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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 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.






2. 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.






3. An operation of arity k is called a






4. If a < b and c < d






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






6. 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.

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7. Can be added and subtracted.






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






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






10. 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.






11. A unary operation






12. Can be combined using logic operations - such as and - or - and not.






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






14. Is an equation involving only algebraic expressions in the unknowns. These are further classified by degree.






15. If a = b and b = c then a = c






16. () 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.






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






18. Logarithm (Log)






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






20. Is an equation involving integrals.






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






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






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






24. 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






25. 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)






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






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






28. 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






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






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






31. 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






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






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






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






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






36. The inner product operation on two vectors produces a






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






38. Is Written as a






39. May not be defined for every possible value.






40. Is an equation of the form aX = b for a > 0 - which has solution






41. Not associative






42. 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)






43. Are called the domains of the operation






44. Operations can have fewer or more than






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






46. An equivalent for y can be deduced by using one of the two equations. Using the second equation: Subtracting 2x from each side of the equation: and multiplying by -1: Using this y value in the first equation in the original system: Adding 2 on each s






47. 0 - which preserves numbers: a + 0 = a






48. A binary operation






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






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