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. In which properties common to all algebraic structures are studied






2. A unary operation






3. Operations can have fewer or more than






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






5. May contain numbers - variables and arithmetical operations. These are conventionally written with 'higher-power' terms on the left






6. A






7. Is a squared (multiplied by itself) number subtracted from another squared number. It refers to the identity






8. If a < b and c < 0






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






10. Applies abstract algebra to the problems of geometry






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






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






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






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






15. There are two common types of operations:






16. An equivalent for y can be deduced by using one of the two equations. Using the second equation: Subtracting 2x from each side of the equation: and multiplying by -1: Using this y value in the first equation in the original system: Adding 2 on each s






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






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






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






21. If a < b and b < c






22. Is a binary relation on a set for which every element is related to itself - i.e. - a relation ~ on S where x~x holds true for every x in S. For example - ~ could be 'is equal to'.






23. 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






24. An operation of arity k is called a






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






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






27. A binary operation






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






29. 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.






30. 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)






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






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






33. Division ( / )






34. 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.






35. 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.


36. May not be defined for every possible value.






37. 1 - which preserves numbers: a^1 = a






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






39. Is Written as ab or a^b






40. 1 - which preserves numbers: a






41. The value produced is called






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






43. Include the binary operations union and intersection and the unary operation of complementation.






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






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






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






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






48. Not associative






49. 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






50. The inner product operation on two vectors produces a