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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. 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.






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






3. As shown earlier - c - di is the complex conjugate of the denominator c + di.






4. 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






5. First axiom of equality






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






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






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






9. 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 -






10. 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.






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






12. Are not necessary. That is - the elements of {2 - 2 - 3 - 4} are simply {2 - 3 - and 4}






13. A number is divisible by 3 if






14. Number T increased by 9






15. 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






16. Are used to indicate sets






17. 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.






18. The objects in a set have at least






19. 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.






20. A number is divisible by 9 if






21. Plus






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






23. 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.






24. Addition of two complex numbers can be done geometrically by






25. The defining characteristic of a position vector is that it has






26. 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.






27. The number without a variable (5m+2). In this case - 2






28. Number X decreased by 12 divided by forty






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






30. 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






31. 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.






32. Number symbols






33. A number is divisible by 8 if






34. A form of coding in which the value of each digit of a number depends upon its position in relation to the other digits of the number. The convention used in our number system is that each digit has a higher place value than those digits to the right






35. 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:






36. 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






37. 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






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






39. Sum






40. The relative greatness of positive and negative numbers






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






42. A number is divisible by 4 if






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






44. Any number that la a multiple of 2 is an






45. 2 -3 -4 -5 -6






46. Increased by






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






48. 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






49. The Arabic numerals from 0 through 9 are called






50. One term (5x or 4)