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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.
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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. This law states that the product of three or more factors is the same regardless of the manner in which they are grouped. Negative signs require no special treatment in the application of this law.






2. Total






3. Number X decreased by 12 divided by forty






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






5. Viewed in this way the multiplication of a complex number by i corresponds to rotating a complex number






6. Number symbols






7. The relative greatness of positive and negative numbers






8. 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.






9. In the Rectangular Coordinate System - the direction to the right along the horizontal line is






10. A letter tat represents a number that is unknown (usually X or Y)






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






12. LAWS FOR COMBINING NUMBERS






13. One term (5x or 4)






14. 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






15. 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:






16. 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






17. Decreased by






18. 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.






19. More than one term (5x+4 contains two)






20. The finiteness or not of the number of rational or integer points on an algebraic curve






21. Sixteen less than number Q






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






23. This law can be applied to subtraction by changing signs in such a way that all negative signs are treated as number signs rather than operational signs.That is - some of the addends can be negative numbers.






24. 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






25. G - E - M - A Grouping - Exponents - Multiply/Divide - Add/Subtract






26. A curve in the plane






27. A number that has factors other than itself and 1 is a






28. More than






29. This formula can be used to compute the multiplicative inverse of a complex number if it is given in






30. Any number that can be divided lnto a given number without a remainder is a






31. 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






32. The objects or symbols in a set are called Numerals - Lines - or Points






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






34. The smallest of four sonsecutive whole numbers - the biggest of which is K+6






35. A number is divisible by 2 if






36. A number is divisible by 4 if






37. Is called the real part of z - and the real number b is often called the imaginary part. By this convention the imaginary part is a real number - not including the imaginary unit: hence b - not bi - is the imaginary part. (Others - however call bi th






38. Product






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






40. This law combines the operations of addition and multiplication. The distribution of a common multiplier among the terms of an additive expression.






41. A number that has no factors except itself and 1 is a






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






43. A number is divisible by 9 if






44. This law can be applied to subtraction by changing signs so that all negative signs become number signs and all signs of operation are positive.






45. Studies algebraic properties and algebraic objects of interest in number theory. (Thus - analytic and algebraic number theory can and do overlap: the former is defined by its methods - the latter by its objects of study.) A key topic is that of the a






46. The base which is most commonly used is ten - and the system with ten as a base is called the decimal system (decem is the Latin word for ten). Any number is assumed - unless indicated - to be a






47. A number is divisible by 6 if it is






48. 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






49. 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.






50. 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.)