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






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






3. Can be added and subtracted.






4. 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).






5. A






6. Are called the domains of the operation






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






8. 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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9. Is an equation involving integrals.






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






12. Some equations are true for all values of the involved variables (such as a + b = b + a); such equations are called






13. A unary operation






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






15. A + b = b + a






16. 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






17. 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.






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






19. Division ( / )






20. Sometimes also called modern algebra - in which algebraic structures such as groups - rings and fields are axiomatically defined and investigated.






21. 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






22. The squaring operation only produces






23. (a






24. Is called the codomain of the operation






25. The inner product operation on two vectors produces a






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






27. Is an action or procedure which produces a new value from one or more input values.






28. Take two values - and include addition - subtraction - multiplication - division - and exponentiation.






29. Applies abstract algebra to the problems of geometry






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






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






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






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






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






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






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






37. 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)






38. If a < b and c > 0






39. Not commutative a^b?b^a






40. 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)






41. May not be defined for every possible value.






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






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






44. If a < b and c < d






45. 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.






46. Logarithm (Log)






47. There are two common types of operations:






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






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






50. Is the claim that two expressions have the same value and are equal.