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






2. Is an equation involving integrals.






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






4. If a < b and c > 0






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






6. 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






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






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






9. The values combined are called






10. Is called the type or arity of the operation






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






12. A unary operation






13. 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






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






15. 0 - which preserves numbers: a + 0 = a






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






17. Symbols that denote numbers - letters from the end of the alphabet - like ...x - y - z - are usually reserved for the






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






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






20. 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






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






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






23. Operations can have fewer or more than






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






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






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






27. The operation of multiplication means _______________: a






28. b = b






29. 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)






30. Is a function of the form ? : V ? Y - where V ? X1






31. 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






32. k-ary operation is a






33. The value produced is called






34. Can be added and subtracted.






35. 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.


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






37. An operation of arity k is called a






38. Applies abstract algebra to the problems of geometry






39. Is to add - subtract - multiply - or divide both sides of the equation by the same number in order to isolate the variable on one side of the equation. Once the variable is isolated - the other side of the equation is the value of the variable.






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






41. 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)






42. A binary operation






43. Logarithm (Log)






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






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






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






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






48. 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






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






50. A + b = b + a