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






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






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






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






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






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






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






8. If a < b and c < d






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






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






11. A






12. 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).






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






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






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






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






17. 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.






18. Applies abstract algebra to the problems of geometry






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






20. b = b






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






22. 0 - which preserves numbers: a + 0 = a






23. Not commutative a^b?b^a






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






25. In an equation with a single unknown - a value of that unknown for which the equation is true is called






26. 1 - which preserves numbers: a






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






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






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






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






31. 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






32. k-ary operation is a






33. 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






34. May not be defined for every possible value.






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






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






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






38. 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).






39. Is Written as a + b






40. Are called the domains of the operation






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






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






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






44. 1 - which preserves numbers: a^1 = a






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






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






47. Is called the codomain of the operation






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






49. Is an equation involving derivatives.






50. An operation of arity k is called a







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