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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. 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)






2. 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






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






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






5. Not associative






6. Can be defined axiomatically up to an isomorphism






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






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






9. Is an action or procedure which produces a new value from one or more input values.






10. Is algebraic equation of degree one






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






12. Is Written as a






13. 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.






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






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






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






17. Is an equation of the form X^m/n = a - for m - n integers - which has solution






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






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






20. Applies abstract algebra to the problems of geometry






21. The operation of multiplication means _______________: a






22. Is an equation involving integrals.






23. Include composition and convolution






24. Can be added and subtracted.






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






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






27. 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.






28. 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).






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






30. If a = b then b = a






31. A






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






33. If a < b and b < c






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






35. Logarithm (Log)






36. The inner product operation on two vectors produces a






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






38. A unary operation






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






40. Are called the domains of the operation






41. 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






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






43. 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).






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






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






46. 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






47. There are two common types of operations:






48. 1 - which preserves numbers: a^1 = a






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






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