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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. If a < b and b < c






2. 1 - which preserves numbers: a^1 = a






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






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






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






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






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






8. 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)






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






10. If a < b and c < 0






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






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






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






14. The value produced is called






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






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






17. If a < b and c > 0






18. 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






19. Is Written as a






20. Logarithm (Log)






21. Not commutative a^b?b^a






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






23. Is Written as ab or a^b






24. If a = b then b = a






25. 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






26. Can be written in terms of n-th roots: a^m/n = (nva)^m and thus even roots of negative numbers do not exist in the real number system - has the property: a^ba^c = a^b+c - has the property: (a^b)^c = a^bc - In general a^b ? b^a and (a^b)^c ? a^(b^c)






27. 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






28. 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






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






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






31. Is Written as a + b






32. The operation of multiplication means _______________: a






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






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






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






36. k-ary operation is a






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






38. The values combined are called






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






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






41. Not associative






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






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






44. 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






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






46. Is called the type or arity of the operation






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






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






50. A