more than






14. 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.






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






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






17. Division ( / )






18. Logarithm (Log)






19. 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.






20. If a < b and c > 0






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






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






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






26. Subtraction ( - )






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






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






29. Is Written as a + b






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






31. 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).






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






33. The squaring operation only produces






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






35. Elementary algebraic techniques are used to rewrite a given equation in the above way before arriving at the solution. then - by subtracting 1 from both sides of the equation - and then dividing both sides by 3 we obtain






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






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






38. Include composition and convolution






39. Symbols that denote numbers - is to allow the making of generalizations in mathematics






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






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






42. A unary operation






43. Is an equation involving integrals.






44. k-ary operation is a






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






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






47. Applies abstract algebra to the problems of geometry






48. 1 - which preserves numbers: a






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






50. 1 - which preserves numbers: a^1 = a