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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. Is called the type or arity of the operation






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






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






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






5. 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






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






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






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






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






10. Is an equation involving only algebraic expressions in the unknowns. These are further classified by degree.






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






12. 0 - which preserves numbers: a + 0 = a






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






14. Logarithm (Log)






15. Applies abstract algebra to the problems of geometry






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






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






18. A + b = b + a






19. Is an equation involving integrals.






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






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






22. Is Written as a + b






23. Can be defined axiomatically up to an isomorphism






24. The operation of multiplication means _______________: a






25. Subtraction ( - )






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






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






28. If a < b and c < d






29. 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.






30. () 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.






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






32. An operation of arity k is called a






33. A vector can be multiplied by a scalar to form another vector






34. Include the binary operations union and intersection and the unary operation of complementation.






35. Include composition and convolution






36. Algebra comes from Arabic al-jebr meaning '______________'. Studies the effects of adding and multiplying numbers - variables - and polynomials - along with their factorization and determining their roots. Works directly with numbers. Also covers sym






37. Are called the domains of the operation






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






39. 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)






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






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. 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






43. If a < b and c < 0






44. 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).






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






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






47. Is called the codomain of the operation






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






49. b = b






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