Test your basic knowledge |

CLEP General Mathematics: Number Systems And Sets

Subjects : clep, math

Instructions:

Answer 50 questions in 15 minutes.
If you are not ready to take this test, you can study here.
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. 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
a complex number is real if and only if it equals its conjugate.
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
subtraction
The multiplication of two complex numbers is defined by the following formula:

2. A number is divisible by 2 if
magnitude and direction
right-hand digit is even
coefficient
Third Axiom of Equality

3. In the Rectangular Coordinate System - On the vertical line - direction _______ is negative
variable
Forth Axiom of Equality
Downward
Composite Number

4. 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 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).
the sum of its digits is divisible by 9
Odd Number
Second Axiom of Equality

5. Another way of encoding points in the complex plane other than using the x- and y-coordinates is to use the distance of a point P to O - the point whose coordinates are (0 - 0) (the origin) - and the angle of the line through P and O. This idea leads
counterclockwise through 90
subtraction
Absolute value and argument
equation

6. Integers greater than zero and less than 5 form a set - as follows:
even and the sum of its digits is divisible by 3
magnitude
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
C or

7. A number is divisible by 5 if its
The real number a of the complex number z = a + bi
Commutative Law of Multiplication
righthand digit is 0 or 5
Digits

8. Implies a collection or grouping of similar - objects or symbols.
difference
Commutative Law of Addition
To separate a number into prime factors
Set

9. Has an equal sign (3x+5 = 14)
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
Set
a curve - a surface or some other such object in n-dimensional space
equation

10. Does not have an equal sign (3x+5) (2a+9b)
expression
multiplication
division
K+6 - K+5 - K+4 K+3.........answer is K+3

11. The smallest of four sonsecutive whole numbers - the biggest of which is K+6
the number formed by the two right-hand digits is divisible by 4
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
a curve - a surface or some other such object in n-dimensional space
K+6 - K+5 - K+4 K+3.........answer is K+3

12. Product
multiplication
Associative Law of Addition
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
variable

13. Product of 16 and the sum of 5 and number R
Members of Elements of the Set
16(5+R)
T+9
Multiple of the given number

14. Quotient
Even Number
division
Place Value Concept
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.

15. The number touching the variable (in the case of 5x - would be 5)
coefficient
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
difference
counterclockwise through 90

16. In the Rectangular Coordinate System - On the vertical line - direction ________ is positive
To separate a number into prime factors
upward
Commutative Law of Addition
Members of Elements of the Set

17. 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
upward
(x-12)/40
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:

18. 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.)
Number fields
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
upward
a complex number is real if and only if it equals its conjugate.

19. The place value which corresponds to a given position in a number is determined by the
equation
Base of the number system
Number fields
consecutive whole numbers

20. A number is divisible by 3 if
its the sum of its digits is divisible by 3
Place Value Concept
Definition of genus
Complex numbers

21. 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.
Complex numbers
equation
a complex number is real if and only if it equals its conjugate.
subtraction

22. 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
its the sum of its digits is divisible by 3
Downward
consecutive whole numbers

23. Work on the problem of general polynomials ultimately led to the fundamental theorem of algebra -
right-hand digit is even
To separate a number into prime factors
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
its the sum of its digits is divisible by 3

24. 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
order of operations
addition
addition
Positional notation (place value)

25. Are not necessary. That is - the elements of {2 - 2 - 3 - 4} are simply {2 - 3 - and 4}
repeated elements
addition
difference
algebraic number

26. The real and imaginary parts of a complex number can be extracted using the conjugate:
Set
Prime Number
a complex number is real if and only if it equals its conjugate.
quadratic field

27. 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
counterclockwise through 90
complex number
Base of the number system
The numbers are conventionally plotted using the real part

28. An equation - or system of equations - in two or more variables defines
division
a curve - a surface or some other such object in n-dimensional space
Digits
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:

29. A branch of geometry studying more general reflections than ones about a line - can also be expressed in terms of complex numbers.
Associative Law of Addition
Algebraic number theory
Inversive geometry
Commutative Law of Addition

30. 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
Commutative Law of Multiplication
Algebraic number theory
consecutive whole numbers
rectangular coordinates

31. Less than
Even Number
T+9
magnitude and direction
subtraction

32. 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
In Diophantine geometry
base-ten number
Digits
Set

33. 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.
Third Axiom of Equality
T+9
Commutative Law of Addition
Members of Elements of the Set

34. More than
Q-16
solutions
addition
order of operations

35. Any number that la a multiple of 2 is an
addition
Equal
one characteristic in common such as similarity of appearance or purpose
Even Number

36. 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
equation
constructing a parallelogram
Absolute value and argument
base-ten number

37. 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.
equation
addition
Algebraic number theory
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.

38. LAWS FOR COMBINING NUMBERS
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.
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
Associative Law of Multiplication
complex number

39. Number T increased by 9
T+9
rectangular coordinates
positive
Commutative Law of Addition

40. Increased by
addition
coefficient
Factor of the given number
Algebraic number theory

41. Any number that can be divided lnto a given number without a remainder is a
subtraction
constant
Factor of the given number
addition

42. The objects in a set have at least
the genus of the curve
positive
one characteristic in common such as similarity of appearance or purpose
Algebraic number theory

43. Sixteen less than number Q
Set
Q-16
Prime Number
Digits

44. Any number that is exactly divisible by a given number is a
Multiple of the given number
Q-16
Algebraic number theory
Third Axiom of Equality

45. 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.
Composite Number
Associative Law of Addition
In Diophantine geometry
base-ten number

46. 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.
Inversive geometry
Forth Axiom of Equality
Prime Number
magnitude

47. Are used to indicate sets
addition
the number formed by the two right-hand digits is divisible by 4
division
Braces

48. Sum
multiplication
addition
Equal
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:

49. A number that has factors other than itself and 1 is a
subtraction
magnitude and direction
Multiple of the given number
Composite Number

50. Viewed in this way the multiplication of a complex number by i corresponds to rotating a complex number
Composite Number
positive
counterclockwise through 90
addition