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






2. Operations can have fewer or more than






3. 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.






4. Subtraction ( - )






5. May not be defined for every possible value.






6. In which properties common to all algebraic structures are studied






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






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






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






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






11. There are two common types of operations:






12. 1 - which preserves numbers: a^1 = a






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






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






15. k-ary operation is a






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






17. 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)






18. Include composition and convolution






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






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






21. 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






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






23. If a < b and b < c






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






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






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






27. The values combined are called






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






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






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






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






32. 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).






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






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






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






36. 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






37. An operation of arity zero is simply an element of the codomain Y - called a






38. Division ( / )






39. often express relationships between given quantities - the knowns - and quantities yet to be determined - the unknowns.






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






41. Is an equation in which a polynomial is set equal to another polynomial.






42. 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.






43. Is called the type or arity of the operation






44. A






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






46. Applies abstract algebra to the problems of geometry






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. Are called the domains of the operation






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






50. Can be defined axiomatically up to an isomorphism