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






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






3. 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.






4. Total






5. A number is divisible by 8 if






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






7. 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:






8. More than






9. 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






10. Remainder






11. Subtraction






12. A number is divisible by 6 if it is






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






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






15. A number is divisible by 4 if






16. As the horizontal component - and imaginary part as vertical These two values used to identify a given complex number are therefore called its Cartesian - rectangular - or algebraic form.






17. Number T increased by 9






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






19. 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






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






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






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






23. First axiom of equality






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






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






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






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






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






30. 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.






31. A number is divisible by 3 if






32. Increased by






33. 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.






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






35. 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






36. 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.






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






38. 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 -






39. 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.






40. Any number that is exactly divisible by a given number is a






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






42. A number is divisible by 2 if






43. 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.)






44. Plus






45. 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






46. The set of all complex numbers is denoted by






47. 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.






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






49. 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






50. 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