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






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 which abstract algebraic methods are used to study combinatorial questions.






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






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






7. Applies abstract algebra to the problems of geometry






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






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






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






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






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






13. A






14. b = b






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






16. The inner product operation on two vectors produces a






17. If a < b and c < d






18. Is Written as a + b






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






20. 0 - which preserves numbers: a + 0 = a






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






22. 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)






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






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






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






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






27. If a < b and c > 0






28. 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.






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






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






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






32. Is Written as ab or a^b






33. Is a way of solving a functional equation of two polynomials for a number of unknown parameters. It relies on the fact that two polynomials are identical precisely when all corresponding coefficients are equal. The method is used to bring formulas in






34. () 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.






35. Is called the codomain of the operation






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






37. A binary operation






38. 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.






39. The values combined are called






40. The squaring operation only produces






41. Subtraction ( - )






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






43. Is algebraic equation of degree one






44. 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






45. 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.






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






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






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






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






50. There are two common types of operations: