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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 codomain is the set of real numbers but the range is the






2. 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






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






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






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






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






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






8. Is called the codomain of the operation






9. An operation of arity k is called a






10. 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.






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






12. Subtraction ( - )






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






14. A + b = b + a






15. If a = b then b = a






16. 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






17. Division ( / )






18. Are true for only some values of the involved variables: x2 - 1 = 4.






19. 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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20. 1 - which preserves numbers: a






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






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






23. 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)






24. The operation of multiplication means _______________: a






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






26. 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






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






28. Is Written as ab or a^b






29. 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.






30. 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.






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






32. If a < b and b < c






33. Is Written as a + b






34. If a < b and c < 0






35. Is algebraic equation of degree one






36. Real numbers can be thought of as points on an infinitely long line where the points corresponding to integers are equally spaced called the






37. May not be defined for every possible value.






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






39. 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).






40. Logarithm (Log)






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






42. Parenthesis and other grouping symbols including brackets - absolute value symbols - and the fraction bar - exponents and roots - multiplication and division - addition and subtraction






43. 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






44. Is an equation involving a transcendental function of one of its variables.






45. 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






46. Is an equation involving derivatives.






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






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






49. The value produced is called






50. 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)