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. 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
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
Numerals
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.

2. Any number that can be divided lnto a given number without a remainder is a
Factor of the given number
coefficient
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
Braces

3. The greatest of 3 consecutive whole numbers - the smallest of which is F
a curve - a surface or some other such object in n-dimensional space
F - F+1 - F+2.......answer is F+2
difference
Third Axiom of Equality

4. An equation - or system of equations - in two or more variables defines
Place Value Concept
complex number
right-hand digit is even
a curve - a surface or some other such object in n-dimensional space

5. In the Rectangular Coordinate System - the direction to the left along the horizontal line is
monomial
Associative Law of Addition
negative
Digits

6. Number symbols
K+6 - K+5 - K+4 K+3.........answer is K+3
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
Commutative Law of Addition
Numerals

7. LAWS FOR COMBINING NUMBERS
subtraction
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
F - F+1 - F+2.......answer is F+2
a curve - a surface or some other such object in n-dimensional space

8. The objects or symbols in a set are called Numerals - Lines - or Points
Members of Elements of the Set
Digits
consecutive whole numbers
expression

9. 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.
Associative Law of Multiplication
Downward
Commutative Law of Addition

10. Any number that la a multiple of 2 is an
Even Number
variable
(x-12)/40
Distributive Law

11. Does not have an equal sign (3x+5) (2a+9b)
In Diophantine geometry
expression
Associative Law of Addition
Associative Law of Addition

12. A number is divisible by 4 if
In Diophantine geometry
upward
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
the number formed by the two right-hand digits is divisible by 4

13. A number that has no factors except itself and 1 is a
the sum of its digits is divisible by 9
Prime Number
the number formed by the three right-hand digits is divisible by 8
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}

14. Viewed in this way the multiplication of a complex number by i corresponds to rotating a complex number
Q-16
positive
counterclockwise through 90
Factor of the given number

15. This formula can be used to compute the multiplicative inverse of a complex number if it is given in
Downward
its the sum of its digits is divisible by 3
rectangular coordinates
one characteristic in common such as similarity of appearance or purpose

16. A letter tat represents a number that is unknown (usually X or Y)
C or
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.
base-ten number

17. 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.
The real number a of the complex number z = a + bi
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
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).

18. In the Rectangular Coordinate System - the direction to the right along the horizontal line is
Braces
positive
Set
In Diophantine geometry

19. Has an equal sign (3x+5 = 14)
Algebraic number theory
equation
quadratic field
multiplication

20. Product of 16 and the sum of 5 and number R
Algebraic number theory
16(5+R)
Associative Law of Addition
Number fields

21. A number that has factors other than itself and 1 is a
complex number
algebraic number
In Diophantine geometry
Composite Number

22. 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.
Definition of genus
constant
repeated elements
Forth Axiom of Equality

23. A number is divisible by 6 if it is
even and the sum of its digits is divisible by 3
algebraic number
C or
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .

24. Decreased by
constructing a parallelogram
In Diophantine geometry
subtraction
multiplication

25. 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
Equal
Digits
a complex number is real if and only if it equals its conjugate.
Absolute value and argument

26. One term (5x or 4)
Equal
addition
multiplication
monomial

27. Any number that is not a multiple of 2 is an
Odd Number
rectangular coordinates
Second Axiom of Equality
an equation in two variables defines

28. 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
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.
monomial

29. In the Rectangular Coordinate System - On the vertical line - direction _______ is negative
Odd Number
Absolute value and argument
Downward
addition

30. 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
Associative Law of Addition
In Diophantine geometry
multiplication
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.

31. 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:
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).
addition
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
In Diophantine geometry

32. The central problem of Diophantine geometry is to determine when a Diophantine equation has
addition
solutions
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).
its the sum of its digits is divisible by 3

33. Addition of two complex numbers can be done geometrically by
constructing a parallelogram
magnitude
Digits
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}

34. 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 -
Third Axiom of Equality
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
righthand digit is 0 or 5
right-hand digit is even

35. 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
Place Value Concept
algebraic number
addition
right-hand digit is even

36. Are not necessary. That is - the elements of {2 - 2 - 3 - 4} are simply {2 - 3 - and 4}
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).
repeated elements
division
right-hand digit is even

37. The complex conjugate of the complex number z = x + yi is defined to be x - yi. It is denoted or . Geometrically - is the

38. 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.
the sum of its digits is divisible by 9
quadratic field
Third Axiom of Equality
K+6 - K+5 - K+4 K+3.........answer is K+3

39. Sixteen less than number Q
Members of Elements of the Set
Q-16
monomial
Set

40. The relative greatness of positive and negative numbers
magnitude
a curve - a surface or some other such object in n-dimensional space
base-ten number
solutions

41. 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.
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
Numerals
Commutative Law of Addition

42. 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
its the sum of its digits is divisible by 3
base-ten number
16(5+R)
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.

43. Implies a collection or grouping of similar - objects or symbols.
Complex numbers
a curve - a surface or some other such object in n-dimensional space
Set
To separate a number into prime factors

44. As shown earlier - c - di is the complex conjugate of the denominator c + di.
even and the sum of its digits is divisible by 3
a curve - a surface or some other such object in n-dimensional space
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
constant

45. Any number that is exactly divisible by a given number is a
7
Multiple of the given number
variable
upward

46. This law combines the operations of addition and multiplication. The distribution of a common multiplier among the terms of an additive expression.
Distributive Law
Analytic number theory
consecutive whole numbers
repeated elements

47. More than one term (5x+4 contains two)
repeated elements
negative
Commutative Law of Multiplication
polynomial

48. 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
Positional notation (place value)
subtraction
Associative Law of Addition
F - F+1 - F+2.......answer is F+2

49. 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
Braces
The real number a of the complex number z = a + bi
Algebraic number theory
the number formed by the three right-hand digits is divisible by 8

50. The Arabic numerals from 0 through 9 are called
Digits
variable
In Diophantine geometry
addition