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






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






3. 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






4. The operation of multiplication means _______________: a






5. Reflexive: b = b; symmetric: if a = b then b = a; transitive: if a = b and b = c then a = c.






6. 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'.






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






8. Implies that the domain of the function is a power of the codomain (i.e. the Cartesian product of one or more copies of the codomain)






9. Is a way of solving a functional equation of two polynomials for a number of unknown parameters. It relies on the fact that two polynomials are identical precisely when all corresponding coefficients are equal. The method is used to bring formulas in






10. Include composition and convolution






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






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






13. 0 - which preserves numbers: a + 0 = a






14. Are called the domains of the operation






15. An operation of arity k is called a






16. A unary operation






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






18. 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.






19. Is Written as ab or a^b






20. 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






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






22. Applies abstract algebra to the problems of geometry






23. If a < b and b < c






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






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






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






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






28. Is algebraic equation of degree one






29. Not commutative a^b?b^a






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






31. 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.






32. The inner product operation on two vectors produces a






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






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






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






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






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






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






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






40. There are two common types of operations:






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






42. Subtraction ( - )






43. 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






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






45. A binary operation






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






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. Is an equation involving integrals.






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






50. Operations can have fewer or more than