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






2. 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)






3. An operation of arity k is called a






4. If a = b then b = a






5. The set which contains the values produced is called the codomain - but the set of actual values attained by the operation is its






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






7. Not associative






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






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






10. The operation of multiplication means _______________: a






11. 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






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






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






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






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






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






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






18. Is Written as ab or a^b






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






20. 1 - which preserves numbers: a^1 = a






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






22. The values for which an operation is defined form a set called its






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






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






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






26. Can be defined axiomatically up to an isomorphism






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






28. Is Written as a + b






29. 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).






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






31. A binary operation






32. May not be defined for every possible value.






33. Applies abstract algebra to the problems of geometry






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






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






36. 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.






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






38. Division ( / )






39. Are called the domains of the operation






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






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






42. Subtraction ( - )






43. 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






44. Is Written as a






45. Introduces the concept of variables representing numbers. Statements based on these variables are manipulated using the rules of operations that apply to numbers - such as addition. This can be done for a variety of reasons - including equation solvi






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






47. If a < b and c < d






48. If a < b and c > 0






49. Include composition and convolution






50. 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'.