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CLEP General Mathematics: Number Systems And Sets

Subjects : clep, math
Instructions:
  • 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. 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






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






3. In the Rectangular Coordinate System - On the vertical line - direction _______ is negative






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






5. Has an equal sign (3x+5 = 14)






6. 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






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






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






9. The Arabic numerals from 0 through 9 are called






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






11. Does not have an equal sign (3x+5) (2a+9b)






12. 2 -3 -4 -5 -6






13. 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.






14. Number symbols






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. A curve in the plane






17. The set of all complex numbers is denoted by






18. Quotient






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






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






21. 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.






22. 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.






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






24. A number is divisible by 2 if






25. The objects in a set have at least






26. 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






27. 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






28. 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






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






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






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






32. 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






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






34. 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.






35. 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






36. 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.






37. An equation - or system of equations - in two or more variables defines






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






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






40. First axiom of equality






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






42. 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.






43. Total






44. 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






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






46. Plus






47. Decreased by






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






49. The number of digits in an integer indicates its rank; that is - whether it is 'in the hundreds -' 'in the thousands -' etc. The idea of ranking numbers in terms of tens - hundreds - thousands - etc. - is based on the






50. The relative greatness of positive and negative numbers