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






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






4. First axiom of equality






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






6. The relative greatness of positive and negative numbers






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. 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






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






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






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






12. 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.






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






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






15. The Arabic numerals from 0 through 9 are called






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






17. Total






18. Sum






19. Number symbols






20. 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.






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






22. In the Rectangular Coordinate System - the direction to the left along the horizontal line is






23. A number is divisible by 2 if






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






25. 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






26. 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.






27. A number is divisible by 5 if its






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






29. 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.






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






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. Increased by






33. 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






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






35. 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






36. Another way of encoding points in the complex plane other than using the x- and y-coordinates is to use the distance of a point P to O - the point whose coordinates are (0 - 0) (the origin) - and the angle of the line through P and O. This idea leads






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






38. 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.






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






40. Are used to indicate sets






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






42. 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.






43. LAWS FOR COMBINING NUMBERS






44. 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






45. 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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46. 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






47. 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.






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






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






50. Decreased by