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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 shown earlier - c - di is the complex conjugate of the denominator c + di.
even and the sum of its digits is divisible by 3
Members of Elements of the Set
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
addition

2. A letter tat represents a number that is unknown (usually X or Y)
addition
rectangular coordinates
variable
the number formed by the three right-hand digits is divisible by 8

3. Has an equal sign (3x+5 = 14)
order of operations
rectangular coordinates
equation
algebraic number

4. Decreased by
Associative Law of Addition
subtraction
Second Axiom of Equality
righthand digit is 0 or 5

5. 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
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.
an equation in two variables defines
righthand digit is 0 or 5
Absolute value and argument

6. 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.
positive
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.
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.

7. A number is divisible by 8 if
Absolute value and argument
Forth Axiom of Equality
Number fields
the number formed by the three right-hand digits is divisible by 8

8. Increased by
Q-16
addition
Analytic number theory
Associative Law of Multiplication

9. Studies algebraic properties and algebraic objects of interest in number theory. (Thus - analytic and algebraic number theory can and do overlap: the former is defined by its methods - the latter by its objects of study.) A key topic is that of the a
Q-16
The multiplication of two complex numbers is defined by the following formula:
a curve - a surface or some other such object in n-dimensional space
Algebraic number theory

10. More than one term (5x+4 contains two)
polynomial
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
rectangular coordinates
The real number a of the complex number z = a + bi

11. A number is divisible by 4 if
Odd Number
coefficient
Commutative Law of Addition
the number formed by the two right-hand digits is divisible by 4

12. G - E - M - A Grouping - Exponents - Multiply/Divide - Add/Subtract
In Diophantine geometry
order of operations
consecutive whole numbers
monomial

13. This law can be applied to subtraction by changing signs so that all negative signs become number signs and all signs of operation are positive.
magnitude
Commutative Law of Addition
Downward
algebraic number

14. 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
an equation in two variables defines
magnitude and direction
even and the sum of its digits is divisible by 3
base-ten number

15. 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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16. 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
a curve - a surface or some other such object in n-dimensional space
16(5+R)
Definition of genus
Commutative Law of Addition

17. Total
addition
T+9
subtraction
division

18. The smallest of four sonsecutive whole numbers - the biggest of which is K+6
(x-12)/40
polynomial
K+6 - K+5 - K+4 K+3.........answer is K+3
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.

19. A number that has no factors except itself and 1 is a
In Diophantine geometry
Set
Number fields
Prime Number

20. 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.
the genus of the curve
Commutative Law of Addition
Analytic number theory
monomial

21. In the Rectangular Coordinate System - On the vertical line - direction ________ is positive
addition
(x-12)/40
division
upward

22. In the Rectangular Coordinate System - the direction to the left along the horizontal line is
The real number a of the complex number z = a + bi
negative
Natural Numbers
Inversive geometry

23. This formula can be used to compute the multiplicative inverse of a complex number if it is given in
To separate a number into prime factors
Associative Law of Multiplication
rectangular coordinates
Commutative Law of Multiplication

24. 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.
positive
Absolute value and argument
Third Axiom of Equality
quadratic field

25. 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.
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
multiplication
expression
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.

26. The greatest of 3 consecutive whole numbers - the smallest of which is F
F - F+1 - F+2.......answer is F+2
constant
Commutative Law of Addition
K+6 - K+5 - K+4 K+3.........answer is K+3

27. Remainder
Commutative Law of Addition
Factor of the given number
subtraction
Multiple of the given number

28. Are used to indicate sets
difference
Braces
constant
quadratic field

29. The Arabic numerals from 0 through 9 are called
Braces
Third Axiom of Equality
Digits
addition

30. 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
base-ten number
The multiplication of two complex numbers is defined by the following formula:
Prime Factor
Place Value Concept

31. Any number that is not a multiple of 2 is an
Even Number
Odd Number
Number fields
Algebraic number theory

32. 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.
Third Axiom of Equality
rectangular coordinates
difference
Associative Law of Addition

33. A number is divisible by 2 if
the number formed by the two right-hand digits is divisible by 4
Prime Number
right-hand digit is even
Forth Axiom of Equality

34. In the Rectangular Coordinate System - On the vertical line - direction _______ is negative
In Diophantine geometry
an equation in two variables defines
Downward
solutions

35. Number X decreased by 12 divided by forty
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.
(x-12)/40
subtraction

36. 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.
Multiple of the given number
T+9
Braces
Second Axiom of Equality

37. Sixteen less than number Q
Analytic number theory
Q-16
constant
Factor of the given number

38. 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
The real number a of the complex number z = a + bi
addition
Downward
equation

39. A number is divisible by 5 if its
righthand digit is 0 or 5
Place Value Concept
consecutive whole numbers
the number formed by the two right-hand digits is divisible by 4

40. The finiteness or not of the number of rational or integer points on an algebraic curve
the genus of the curve
algebraic number
polynomial
Prime Factor

41. A number is divisible by 6 if it is
Distributive Law
In Diophantine geometry
even and the sum of its digits is divisible by 3
righthand digit is 0 or 5

42. A number is divisible by 3 if
Definition of genus
Equal
Multiple of the given number
its the sum of its digits is divisible by 3

43. 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.
addition
Commutative Law of Multiplication
Set
Members of Elements of the Set

44. Product
quadratic field
T+9
Distributive Law
multiplication

45. Work on the problem of general polynomials ultimately led to the fundamental theorem of algebra -
order of operations
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
Absolute value and argument
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.

46. 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.
Natural Numbers
expression
upward
Associative Law of Multiplication

47. Are not necessary. That is - the elements of {2 - 2 - 3 - 4} are simply {2 - 3 - and 4}
Definition of genus
Set
repeated elements
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .

48. 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.)
Number fields
quadratic field
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
The absolute value (or modulus or magnitude) of a complex number z = x + yi is

49. 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:
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).
Base of the number system
T+9
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:

50. 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
consecutive whole numbers
equation
In Diophantine geometry
The multiplication of two complex numbers is defined by the following formula: