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






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






3. Involve only one value - such as negation and trigonometric functions.






4. 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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5. Include composition and convolution






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






7. If a < b and c > 0






8. Is called the type or arity of the operation






9. Applies abstract algebra to the problems of geometry






10. Is an equation involving a transcendental function of one of its variables.






11. 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)






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






13. Division ( / )






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






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






17. Is an equation involving integrals.






18. If a < b and b < c






19. A value that represents a quantity along a continuum - such as -5 (an integer) - 4/3 (a rational number that is not an integer) - 8.6 (a rational number given by a finite decimal representation) - v2 (the square root of two - an algebraic number that






20. Is an equation involving derivatives.






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






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






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






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






25. The operation of multiplication means _______________: a






26. Subtraction ( - )






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






28. The squaring operation only produces






29. 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






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






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






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






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






34. k-ary operation is a






35. 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






36. Operations can have fewer or more than






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






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






39. 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






40. Take two values - and include addition - subtraction - multiplication - division - and exponentiation.






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






42. 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.






43. 0 - which preserves numbers: a + 0 = a






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






45. May not be defined for every possible value.






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






47. () 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.






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






49. The values combined are called






50. The inner product operation on two vectors produces a