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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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1. 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.
7
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
order of operations
coefficient

2. 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
Positional notation (place value)
Commutative Law of Addition
the number formed by the two right-hand digits is divisible by 4
C or

3. As shown earlier - c - di is the complex conjugate of the denominator c + di.
division
addition corresponds to vector addition while multiplication corresponds to multiplying their magnitudes and adding their arguments (i.e. the angles they make with the x axis).
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
Downward

4. In the Rectangular Coordinate System - On the vertical line - direction ________ is positive
magnitude and direction
The numbers are conventionally plotted using the real part
The real number a of the complex number z = a + bi
upward

5. The finiteness or not of the number of rational or integer points on an algebraic curve
the genus of the curve
Composite Number
To separate a number into prime factors
The absolute value (or modulus or magnitude) of a complex number z = x + yi is

6. A number is divisible by 4 if
subtraction
the number formed by the two right-hand digits is divisible by 4
equation
monomial

7. The numbers which are used for counting in our number system are sometimes called
Place Value Concept
Natural Numbers
even and the sum of its digits is divisible by 3
If the same quantity is added to each of two equal quantities - the resulting quantities are equal. If equals are added to equals - the results are equal.

8. 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.
Algebraic number theory
Third Axiom of Equality
Associative Law of Addition
The multiplication of two complex numbers is defined by the following formula:

9. 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
To separate a number into prime factors
consecutive whole numbers
T+9
In Diophantine geometry

10. Has an equal sign (3x+5 = 14)
magnitude and direction
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
F - F+1 - F+2.......answer is F+2
equation

11. Product of 16 and the sum of 5 and number R
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
16(5+R)
Multiple of the given number
a curve - a surface or some other such object in n-dimensional space

12. 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
complex number
consecutive whole numbers
In Diophantine geometry
one characteristic in common such as similarity of appearance or purpose

13. Sum
addition
Commutative Law of Addition
a curve - a surface or some other such object in n-dimensional space
counterclockwise through 90

14. 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
expression
subtraction
complex number
Factor of the given number

15. A number is divisible by 2 if
right-hand digit is even
Set
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
its the sum of its digits is divisible by 3

16. 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
counterclockwise through 90
righthand digit is 0 or 5
Place Value Concept
7

17. LAWS FOR COMBINING NUMBERS
order of operations
The multiplication of two complex numbers is defined by the following formula:
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.

18. A number that has factors other than itself and 1 is a
The numbers are conventionally plotted using the real part
Third Axiom of Equality
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
Composite Number

19. 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
The real number a of the complex number z = a + bi
Equal
Place Value Concept
Numerals

20. 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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21. Product
magnitude
multiplication
its the sum of its digits is divisible by 3
Associative Law of Multiplication

22. This formula can be used to compute the multiplicative inverse of a complex number if it is given in
Q-16
addition
expression
rectangular coordinates

23. In the Rectangular Coordinate System - the direction to the right along the horizontal line is
positive
subtraction
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
algebraic number

24. The Arabic numerals from 0 through 9 are called
Commutative Law of Addition
Downward
Third Axiom of Equality
Digits

25. More than one term (5x+4 contains two)
Associative Law of Addition
Place Value Concept
polynomial
Number fields

26. Increased by
Members of Elements of the Set
addition
constructing a parallelogram
If the same quantity is added to each of two equal quantities - the resulting quantities are equal. If equals are added to equals - the results are equal.

27. The objects or symbols in a set are called Numerals - Lines - or Points
Absolute value and argument
righthand digit is 0 or 5
Set
Members of Elements of the Set

28. First axiom of equality
even and the sum of its digits is divisible by 3
repeated elements
difference
If the same quantity is added to each of two equal quantities - the resulting quantities are equal. If equals are added to equals - the results are equal.

29. 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.
Commutative Law of Addition
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
polynomial
Forth Axiom of Equality

30. 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.
difference
positive
Associative Law of Multiplication
The numbers are conventionally plotted using the real part

31. Less than
Commutative Law of Addition
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
consecutive whole numbers
subtraction

32. Consists of all numbers of the form - where a and b are rational numbers and d is a fixed rational number whose square root is not rational.
Third Axiom of Equality
To separate a number into prime factors
quadratic field
addition

33. The defining characteristic of a position vector is that it has
(x-12)/40
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
magnitude and direction
Second Axiom of Equality

34. 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.
subtraction
Forth Axiom of Equality
Definition of genus
the genus of the curve

35. A letter tat represents a number that is unknown (usually X or Y)
even and the sum of its digits is divisible by 3
Prime Factor
variable
addition corresponds to vector addition while multiplication corresponds to multiplying their magnitudes and adding their arguments (i.e. the angles they make with the x axis).

36. Quotient
expression
counterclockwise through 90
division
Number fields

37. 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
Definition of genus
Multiple of the given number
Inversive geometry
algebraic number

38. A curve in the plane
addition
Downward
an equation in two variables defines
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.

39. Any number that is exactly divisible by a given number is a
The numbers are conventionally plotted using the real part
magnitude and direction
F - F+1 - F+2.......answer is F+2
Multiple of the given number

40. 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.
Analytic number theory
addition
Complex numbers
Members of Elements of the Set

41. 2 -3 -4 -5 -6
Place Value Concept
Numerals
Complex numbers
consecutive whole numbers

42. Viewed in this way the multiplication of a complex number by i corresponds to rotating a complex number
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
polynomial
counterclockwise through 90
the sum of its digits is divisible by 9

43. 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
addition
Associative Law of Addition
The multiplication of two complex numbers is defined by the following formula:
addition corresponds to vector addition while multiplication corresponds to multiplying their magnitudes and adding their arguments (i.e. the angles they make with the x axis).

44. 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
addition corresponds to vector addition while multiplication corresponds to multiplying their magnitudes and adding their arguments (i.e. the angles they make with the x axis).
The real number a of the complex number z = a + bi
Even Number
constant

45. Any number that can be divided lnto a given number without a remainder is a
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
addition
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
Factor of the given number

46. Any number that la a multiple of 2 is an
Analytic number theory
coefficient
Even Number
The real number a of the complex number z = a + bi

47. A branch of geometry studying more general reflections than ones about a line - can also be expressed in terms of complex numbers.
constant
The real number a of the complex number z = a + bi
subtraction
Inversive geometry

48. Total
a curve - a surface or some other such object in n-dimensional space
the number formed by the three right-hand digits is divisible by 8
addition
Digits

49. Are used to indicate sets
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
addition
Braces
The multiplication of two complex numbers is defined by the following formula:

50. Addition of two complex numbers can be done geometrically by
even and the sum of its digits is divisible by 3
constructing a parallelogram
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
addition