Test your basic knowledge |

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






2. The value produced is called






3. Is an equation involving integrals.






4. 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






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






6. 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






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






8. 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)






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






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






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






12. Can be added and subtracted.






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






14. The values combined are called






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






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






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






18. 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).






19. A vector can be multiplied by a scalar to form another vector






20. If a < b and c < 0






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






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






24. Division ( / )






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






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






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






28. A + b = b + a






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






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






31. k-ary operation is a






32. Is called the codomain of the operation






33. 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






34. May not be defined for every possible value.






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






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






37. An operation of arity k is called a






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






39. Not commutative a^b?b^a






40. 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.






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






42. Not associative






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






44. 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)






45. Is Written as ab or a^b






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






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






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






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






50. b = b