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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.
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. Plus
solutions
Prime Factor
addition
Definition of genus

2. This law combines the operations of addition and multiplication. The distribution of a common multiplier among the terms of an additive expression.
Distributive Law
equation
coefficient
repeated elements

3. 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.
righthand digit is 0 or 5
one characteristic in common such as similarity of appearance or purpose
Third Axiom of Equality
Complex numbers

4. A branch of geometry studying more general reflections than ones about a line - can also be expressed in terms of complex numbers.
Inversive geometry
an equation in two variables defines
Third Axiom of Equality
K+6 - K+5 - K+4 K+3.........answer is K+3

5. A number that has factors other than itself and 1 is a
Odd Number
Composite Number
polynomial
constructing a parallelogram

6. The greatest of 3 consecutive whole numbers - the smallest of which is F
difference
F - F+1 - F+2.......answer is F+2
positive
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.

7. If a factor of a number is prime - it is called a
Absolute value and argument
Complex numbers
complex number
Prime Factor

8. A number is divisible by 2 if
right-hand digit is even
Definition of genus
Forth Axiom of Equality
solutions

9. 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.
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
Analytic number theory
negative
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.

10. 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 -
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
one characteristic in common such as similarity of appearance or purpose
polynomial
Set

11. A letter tat represents a number that is unknown (usually X or Y)
variable
upward
even and the sum of its digits is divisible by 3
Number fields

12. This formula can be used to compute the multiplicative inverse of a complex number if it is given in
Place Value Concept
Distributive Law
the genus of the curve
rectangular coordinates

13. Any number that can be divided lnto a given number without a remainder is a
the number formed by the two right-hand digits is divisible by 4
The real number a of the complex number z = a + bi
In Diophantine geometry
Factor of the given number

14. Viewed in this way the multiplication of a complex number by i corresponds to rotating a complex number
Natural Numbers
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).
Members of Elements of the Set
counterclockwise through 90

15. The defining characteristic of a position vector is that it has
variable
The real number a of the complex number z = a + bi
its the sum of its digits is divisible by 3
magnitude and direction

16. Has an equal sign (3x+5 = 14)
Associative Law of Addition
Algebraic number theory
complex number
equation

17. 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
Odd Number
The real number a of the complex number z = a + bi
its the sum of its digits is divisible by 3
coefficient

18. Any number that is not a multiple of 2 is an
addition
Odd Number
(x-12)/40
Prime Factor

19. The Arabic numerals from 0 through 9 are called
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
Digits
monomial
consecutive whole numbers

20. 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.
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
Associative Law of Multiplication
Natural Numbers
Multiple of the given number

21. 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.
the sum of its digits is divisible by 9
16(5+R)
quadratic field
one characteristic in common such as similarity of appearance or purpose

22. Total
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
addition
the sum of its digits is divisible by 9

23. The place value which corresponds to a given position in a number is determined by the
Base of the number system
Natural Numbers
Absolute value and argument
algebraic number

24. Less than
multiplication
Commutative Law of Addition
subtraction
T+9

25. Are not necessary. That is - the elements of {2 - 2 - 3 - 4} are simply {2 - 3 - and 4}
rectangular coordinates
repeated elements
a complex number is real if and only if it equals its conjugate.
In Diophantine geometry

26. 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
equation
Digits
complex number
The multiplication of two complex numbers is defined by the following formula:

27. Product
Second Axiom of Equality
multiplication
Multiple of the given number
addition

28. 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
Place Value Concept
one characteristic in common such as similarity of appearance or purpose
base-ten number
Second Axiom of Equality

29. No short method has been found for determining whether a number is divisible by
7
In Diophantine geometry
Prime Number
Commutative Law of Multiplication

30. Any number that is exactly divisible by a given number is a
Forth Axiom of Equality
addition
Associative Law of Addition
Multiple of the given number

31. 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
Odd Number
Positional notation (place value)
Commutative Law of Addition

32. As shown earlier - c - di is the complex conjugate of the denominator c + di.
Braces
(x-12)/40
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
Natural Numbers

33. 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.
division
C or
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
magnitude

34. In the Rectangular Coordinate System - the direction to the right along the horizontal line is
Third Axiom of Equality
The numbers are conventionally plotted using the real part
constructing a parallelogram
positive

35. Product of 16 and the sum of 5 and number R
Third Axiom of Equality
Q-16
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
16(5+R)

36. Number T increased by 9
right-hand digit is even
addition
T+9
a curve - a surface or some other such object in n-dimensional space

37. A number is divisible by 9 if
quadratic field
Commutative Law of Multiplication
a complex number is real if and only if it equals its conjugate.
the sum of its digits is divisible by 9

38. 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.
Algebraic number theory
Forth Axiom of Equality
Prime Factor
Third Axiom of Equality

39. 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
base-ten number
one characteristic in common such as similarity of appearance or purpose
Definition of genus
Set

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. 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.
Algebraic number theory
Odd Number
Associative Law of Addition
Members of Elements of the Set

42. The objects or symbols in a set are called Numerals - Lines - or Points
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
Members of Elements of the Set
variable
Place Value Concept

43. Decreased by
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
subtraction
The real number a of the complex number z = a + bi
division

44. Integers greater than zero and less than 5 form a set - as follows:
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
Prime Number
addition
Place Value Concept

45. 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
its the sum of its digits is divisible by 3
Q-16
Even Number
In Diophantine geometry

46. A number is divisible by 8 if
the number formed by the three right-hand digits is divisible by 8
difference
In Diophantine geometry
Inversive geometry

47. First axiom of equality
Factor of the given number
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.
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
base-ten number

48. The relative greatness of positive and negative numbers
Absolute value and argument
algebraic number
variable
magnitude

49. A number is divisible by 5 if its
Odd Number
complex number
addition
righthand digit is 0 or 5

50. The objects in a set have at least
algebraic number
one characteristic in common such as similarity of appearance or purpose
Analytic number theory
expression