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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. Transivity: if a < b and b < c then a < c; that if a < b and c < d then a + c < b + d; that if a < b and c > 0 then ac < bc; that if a < b and c < 0 then bc < ac.






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






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






4. There are two common types of operations:






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






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






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






8. 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






9. 0 - which preserves numbers: a + 0 = a






10. Is algebraic equation of degree one






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






12. b = b






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






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






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






16. The values combined are called






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






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






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






20. The squaring operation only produces






21. Is called the codomain of the operation






22. If it holds for all a and b in X that if a is related to b then b is related to a.






23. Is an equation involving derivatives.






24. Is a function of the form ? : V ? Y - where V ? X1






25. Can be added and subtracted.






26. 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).






27. 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.






28. Operations can have fewer or more than






29. 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






30. 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.






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






32. Division ( / )






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






34. Is Written as a






35. The value produced is called






36. If a < b and b < c






37. Applies abstract algebra to the problems of geometry






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






39. Are called the domains of the operation






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






41. The operation of multiplication means _______________: a






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






43. 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).






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






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






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






47. 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.






48. May not be defined for every possible value.






49. Include composition and convolution






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