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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 the Rectangular Coordinate System - On the vertical line - direction ________ is positive
upward
Multiple of the given number
addition
Third Axiom of Equality

2. 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
The multiplication of two complex numbers is defined by the following formula:
Odd Number
Absolute value and argument

3. Quotient
division
complex number
the number formed by the two right-hand digits is divisible by 4
subtraction

4. In the Rectangular Coordinate System - the direction to the right along the horizontal line is
Downward
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).
positive
an equation in two variables defines

5. Number X decreased by 12 divided by forty
constant
rectangular coordinates
(x-12)/40
Complex numbers

6. A number that has factors other than itself and 1 is a
polynomial
Composite Number
Inversive geometry
equation

7. Less than
subtraction
variable
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.
Set

8. 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.
the genus of the curve
F - F+1 - F+2.......answer is F+2
The numbers are conventionally plotted using the real part
the number formed by the two right-hand digits is divisible by 4

9. 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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10. Any number that is exactly divisible by a given number is a
Odd Number
Multiple of the given number
Numerals
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.

11. A curve in the plane
an equation in two variables defines
F - F+1 - F+2.......answer is F+2
the number formed by the three right-hand digits is divisible by 8
addition

12. The place value which corresponds to a given position in a number is determined by the
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
Number fields
Base of the number system

13. A number is divisible by 3 if
Definition of genus
its the sum of its digits is divisible by 3
The real number a of the complex number z = a + bi
Natural Numbers

14. A branch of geometry studying more general reflections than ones about a line - can also be expressed in terms of complex numbers.
C or
constructing a parallelogram
Inversive geometry
positive

15. Number symbols
7
Numerals
counterclockwise through 90
Members of Elements of the Set

16. A number is divisible by 5 if its
quadratic field
Composite Number
righthand digit is 0 or 5
addition

17. 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.
algebraic number
Second Axiom of Equality
In Diophantine geometry
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .

18. Sixteen less than number Q
Q-16
Commutative Law of Multiplication
Numerals
Members of Elements of the Set

19. A number that has no factors except itself and 1 is a
Odd Number
coefficient
Prime Number
Natural Numbers

20. 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.
base-ten number
Third Axiom of Equality
Analytic number theory
In Diophantine geometry

21. Does not have an equal sign (3x+5) (2a+9b)
expression
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
Set
C or

22. First axiom of equality
Members of Elements of the Set
The multiplication of two complex numbers is defined by the following formula:
rectangular coordinates
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.

23. The Arabic numerals from 0 through 9 are called
Number fields
constructing a parallelogram
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
Digits

24. 2 -3 -4 -5 -6
order of operations
consecutive whole numbers
addition
a curve - a surface or some other such object in n-dimensional space

25. A number is divisible by 6 if it is
a curve - a surface or some other such object in n-dimensional space
Q-16
even and the sum of its digits is divisible by 3
the sum of its digits is divisible by 9

26. Any number that is not a multiple of 2 is an
consecutive whole numbers
difference
Odd Number
addition

27. The central problem of Diophantine geometry is to determine when a Diophantine equation has
In Diophantine geometry
Analytic number theory
solutions
Inversive geometry

28. 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:
Base of the number system
counterclockwise through 90
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-ten number

29. 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
Set
The real number a of the complex number z = a + bi

30. Plus
division
addition
algebraic number
a complex number is real if and only if it equals its conjugate.

31. 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
the number formed by the two right-hand digits is divisible by 4
Positional notation (place value)
polynomial
Distributive Law

32. Number T increased by 9
T+9
the genus of the curve
the number formed by the two right-hand digits is divisible by 4
addition

33. More than one term (5x+4 contains two)
polynomial
addition
Set
algebraic number

34. A number is divisible by 8 if
Braces
7
Members of Elements of the Set
the number formed by the three right-hand digits is divisible by 8

35. 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
(x-12)/40
Definition of genus
Inversive geometry

36. 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.
the genus of the curve
Complex numbers
Commutative Law of Multiplication
subtraction

37. More than
addition
upward
T+9
In Diophantine geometry

38. The defining characteristic of a position vector is that it has
magnitude and direction
righthand digit is 0 or 5
negative
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}

39. 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.
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.
an equation in two variables defines
Natural Numbers

40. Viewed in this way the multiplication of a complex number by i corresponds to rotating a complex number
Complex numbers
Natural Numbers
counterclockwise through 90
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.

41. Are used to indicate sets
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
Braces
addition
even and the sum of its digits is divisible by 3

42. LAWS FOR COMBINING NUMBERS
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
quadratic field
addition
repeated elements

43. Any number that can be divided lnto a given number without a remainder is a
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
Factor of the given number
righthand digit is 0 or 5
Second Axiom of Equality

44. Decreased by
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
equation
subtraction
the sum of its digits is divisible by 9

45. A number is divisible by 2 if
negative
base-ten number
the number formed by the three right-hand digits is divisible by 8
right-hand digit is even

46. Subtraction
difference
To separate a number into prime factors
The real number a of the complex number z = a + bi
Equal

47. 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
constructing a parallelogram
Commutative Law of Multiplication
Commutative Law of Addition
Equal

48. 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
Second Axiom of Equality
Place Value Concept
Distributive Law
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.

49. 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.
Composite Number
Absolute value and argument
Forth Axiom of Equality
Algebraic number theory

50. 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.)
addition
Associative Law of Addition
Number fields
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).