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






2. 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.






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






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






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






6. A






7. k-ary operation is a






8. 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






9. 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






10. Can be combined using the function composition operation - performing the first rotation and then the second.






11. Is an equation involving integrals.






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






13. 1 - which preserves numbers: a






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






15. 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.






16. The squaring operation only produces






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






19. Are called the domains of the operation






20. Division ( / )






21. The inner product operation on two vectors produces a






22. Are denoted by letters at the end of the alphabet - x - y - z - w - ...






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






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






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






26. Are denoted by letters at the beginning - a - b - c - d - ...






27. 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.






28. A unary operation






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






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






31. Is called the codomain of the operation






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






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






34. An operation of arity k is called a






35. If a < b and b < c






36. Subtraction ( - )






37. Logarithm (Log)






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






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






40. 0 - which preserves numbers: a + 0 = a






41. 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






42. 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).






43. 1 - which preserves numbers: a^1 = a






44. 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).






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






46. 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.






47. There are two common types of operations:






48. () 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.






49. 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






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