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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. 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






2. Not commutative a^b?b^a






3. A






4. Is an assignment of values to all the unknowns so that all of the equations are true. also called set simultaneous equations.






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






6. () 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.






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






8. There are two common types of operations:






9. An operation of arity k is called a






10. 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)






11. The value produced is called






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






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






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






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






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






17. 0 - which preserves numbers: a + 0 = a






18. The values combined are called






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






20. 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.






21. 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).






22. If a < b and c < 0






23. Can be defined axiomatically up to an isomorphism






24. Are called the domains of the operation






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






26. 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.






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






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






29. A unary operation






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






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






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






33. Is an equation involving integrals.






34. The inner product operation on two vectors produces a






35. 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






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






38. Include composition and convolution






39. 1 - which preserves numbers: a






40. 1 - which preserves numbers: a^1 = a






41. Not associative






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






43. The set which contains the values produced is called the codomain - but the set of actual values attained by the operation is its






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






45. Can be added and subtracted.






46. May not be defined for every possible value.






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






48. Subtraction ( - )






49. The squaring operation only produces






50. Is an equation in which the unknowns are functions rather than simple quantities.