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






2. 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).






3. 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






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






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






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






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






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






9. 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.






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






11. Is Written as a + b






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






13. Is called the codomain of the operation






14. If a < b and b < c






15. May not be defined for every possible value.






16. A






17. b = b






18. 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)






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






20. Operations can have fewer or more than






21. Is a squared (multiplied by itself) number subtracted from another squared number. It refers to the identity






22. (a






23. Include composition and convolution






24. Not commutative a^b?b^a






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






26. Can be defined axiomatically up to an isomorphism






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






28. 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)






29. Is called the type or arity of the operation






30. 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.


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






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






33. If a = b then b = a






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






35. If a < b and c > 0






36. 0 - which preserves numbers: a + 0 = a






37. 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






38. If a < b and c < d






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






40. Is Written as ab or a^b






41. 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.






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






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






44. Subtraction ( - )






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






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






47. The values combined are called






48. 1 - which preserves numbers: 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. Is an equation involving derivatives.