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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. 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






2. 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






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






4. Means repeated addition of ones: a + n = a + 1 + 1 +...+ 1 (n number of times) - has an inverse operation called subtraction: (a + b) - b = a - which is the same as adding a negative number - a - b = a + (-b)






5. The squaring operation only produces






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






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






8. Is Written as a + b






9. 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'.






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






11. 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).






12. The inner product operation on two vectors produces a






13. 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.






14. Real numbers can be thought of as points on an infinitely long line where the points corresponding to integers are equally spaced called the






15. Not associative






16. 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)






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






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






19. There are two common types of operations:






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






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






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






23. 0 - which preserves numbers: a + 0 = a






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






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






26. Subtraction ( - )






27. An operation of arity zero is simply an element of the codomain Y - called a






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






29. Logarithm (Log)






30. 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






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






32. Operations can have fewer or more than






33. Is called the type or arity of the operation






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






35. Is Written as ab or a^b






36. Are called the domains of the operation






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






38. Is an equation involving derivatives.






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






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






41. An operation of arity k is called a






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






43. 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






44. Can be defined axiomatically up to an isomorphism






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






46. 1 - which preserves numbers: a






47. 1 - which preserves numbers: a^1 = a






48. 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.






49. If a = b then b = a






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