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. Is Written as ab or a^b






2. A + b = b + a






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






4. A






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






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






7. Is Written as a






8. The squaring operation only produces






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






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






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






12. Can be defined axiomatically up to an isomorphism






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






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






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






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






17. If a < b and c > 0






18. 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.






19. Include composition and convolution






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






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






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






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






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






25. 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.






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






27. There are two common types of operations:






28. 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.






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






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






31. 1 - which preserves numbers: a^1 = a






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






33. 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)






34. Is called the type or arity of the operation






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






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






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






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






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






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






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






42. An operation of arity k is called a






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






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






45. Not commutative a^b?b^a






46. May contain numbers - variables and arithmetical operations. These are conventionally written with 'higher-power' terms on the left






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






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






49. 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)






50. If a < b and c < 0