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






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






3. No short method has been found for determining whether a number is divisible by






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






5. A number is divisible by 3 if






6. 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






7. The objects in a set have at least






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






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






11. 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:






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






13. A curve in the plane






14. 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.






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






16. Sixteen less than number Q






17. 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






18. Increased by






19. 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






20. 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.






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






22. Less than






23. Sum






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






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






26. A number is divisible by 8 if






27. A number is divisible by 9 if






28. 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.






29. Subtraction






30. 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






31. Plus






32. Number X decreased by 12 divided by forty






33. In the Rectangular Coordinate System - On the vertical line - direction ________ is positive






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






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






36. First axiom of equality






37. 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






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






39. 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.






40. 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.






41. 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






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






43. Number symbols






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






45. One term (5x or 4)






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






47. 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.






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






49. 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






50. 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.







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