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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. Is called the type or arity of the operation






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






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






4. If a < b and c < d






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






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






7. The values combined are called






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






9. 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.


10. 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'.






11. There are two common types of operations:






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






13. 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






14. 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






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






16. 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.






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






18. Can be combined using the function composition operation - performing the first rotation and then the second.






19. An operation of arity k is called a






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






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






22. 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






23. A + b = b + a






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






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






26. Are called the domains of the operation






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






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






29. Can be defined axiomatically up to an isomorphism






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






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






32. Elementary algebraic techniques are used to rewrite a given equation in the above way before arriving at the solution. then - by subtracting 1 from both sides of the equation - and then dividing both sides by 3 we obtain






33. (a






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






35. 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)






36. 0 - which preserves numbers: a + 0 = a






37. May not be defined for every possible value.






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






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






40. 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)






41. 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.






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






43. 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






44. If a < b and c < 0






45. Can be combined using logic operations - such as and - or - and not.






46. The value produced is called






47. 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






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






49. A binary operation






50. 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).