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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. The relation of equality (=) is...reflexive: b = b; symmetric: if a = b then b = a; transitive: if a = b and b = c then a = c.






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






3. Can be defined axiomatically up to an isomorphism






4. A value that represents a quantity along a continuum - such as -5 (an integer) - 4/3 (a rational number that is not an integer) - 8.6 (a rational number given by a finite decimal representation) - v2 (the square root of two - an algebraic number that






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






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






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






8. Is an equation involving integrals.






9. The value produced is called






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






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






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






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






14. 0 - which preserves numbers: a + 0 = a






15. Not associative






16. 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)






17. 1 - which preserves numbers: a^1 = a






18. Include composition and convolution






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






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






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






22. If a < b and c < 0






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






24. 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






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






26. A unary operation






27. The squaring operation only produces






28. Two equations in two variables - it is often possible to find the solutions of both variables that satisfy both equations.






29. 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)






30. Can be added and subtracted.






31. 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.






32. An operation of arity k is called a






33. The operation of multiplication means _______________: a






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






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






36. Operations can have fewer or more than






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






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






39. 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






40. A + b = b + a






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






42. 1 - which preserves numbers: a






43. Logarithm (Log)






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






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






46. 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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47. using factorization (the reverse process of which is expansion - but for two linear terms is sometimes denoted foiling).






48. If a < b and c < d






49. Is Written as ab or a^b






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