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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 process of expressing the unknowns in terms of the knowns is called






2. Is a way of solving a functional equation of two polynomials for a number of unknown parameters. It relies on the fact that two polynomials are identical precisely when all corresponding coefficients are equal. The method is used to bring formulas in






3. Is Written as ab or a^b






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






5. 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.






6. A + b = b + a






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






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






9. If a < b and c > 0






10. Is an algebraic 'sentence' containing an unknown quantity.






11. A binary operation






12. Is an equation involving integrals.






13. The operation of multiplication means _______________: a






14. Applies abstract algebra to the problems of geometry






15. Not associative






16. Is algebraic equation of degree one






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






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






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






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






21. b = b






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






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






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






25. There are two common types of operations:






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






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






28. A






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






30. Operations can have fewer or more than






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






32. Can be added and subtracted.






33. 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






34. 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)






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






36. May contain numbers - variables and arithmetical operations. These are conventionally written with 'higher-power' terms on the left






37. Not commutative a^b?b^a






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






39. 1 - which preserves numbers: a






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






41. Can be defined axiomatically up to an isomorphism






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






43. If a < b and c < 0






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






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






47. 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.






48. 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






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






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