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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. Decreased by






2. 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.






3. A number is divisible by 3 if






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






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






6. 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.






7. 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.






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






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






10. 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






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






12. 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.






13. 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






14. A curve in the plane






15. LAWS FOR COMBINING NUMBERS






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






18. 2 -3 -4 -5 -6






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






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






21. 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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22. 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.






23. 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






24. Total






25. Subtraction






26. Increased by






27. The set of all complex numbers is denoted by






28. 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 -






29. 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






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






31. Number symbols






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






33. 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.






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






35. A letter tat represents a number that is unknown (usually X or Y)






36. A number is divisible by 8 if






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






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






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






40. 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.






41. 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






42. One term (5x or 4)






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






44. 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.






45. Remainder






46. 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






47. A number is divisible by 2 if






48. 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






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






50. 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.