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






2. A






3. Applies abstract algebra to the problems of geometry






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






5. 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.






6. k-ary operation is a






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






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






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






10. 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.






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






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






13. Subtraction ( - )






14. The inner product operation on two vectors produces a






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






16. 1 - which preserves numbers: a^1 = a






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






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






19. Is called the type or arity of the operation






20. Is Written as a + b






21. 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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22. 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






23. If a < b and c > 0






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






25. Can be defined axiomatically up to an isomorphism






26. Are called the domains of the operation






27. 0 - which preserves numbers: a + 0 = a






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






29. Is an equation involving integrals.






30. Division ( / )






31. Are denoted by letters at the beginning - a - b - c - d - ...






32. The values combined are called






33. 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).






34. The squaring operation only produces






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






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






37. 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)






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






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






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






41. Not commutative a^b?b^a






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






43. 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)






44. Logarithm (Log)






45. () 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.






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






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






48. If a = b then b = a






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






50. There are two common types of operations: