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






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






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






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






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






6. 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).






7. Logarithm (Log)






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






9. 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)






10. If a < b and b < c






11. 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






12. 1 - which preserves numbers: a^1 = a






13. 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)






14. There are two common types of operations:






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






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






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






18. Not associative






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






20. 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'.






21. Can be added and subtracted.






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






23. 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






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






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






26. The operation of multiplication means _______________: a






27. 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.






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






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






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






31. Is called the codomain of the operation






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






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






34. Division ( / )






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






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






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






38. May not be defined for every possible value.






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






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






41. 0 - which preserves numbers: a + 0 = a






42. 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.






43. Can be defined axiomatically up to an isomorphism






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






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






46. The squaring operation only produces






47. (a






48. 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






49. Are called the domains of the operation






50. () 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.







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