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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. 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.






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






3. First axiom of equality






4. A curve in the plane






5. 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.






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






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






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






9. Increased by






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






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






12. A number is divisible by 9 if






13. 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 -






14. 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.






15. Quotient






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






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






18. 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






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






20. 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:






21. 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






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






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






24. Has an equal sign (3x+5 = 14)






25. Sum






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






27. 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






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






29. 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






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






31. 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.






32. Sixteen less than number Q






33. A number is divisible by 4 if






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






36. A number is divisible by 5 if its






37. LAWS FOR COMBINING NUMBERS






38. 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






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






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






42. 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.






43. 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.






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






45. 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






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






47. A number is divisible by 3 if






48. 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






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






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