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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 of the variables which make the equation true are the solutions of the equation and can be found through






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






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






4. If a = b then b = a






5. An operation of arity k is called a






6. Is called the codomain of the operation






7. The inner product operation on two vectors produces a






8. Is called the type or arity of the operation






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






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






11. Is Written as a






12. A






13. May not be defined for every possible value.






14. Subtraction ( - )






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






16. 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






17. 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






18. 0 - which preserves numbers: a + 0 = a






19. (a






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






21. () 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.






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






23. 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'.






24. A unary operation






25. A + b = b + a






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






27. If a < b and c > 0






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






29. Not commutative a^b?b^a






30. The squaring operation only produces






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






32. Operations can have fewer or more than






33. Logarithm (Log)






34. Involve only one value - such as negation and trigonometric functions.






35. 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.






36. 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.






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






38. There are two common types of operations:






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. If a < b and c < 0






41. 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.






42. Include composition and convolution






43. The operation of exponentiation means ________________: a^n = a






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






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






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






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






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






49. 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)






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