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. Is an equation involving only algebraic expressions in the unknowns. These are further classified by degree.






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






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






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






5. The operation of multiplication means _______________: a






6. The squaring operation only produces






7. If a < b and c < 0






8. 1 - which preserves numbers: a^1 = a






9. 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






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






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






12. Applies abstract algebra to the problems of geometry






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






14. 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.






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






16. 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.






17. Is Written as a + b






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






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






20. 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






21. 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






22. Is an equation involving integrals.






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






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






25. 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'.






26. There are two common types of operations:






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






28. The value produced is called






29. Operations can have fewer or more than






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






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






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






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






34. The values combined are called






35. A binary operation






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






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






38. 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)






39. Not commutative a^b?b^a






40. Is a basic technique used to simplify problems in which the original variables are replaced with new ones; the new and old variables being related in some specified way.






41. Is an equation involving a transcendental function of one of its variables.






42. Division ( / )






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






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






45. 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.






46. Can be defined axiomatically up to an isomorphism






47. 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)






48. The inner product operation on two vectors produces a






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






50. If a < b and c > 0