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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 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






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






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






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






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 squared (multiplied by itself) number subtracted from another squared number. It refers to the identity






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. The inner product operation on two vectors produces a






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






10. Can be defined axiomatically up to an isomorphism






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






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






13. 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).






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






15. Not associative






16. Applies abstract algebra to the problems of geometry






17. Is an equation involving derivatives.






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






19. Is algebraic equation of degree one






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






21. 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






22. If a = b then b = a






23. 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.






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






25. Not commutative a^b?b^a






26. The squaring operation only produces






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






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






29. 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'.






30. 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.

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31. 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)






32. 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.






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






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






36. The process of expressing the unknowns in terms of the knowns is called






37. 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.






38. 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).






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






40. If a < b and c < 0






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






42. May not be defined for every possible value.






43. Division ( / )






44. 1 - which preserves numbers: a






45. Are called the domains of the operation






46. If it holds for all a and b in X that if a is related to b then b is related to a.






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






48. Logarithm (Log)






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






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