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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. 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
subtraction
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
The multiplication of two complex numbers is defined by the following formula:
its the sum of its digits is divisible by 3

2. A number that has no factors except itself and 1 is a
magnitude
Prime Number
an equation in two variables defines
The multiplication of two complex numbers is defined by the following formula:

3. In the Rectangular Coordinate System - On the vertical line - direction _______ is negative
Downward
difference
right-hand digit is even
K+6 - K+5 - K+4 K+3.........answer is K+3

4. The place value which corresponds to a given position in a number is determined by the
subtraction
Associative Law of Addition
magnitude and direction
Base of the number system

5. Has an equal sign (3x+5 = 14)
the number formed by the two right-hand digits is divisible by 4
F - F+1 - F+2.......answer is F+2
equation
addition

6. 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
C or
addition
Positional notation (place value)
counterclockwise through 90

7. G - E - M - A Grouping - Exponents - Multiply/Divide - Add/Subtract
rectangular coordinates
order of operations
constant
Commutative Law of Multiplication

8. Any number that is not a multiple of 2 is an
Equal
Odd Number
K+6 - K+5 - K+4 K+3.........answer is K+3
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.

9. The Arabic numerals from 0 through 9 are called
subtraction
Digits
Natural Numbers
Analytic number theory

10. Product of 16 and the sum of 5 and number R
Algebraic number theory
negative
16(5+R)
Forth Axiom of Equality

11. Does not have an equal sign (3x+5) (2a+9b)
its the sum of its digits is divisible by 3
counterclockwise through 90
repeated elements
expression

12. 2 -3 -4 -5 -6
subtraction
complex number
consecutive whole numbers
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .

13. 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.
16(5+R)
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
multiplication
Q-16

14. Number symbols
rectangular coordinates
addition
Numerals
F - F+1 - F+2.......answer is F+2

15. 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
right-hand digit is even
In Diophantine geometry
coefficient
The multiplication of two complex numbers is defined by the following formula:

16. A curve in the plane
an equation in two variables defines
base-ten number
positive
rectangular coordinates

17. The set of all complex numbers is denoted by
one characteristic in common such as similarity of appearance or purpose
C or
magnitude and direction
T+9

18. Quotient
the number formed by the two right-hand digits is divisible by 4
addition
equation
division

19. The smallest of four sonsecutive whole numbers - the biggest of which is K+6
16(5+R)
K+6 - K+5 - K+4 K+3.........answer is K+3
Associative Law of Multiplication
T+9

20. As shown earlier - c - di is the complex conjugate of the denominator c + di.
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
Definition of genus
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).
Associative Law of Addition

21. 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.
Associative Law of Addition
a curve - a surface or some other such object in n-dimensional space
Forth Axiom of Equality
Members of Elements of the Set

22. 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.
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
the genus of the curve
upward
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.

23. The real and imaginary parts of a complex number can be extracted using the conjugate:
Third Axiom of Equality
a complex number is real if and only if it equals its conjugate.
Prime Factor
its the sum of its digits is divisible by 3

24. A number is divisible by 2 if
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
right-hand digit is even
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
16(5+R)

25. The objects in a set have at least
Second Axiom of Equality
monomial
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
one characteristic in common such as similarity of appearance or purpose

26. 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
coefficient
K+6 - K+5 - K+4 K+3.........answer is K+3
Prime Factor
In Diophantine geometry

27. 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
subtraction
subtraction
Equal
solutions

28. 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
a curve - a surface or some other such object in n-dimensional space
algebraic number
complex number
quadratic field

29. The objects or symbols in a set are called Numerals - Lines - or Points
Members of Elements of the Set
difference
the number formed by the three right-hand digits is divisible by 8
subtraction

30. The greatest of 3 consecutive whole numbers - the smallest of which is F
Second Axiom of Equality
F - F+1 - F+2.......answer is F+2
upward
subtraction

31. More than one term (5x+4 contains two)
Commutative Law of Addition
polynomial
monomial
In Diophantine geometry

32. 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
Digits
addition
counterclockwise through 90
Definition of genus

33. In the Rectangular Coordinate System - the direction to the right along the horizontal line is
Factor of the given number
positive
Algebraic number theory
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.

34. 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
Third Axiom of Equality
subtraction
addition

35. 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
constant
Commutative Law of Addition
Distributive Law
Algebraic number theory

36. 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.
F - F+1 - F+2.......answer is F+2
monomial
Base of the number system
Complex numbers

37. An equation - or system of equations - in two or more variables defines
Positional notation (place value)
the number formed by the two right-hand digits is divisible by 4
a curve - a surface or some other such object in n-dimensional space
a complex number is real if and only if it equals its conjugate.

38. If a factor of a number is prime - it is called a
F - F+1 - F+2.......answer is F+2
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
the number formed by the two right-hand digits is divisible by 4
Prime Factor

39. Implies a collection or grouping of similar - objects or symbols.
Set
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
addition
16(5+R)

40. First axiom of equality
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
Absolute value and argument
Analytic number theory

41. This law combines the operations of addition and multiplication. The distribution of a common multiplier among the terms of an additive expression.
the number formed by the two right-hand digits is divisible by 4
The real number a of the complex number z = a + bi
Distributive Law
Third Axiom of Equality

42. 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.
expression
Multiple of the given number
Third Axiom of Equality
algebraic number

43. Total
addition
base-ten number
F - F+1 - F+2.......answer is F+2
T+9

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
Digits
righthand digit is 0 or 5
The real number a of the complex number z = a + bi
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.

45. The finiteness or not of the number of rational or integer points on an algebraic curve
its the sum of its digits is divisible by 3
Analytic number theory
Inversive geometry
the genus of the curve

46. Plus
righthand digit is 0 or 5
addition
Q-16
Commutative Law of Addition

47. Decreased by
Inversive geometry
Numerals
subtraction
constructing a parallelogram

48. A branch of geometry studying more general reflections than ones about a line - can also be expressed in terms of complex numbers.
addition
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
addition
Inversive geometry

49. 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
one characteristic in common such as similarity of appearance or purpose
Commutative Law of Addition
Place Value Concept
Positional notation (place value)

50. The relative greatness of positive and negative numbers
counterclockwise through 90
magnitude
Prime Factor
equation