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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. 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)






2. There are two common types of operations:






3. Not associative






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






5. The squaring operation only produces






6. Is an equation involving integrals.






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






8. If a < b and c < d






9. b = b






10. Is an equation involving derivatives.






11. 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.

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12. Is an equation of the form aX = b for a > 0 - which has solution






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






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






15. Subtraction ( - )






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






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






18. In which properties common to all algebraic structures are studied






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






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






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






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






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






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






25. 1 - which preserves numbers: a^1 = a






26. The value produced is called






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






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






29. Is algebraic equation of degree one






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






31. 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).






32. Is Written as a + b






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






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






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






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






37. Can be added and subtracted.






38. The operation of multiplication means _______________: a






39. Division ( / )






40. The inner product operation on two vectors produces a






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






42. 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.






43. 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).






44. 1 - which preserves numbers: a






45. A binary operation






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






47. If a < b and c > 0






48. The values combined are called






49. 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






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