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






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






3. The values combined are called






4. Is called the codomain of the operation






5. Is Written as a + b






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






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






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






9. 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






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






11. Is algebraic equation of degree one






12. May not be defined for every possible value.






13. 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'.






14. Can be added and subtracted.






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






16. 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)






17. 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)






18. Is Written as a






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






20. 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






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






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






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






24. Not commutative a^b?b^a






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






26. There are two common types of operations:






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






28. Letters from the beginning of the alphabet like a - b - c... often denote






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






30. 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)






31. 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.






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






33. 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.






34. 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.






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






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






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






38. Subtraction ( - )






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






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






41. 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






42. 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.






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






44. 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






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






46. Is an equation involving derivatives.






47. Include composition and convolution






48. If a < b and c < d






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






50. 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