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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. A number is divisible by 5 if its
addition
one characteristic in common such as similarity of appearance or purpose
To separate a number into prime factors
righthand digit is 0 or 5

2. Decreased by
subtraction
Prime Number
F - F+1 - F+2.......answer is F+2
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.

3. The numbers which are used for counting in our number system are sometimes called
Prime Number
Base of the number system
Natural Numbers
consecutive whole numbers

4. The defining characteristic of a position vector is that it has
polynomial
Composite Number
subtraction
magnitude and direction

5. 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.
addition
Number fields
Second Axiom of Equality
Braces

6. A number is divisible by 8 if
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
the number formed by the three right-hand digits is divisible by 8
Associative Law of Addition

7. 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.
rectangular coordinates
Prime Number
Commutative Law of Addition
Q-16

8. 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.
Definition of genus
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
magnitude and direction
Natural Numbers

9. A number that has factors other than itself and 1 is a
variable
Composite 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.
magnitude and direction

10. Any number that is exactly divisible by a given number is a
Digits
16(5+R)
The real number a of the complex number z = a + bi
Multiple of the given number

11. If a factor of a number is prime - it is called a
one characteristic in common such as similarity of appearance or purpose
even and the sum of its digits is divisible by 3
subtraction
Prime Factor

12. 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.)
The numbers are conventionally plotted using the real part
Number fields
Composite Number
a complex number is real if and only if it equals its conjugate.

13. Any number that la a multiple of 2 is an
Even Number
The multiplication of two complex numbers is defined by the following formula:
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
In Diophantine geometry

14. 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:
multiplication
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).
Q-16
Members of Elements of the Set

15. The finiteness or not of the number of rational or integer points on an algebraic curve
To separate a number into prime factors
the genus of the curve
7
F - F+1 - F+2.......answer is F+2

16. In the Rectangular Coordinate System - the direction to the left along the horizontal line is
negative
equation
Third Axiom of Equality
16(5+R)

17. Does not have an equal sign (3x+5) (2a+9b)
the genus of the curve
Complex numbers
expression
coefficient

18. Subtraction
difference
expression
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.

19. 2 -3 -4 -5 -6
Associative Law of Multiplication
the number formed by the three right-hand digits is divisible by 8
counterclockwise through 90
consecutive whole numbers

20. Increased by
Multiple of the given number
addition
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
subtraction

21. 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.
counterclockwise through 90
Associative Law of Multiplication
Positional notation (place value)
Equal

22. 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.
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
7
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.

23. Product of 16 and the sum of 5 and number R
16(5+R)
T+9
polynomial
addition

24. Any number that can be divided lnto a given number without a remainder is a
one characteristic in common such as similarity of appearance or purpose
multiplication
difference
Factor of the given number

25. 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.
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
Complex numbers
constant
complex number

26. 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.
positive
addition
Analytic number theory
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.

27. Less than
subtraction
Place Value Concept
(x-12)/40
Braces

28. Total
Digits
F - F+1 - F+2.......answer is F+2
K+6 - K+5 - K+4 K+3.........answer is K+3
addition

29. 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
the sum of its digits is divisible by 9
C or
Downward

30. The greatest of 3 consecutive whole numbers - the smallest of which is F
base-ten number
F - F+1 - F+2.......answer is F+2
complex number
Numerals

31. Number X decreased by 12 divided by forty
(x-12)/40
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
addition
Commutative Law of Addition

32. The Arabic numerals from 0 through 9 are called
consecutive whole numbers
Digits
addition
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.

33. 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
solutions
magnitude
a curve - a surface or some other such object in n-dimensional space
Algebraic number theory

34. Number symbols
Place Value Concept
Inversive geometry
Numerals
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:

35. Plus
addition
one characteristic in common such as similarity of appearance or purpose
16(5+R)
subtraction

36. Any number that is not a multiple of 2 is an
an equation in two variables defines
multiplication
Odd Number
Braces

37. 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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38. In the Rectangular Coordinate System - On the vertical line - direction _______ is negative
Downward
negative
Members of Elements of the Set
K+6 - K+5 - K+4 K+3.........answer is K+3

39. A number is divisible by 3 if
Number fields
the sum of its digits is divisible by 9
C or
its the sum of its digits is divisible by 3

40. 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
Q-16
Place Value Concept
T+9
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.

41. In the Rectangular Coordinate System - On the vertical line - direction ________ is positive
monomial
7
Associative Law of Addition
upward

42. Product
equation
multiplication
Commutative Law of Addition
Number fields

43. More than
addition
Set
The real number a of the complex number z = a + bi
one characteristic in common such as similarity of appearance or purpose

44. A number is divisible by 4 if
Forth Axiom of Equality
the number formed by the two right-hand digits is divisible by 4
Third Axiom of Equality
To separate a number into prime factors

45. 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
algebraic number
monomial
Commutative Law of Addition
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.

46. The objects in a set have at least
one characteristic in common such as similarity of appearance or purpose
Forth Axiom of Equality
consecutive whole numbers
division

47. A number is divisible by 2 if
Base of the number system
difference
right-hand digit is even
coefficient

48. LAWS FOR COMBINING NUMBERS
the sum of its digits is divisible by 9
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
the number formed by the three right-hand digits is divisible by 8
a complex number is real if and only if it equals its conjugate.

49. G - E - M - A Grouping - Exponents - Multiply/Divide - Add/Subtract
addition
Absolute value and argument
order of operations
quadratic field

50. 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
(x-12)/40
constructing a parallelogram
complex number
Associative Law of Multiplication