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






2. Can be added and subtracted.






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






4. 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.






5. 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)






6. If a < b and c < 0






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






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. 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.






10. Is an equation involving integrals.






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






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






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






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






16. 1 - which preserves numbers: a






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






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






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






20. 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'.






21. Is algebraic equation of degree one






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






23. Not associative






24. A binary operation






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






26. The squaring operation only produces






27. Include composition and convolution






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






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






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






31. Applies abstract algebra to the problems of geometry






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






33. 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.






34. A






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






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






37. The value produced is called






38. Is Written as a + b






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






40. 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).






41. Is called the codomain of the operation






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






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






44. 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






45. b = b






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






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






48. 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).






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






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