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CLEP General Mathematics: Number Systems And Sets

Subjects : clep, math
Instructions:
  • Answer 50 questions in 15 minutes.
  • If you are not ready to take this test, you can study here.
  • Match each statement with the correct term.
  • Don't refresh. All questions and answers are randomly picked and ordered every time you load a test.

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. 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.






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






3. 2 -3 -4 -5 -6






4. Product






5. 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






6. 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.)






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






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






9. The Arabic numerals from 0 through 9 are called






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






11. A number is divisible by 3 if






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






13. 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.






14. 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:






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






16. 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






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






18. 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






19. 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






20. 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






21. One term (5x or 4)






22. More than






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






24. Sum






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






26. 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






27. 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






28. 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.






29. 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.






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






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






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






33. The greatest of 3 consecutive whole numbers - the smallest of which is F






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






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






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






37. First axiom of equality






38. Quotient






39. 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.






40. The set of all complex numbers is denoted by






41. A number is divisible by 9 if






42. Remainder






43. Sixteen less than number Q






44. Are used to indicate sets






45. Increased by






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






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






48. 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






49. 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






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