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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 an equation where the unknowns are required to be integers.






2. An operation of arity k is called a






3. 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






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






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






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






7. 1 - which preserves numbers: a






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






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






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






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






12. There are two common types of operations:






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






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






15. 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.






16. 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.


17. 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)






18. 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






19. 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)






20. Is called the type or arity of the operation






21. Can be added and subtracted.






22. Is Written as a






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






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






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






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






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






28. b = b






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






30. A binary operation






31. If a < b and c < 0






32. 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






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






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






35. 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).






36. The inner product operation on two vectors produces a






37. 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.






38. 1 - which preserves numbers: a^1 = a






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






41. k-ary operation is a






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






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






44. Is algebraic equation of degree one






45. 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






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






47. 0 - which preserves numbers: a + 0 = a






48. () 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.






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






50. Referring to the finite number of arguments (the value k)