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






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






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






4. often express relationships between given quantities - the knowns - and quantities yet to be determined - the unknowns.






5. () 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.






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






7. Not commutative a^b?b^a






8. 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)






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






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






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






12. 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.






13. The operation of multiplication means _______________: a






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






15. 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).






16. If a < b and c > 0






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






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






19. b = b






20. Is called the type or arity of the operation






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






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






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






24. Symbols that denote numbers - letters from the end of the alphabet - like ...x - y - z - are usually reserved for the






25. Is Written as ab or a^b






26. (a






27. 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






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






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






30. A






31. 1 - which preserves numbers: a






32. 0 - which preserves numbers: a + 0 = a






33. (a + b) + c = a + (b + c)






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






35. Introduces the concept of variables representing numbers. Statements based on these variables are manipulated using the rules of operations that apply to numbers - such as addition. This can be done for a variety of reasons - including equation solvi






36. Is an assignment of values to all the unknowns so that all of the equations are true. also called set simultaneous equations.






37. Is Written as a






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






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






40. Logarithm (Log)






41. 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






42. 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.


43. 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.






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






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






46. Include composition and convolution






47. 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).






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






49. Applies abstract algebra to the problems of geometry






50. An operation of arity k is called a