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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. Total






2. 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






3. A number is divisible by 4 if






4. The objects in a set have at least






5. Sum






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






7. First axiom of equality






8. 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.






9. 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.






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






11. Number symbols






12. LAWS FOR COMBINING NUMBERS






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






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






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






16. 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






17. 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.)






18. A curve in the plane






19. 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.






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






21. 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.






22. The set of all complex numbers is denoted by






23. 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






24. 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.






25. Sixteen less than number Q






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






27. A number is divisible by 6 if it is






28. 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






29. Work on the problem of general polynomials ultimately led to the fundamental theorem of algebra -






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






31. 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:






32. 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






33. Are used to indicate sets






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






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






36. 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






37. The complex conjugate of the complex number z = x + yi is defined to be x - yi. It is denoted or . Geometrically - is the

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38. 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.






39. Product






40. Number T increased by 9






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






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






43. 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






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






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






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






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






48. A number is divisible by 5 if its






49. 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.






50. 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