Test your basic knowledge |

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. If a = b then b = a






2. Not commutative a^b?b^a






3. Are called the domains of the operation






4. 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.






5. 0 - which preserves numbers: a + 0 = a






6. Is Written as a






7. 1 - which preserves numbers: a






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






9. The operation of multiplication means _______________: a






10. Operations can have fewer or more than






11. Can be defined axiomatically up to an isomorphism






12. 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)






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






14. 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.






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






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






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






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






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






20. Is an equation involving derivatives.






21. Is called the codomain of the operation






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






23. 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






24. A unary operation






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






26. If a < b and c > 0






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






28. Is an equation involving integrals.






29. Division ( / )






30. There are two common types of operations:






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






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






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






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






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. An operation of arity k is called a






37. The values combined are called






38. A + b = b + a






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






40. Can be added and subtracted.






41. Applies abstract algebra to the problems of geometry






42. Not associative






43. Include composition and convolution






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






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






46. k-ary operation is a






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






49. (a






50. 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.