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CLEP College Algebra: Algebra Principles

Subjects : clep, math, algebra
  • Answer 50 questions in 15 minutes.
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  • Match each statement with the correct term.
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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. If a = b and b = c then a = c

2. 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

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

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

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

6. The values combined are called

7. Applies abstract algebra to the problems of geometry

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

9. 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.

10. 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.

11. 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)

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

13. There are two common types of operations:

14. () is the branch of mathematics concerning the study of the rules of operations and relations - and the constructions and concepts arising from them - including terms - polynomials - equations and algebraic structures.

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

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

17. If a < b and c < d

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

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

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

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

22. The value produced is called

23. A + b = b + a

24. 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.

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

26. 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

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

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

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

30. Is an equation involving derivatives.

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

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

33. 1 - which preserves numbers: a

34. 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.

35. 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

36. 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.

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

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

39. Logarithm (Log)

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

41. If a = b then b = a

42. May not be defined for every possible value.

43. 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

44. A binary operation

45. Is an equation involving integrals.

46. The inner product operation on two vectors produces a

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

48. A

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

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