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. In which properties common to all algebraic structures are studied






2. Operations can have fewer or more than






3. 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)






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






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






6. Transivity: if a < b and b < c then a < c; that if a < b and c < d then a + c < b + d; that if a < b and c > 0 then ac < bc; that if a < b and c < 0 then bc < ac.






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






8. Is an equation involving derivatives.






9. Is algebraic equation of degree one






10. Is an equation involving integrals.






11. Are called the domains of the operation






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






13. 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)






14. A + b = b + a






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






16. (a






17. 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.






18. If a = b then b = a






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






20. 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'.






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






22. Subtraction ( - )






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






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






25. Are linear equations that have only one variable. They contain only constant numbers and a single variable without an exponent. For example:






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






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






28. Can be defined axiomatically up to an isomorphism






29. () 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.






30. An operation of arity k is called a






31. Is synonymous with function - map and mapping - that is - a relation - for which each element of the domain (input set) is associated with exactly one element of the codomain (set of possible outputs).






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






33. 1 - which preserves numbers: a^1 = a






34. Not associative






35. A unary operation






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






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






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






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






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






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






42. The value produced is called






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






44. If a < b and c > 0






45. 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






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






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






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






49. 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






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