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CLEP General Mathematics: Number Systems And Sets

Subjects : clep, math
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. In the Rectangular Coordinate System - the direction to the right along the horizontal line is






2. Sixteen less than number Q






3. Product of 16 and the sum of 5 and number R






4. No short method has been found for determining whether a number is divisible by






5. The Arabic numerals from 0 through 9 are called






6. Allow the variables in f(x -y) = 0 to be complex numbers; then f(x -y) = 0 defines a 2-dimensional surface in (projective) 4-dimensional space (since two complex variables can be decomposed into four real variables - i.e. - four dimensions). Count th






7. The place value which corresponds to a given position in a number is determined by the






8. This law states that the sum of two or more addends is the same regardless of the order in which they are arranged. Means to change - substitute or move from place to place.






9. The real and imaginary parts of a complex number can be extracted using the conjugate:






10. Implies a collection or grouping of similar - objects or symbols.






11. The central problem of Diophantine geometry is to determine when a Diophantine equation has






12. The number touching the variable (in the case of 5x - would be 5)






13. Since the elements of the set {2 - 4 - e} are the same as the elements of{4 - 2 - e} - these two sets are said to be






14. Subtraction






15. Consists of all numbers of the form - where a and b are rational numbers and d is a fixed rational number whose square root is not rational.






16. In particular - the square of the imaginary unit is -1: The preceding definition of multiplication of general complex numbers follows naturally from this fundamental property of the imaginary unit. Indeed - if i is treated as a number so that di mean






17. If a factor of a number is prime - it is called a






18. Any number that is not a multiple of 2 is an






19. A number is divisible by 3 if






20. This law states that the product of two or more factors is the same regardless of the order in which the factors are arranged. Negative signs require no special treatment in the application of this law.






21. If the same quantity is subtracted from each of two equal quantities - the resulting quantities are equal. If equals are subtracted from equals - the results are equal.






22. Total






23. If z is a real number (i.e. - y = 0) - then r = |x|. In general - by Pythagoras' theorem - r is the distance of the point P representing the complex number z to the origin.






24. Are often studied as extensions of smaller number fields: a field L is said to be an extension of a field K if L contains K. (For example - the complex numbers C are an extension of the reals R - and the reals R are an extension of the rationals Q.)






25. These are emphasised in a complex number's polar form and it turns out notably that the operations of addition and multiplication take on a very natural geometric character when complex numbers are viewed as position vectors:






26. A number is divisible by 2 if






27. Number T increased by 9






28. Integers greater than zero and less than 5 form a set - as follows:






29. The sum of two complex numbers A and B - interpreted as points of the complex plane - is the point X obtained by building a parallelogram three of whose vertices are O - A and B. Equivalently - X is the point such that the triangles with vertices O -






30. The greatest of 3 consecutive whole numbers - the smallest of which is F






31. Is a number that can be expressed in the form where a and b are real numbers and i is the imaginary unit - satisfying i2 = -1. For example - -3.5 + 2i is a complex number. It is common to write a for a + 0i and bi for 0 + bi. Moreover - when the imag






32. One asks whether there are any rational points (points all of whose coordinates are rationals) or integral points (points all of whose coordinates are integers) on the curve or surface. If there are any such points - the next step is to ask how many






33. If two equal quantities are divided by the same quantity - the resulting quotients are equal. If equals are divided by equals - the results are equal.






34. Begin by taking out the smallest factor If the number is even - take out all the 2's first - then try 3 as a factor






35. Remainder






36. If two equal quantities are multiplied by the same quantity - the resulting products are equal. If equals are multiplied by equals - the products are equal.






37. One term (5x or 4)






38. In the Rectangular Coordinate System - On the vertical line - direction ________ is positive






39. Quotient






40. This law states that the sum of three or more addends is the same regardless of the manner in which they are grouped. suggests association or grouping.






41. In terms of its tools - as the study of the integers by means of tools from real and complex analysis - in terms of its concerns - as the study within number theory of estimates on size and density - as opposed to identities.






42. Sum






43. The numbers which are used for counting in our number system are sometimes called






44. Number X decreased by 12 divided by forty






45. The square roots of a + bi (with b ? 0) are - where and where sgn is the signum function. This can be seen by squaring to obtain a + bi.






46. Is any complex number that is a solution to some polynomial equation with rational coefficients; for example - every solution x of (say) is an algebraic number. Fields of algebraic numbers are also called algebraic number fields - or shortly number f






47. LAWS FOR COMBINING NUMBERS






48. A branch of geometry studying more general reflections than ones about a line - can also be expressed in terms of complex numbers.






49. Allow for solutions to certain equations that have no real solution: the equation has no real solution - since the square of a real number is 0 or positive.






50. One asks whether there are any rational points (points all of whose coordinates are rationals) or integral points (points all of whose coordinates are integers) on the curve or surface. If there are any such points - the next step is to ask how many