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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. A number is divisible by 5 if its
righthand digit is 0 or 5
magnitude and direction
Associative Law of Addition
polynomial

2. 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
Members of Elements of the Set
complex number
Place Value Concept
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).

3. 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.
Complex numbers
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
addition
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.

4. A number is divisible by 3 if
its the sum of its digits is divisible by 3
Members of Elements of the Set
order of operations
division

5. Total
Definition of genus
complex number
addition
In Diophantine geometry

6. Work on the problem of general polynomials ultimately led to the fundamental theorem of algebra -
Positional notation (place value)
Commutative Law of Addition
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
polynomial

7. 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.
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
The numbers are conventionally plotted using the real part
addition
upward

8. Number X decreased by 12 divided by forty
constant
difference
(x-12)/40
Inversive geometry

9. 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.
addition
Commutative Law of Addition
(x-12)/40
its the sum of its digits is divisible by 3

10. The finiteness or not of the number of rational or integer points on an algebraic curve
the genus of the curve
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
Definition of genus
Prime Factor

11. 2 -3 -4 -5 -6
(x-12)/40
In Diophantine geometry
consecutive whole numbers
its the sum of its digits is divisible by 3

12. Decreased by
variable
right-hand digit is even
subtraction
magnitude and direction

13. Does not have an equal sign (3x+5) (2a+9b)
Distributive Law
expression
coefficient
subtraction

14. 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
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.
Q-16
Algebraic number theory

15. Increased by
addition
positive
Commutative Law of Multiplication
C or

16. The defining characteristic of a position vector is that it has
magnitude and direction
Multiple of the given number
variable
positive

17. The numbers which are used for counting in our number system are sometimes called
counterclockwise through 90
magnitude
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
Natural Numbers

18. The number without a variable (5m+2). In this case - 2
the sum of its digits is divisible by 9
positive
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
constant

19. A number is divisible by 9 if
the sum of its digits is divisible by 9
16(5+R)
the genus of the curve
Even Number

20. The objects in a set have at least
subtraction
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
one characteristic in common such as similarity of appearance or purpose

21. Remainder
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).
counterclockwise through 90
subtraction
Prime Number

22. 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
Downward
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
Associative Law of Addition

23. A number that has factors other than itself and 1 is a
quadratic field
Composite Number
polynomial
addition

24. The smallest of four sonsecutive whole numbers - the biggest of which is K+6
K+6 - K+5 - K+4 K+3.........answer is K+3
C or
Q-16
Number fields

25. A number is divisible by 6 if it is
Associative Law of Multiplication
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
The multiplication of two complex numbers is defined by the following formula:
even and the sum of its digits is divisible by 3

26. 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.)
Even Number
Number fields
Digits
expression

27. A number that has no factors except itself and 1 is a
negative
Absolute value and argument
algebraic number
Prime Number

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

29. 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
base-ten number
the number formed by the two right-hand digits is divisible by 4
Associative Law of Addition
addition

30. 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
Q-16
(x-12)/40
monomial
complex number

31. The place value which corresponds to a given position in a number is determined by the
Associative Law of Addition
Base of the number system
Absolute value and argument
upward

32. This law can be applied to subtraction by changing signs in such a way that all negative signs are treated as number signs rather than operational signs.That is - some of the addends can be negative numbers.
The real number a of the complex number z = a + bi
Prime Factor
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
Associative Law of Addition

33. First axiom of equality
a curve - a surface or some other such object in n-dimensional space
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.
K+6 - K+5 - K+4 K+3.........answer is K+3
Members of Elements of the Set

34. Plus
Number fields
addition
T+9
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.

35. As shown earlier - c - di is the complex conjugate of the denominator c + di.
positive
Inversive geometry
Digits
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.

36. 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.
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
Place Value Concept
difference
Forth Axiom of Equality

37. In the Rectangular Coordinate System - On the vertical line - direction _______ is negative
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
Commutative Law of Addition
addition
Downward

38. 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.
expression
rectangular coordinates
Associative Law of Addition
upward

39. 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.
subtraction
division
Third Axiom of Equality
(x-12)/40

40. 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.
Commutative Law of Addition
Commutative Law of Multiplication
expression
addition

41. Quotient
division
Even Number
(x-12)/40
The absolute value (or modulus or magnitude) of a complex number z = x + yi is

42. An equation - or system of equations - in two or more variables defines
In Diophantine geometry
difference
a curve - a surface or some other such object in n-dimensional space
Second Axiom of Equality

43. Implies a collection or grouping of similar - objects or symbols.
difference
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
Set
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.

44. The set of all complex numbers is denoted by
Distributive Law
C or
Associative Law of Addition
subtraction

45. 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.
constructing a parallelogram
addition
Associative Law of Multiplication
Complex numbers

46. 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.
Commutative Law of Multiplication
Q-16
Factor of the given number
equation

47. Number symbols
constructing a parallelogram
In Diophantine geometry
coefficient
Numerals

48. 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.
one characteristic in common such as similarity of appearance or purpose
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
Second Axiom of Equality
right-hand digit is even

49. LAWS FOR COMBINING NUMBERS
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
constructing a parallelogram
the sum of its digits is divisible by 9
algebraic number

50. 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.
quadratic field
repeated elements
the sum of its digits is divisible by 9
multiplication