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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. Less than






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






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






5. A number is divisible by 4 if






6. 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






7. Number T increased by 9






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






9. More than






10. A number is divisible by 3 if






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






12. 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.






13. 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






14. A number is divisible by 2 if






15. 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 -






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






17. The objects in a set have at least






18. Increased by






19. Subtraction






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






21. 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






22. Number symbols






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






24. 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






25. A number is divisible by 9 if






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






27. 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






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






29. 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.






30. 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.)






31. The set of all complex numbers is denoted by






32. LAWS FOR COMBINING NUMBERS






33. 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.






34. 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.






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






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






38. First axiom of equality






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






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






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






42. 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:






43. A number is divisible by 6 if it is






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






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






46. One term (5x or 4)






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






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






49. Number X decreased by 12 divided by forty






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