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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. If a < b and b < c






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






3. 0 - which preserves numbers: a + 0 = a






4. Applies abstract algebra to the problems of geometry






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






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






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






8. That 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.






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






10. Is called the codomain of the operation






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






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






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. 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)






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






16. Can be added and subtracted.






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






18. 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).






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






20. Is Written as ab or a^b






21. 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.

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






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






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






25. Division ( / )






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






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






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






29. k-ary operation is a






30. Is Written as a






31. If a = b then b = a






32. The value produced is called






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






34. A binary operation






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






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






37. () 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.






38. Not commutative a^b?b^a






39. An operation of arity k is called a






40. Is an equation of the form log`a^X = b for a > 0 - which has solution






41. 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)






42. 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)






43. A + b = b + a






44. There are two common types of operations:






45. 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.






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






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






48. 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






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






50. b = b