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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. A unary operation






2. Is called the codomain of the operation






3. The value produced is called






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






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






6. 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.






7. (a






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






9. 0 - which preserves numbers: a + 0 = a






10. 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






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






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






13. 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






14. Are called the domains of the operation






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






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






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






18. A binary operation






19. Applies abstract algebra to the problems of geometry






20. A distinction is made between the equality sign ( = ) for an equation and the equivalence symbol () for an






21. Is an equation where the unknowns are required to be integers.






22. If a < b and c < 0






23. If a < b and c > 0






24. Not commutative a^b?b^a






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






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






27. The squaring operation only produces






28. 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).






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






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






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






32. An operation of arity k is called a






33. The inner product operation on two vectors produces a






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






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






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






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






38. A + b = b + a






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






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






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






42. The values combined are called






43. 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.






44. Is a binary relation on a set for which every element is related to itself - i.e. - a relation ~ on S where x~x holds true for every x in S. For example - ~ could be 'is equal to'.






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






46. Is Written as a + b






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






48. Are linear equations that have only one variable. They contain only constant numbers and a single variable without an exponent. For example:






49. If a = b then b = a






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