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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. () 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.






2. Not associative






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






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






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






6. 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'.






7. Is Written as a + b






8. Is a function of the form ? : V ? Y - where V ? X1






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






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






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






12. A unary operation






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






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






15. 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)






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






17. A






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






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






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






21. 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)






22. Division ( / )






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






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






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






26. If a < b and c > 0






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






28. 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.






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






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






31. A distinction is made between the equality sign ( = ) for an equation and the equivalence symbol () for an






32. Is synonymous with function - map and mapping - that is - a relation - for which each element of the domain (input set) is associated with exactly one element of the codomain (set of possible outputs).






33. The squaring operation only produces






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






35. 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.






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






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






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






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






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






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






42. The inner product operation on two vectors produces a






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






44. Is an equation involving integrals.






45. 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






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






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






48. 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






49. 1 - which preserves numbers: a^1 = a






50. May not be defined for every possible value.







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