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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 values combined are called






2. 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.






3. 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.






4. Is called the type or arity of the operation






5. Is Written as a






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






7. If a < b and c < d






8. 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.






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






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






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






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






13. (a






14. The value produced is called






15. There are two common types of operations:






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






17. 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






18. An operation of arity k is called a






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






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






21. Logarithm (Log)






22. Are called the domains of the operation






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






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






25. 1 - which preserves numbers: a






26. 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






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






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






29. 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'.






30. The inner product operation on two vectors produces a






31. 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.






32. If a = b and b = c then a = c






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






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






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






36. 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)






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






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






39. 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






40. 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).






41. 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.


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






43. Applies abstract algebra to the problems of geometry






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






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






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






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






48. Is algebraic equation of degree one






49. Is Written as ab or a^b






50. Subtraction ( - )