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Test your basic knowledge |
CLEP General Mathematics: Number Systems And Sets
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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. A number is divisible by 2 if
right-hand digit is even
Factor of the given number
Braces
an equation in two variables defines
2. If a factor of a number is prime - it is called a
Second Axiom of Equality
Prime Factor
negative
Complex numbers
3. 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.
Analytic number theory
Commutative Law of Multiplication
counterclockwise through 90
Numerals
4. A curve in the plane
Analytic number theory
an equation in two variables defines
addition
difference
5. In the Rectangular Coordinate System - the direction to the right along the horizontal line is
positive
division
righthand digit is 0 or 5
In Diophantine geometry
6. The defining characteristic of a position vector is that it has
polynomial
Associative Law of Addition
7
magnitude and direction
7. 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
Numerals
Associative Law of Multiplication
the genus of the curve
8. Implies a collection or grouping of similar - objects or symbols.
Members of Elements of the Set
right-hand digit is even
Set
the genus of the curve
9. 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
Even Number
subtraction
Place Value Concept
upward
10. 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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11. 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.
upward
Third Axiom of Equality
Associative Law of Multiplication
12. Are not necessary. That is - the elements of {2 - 2 - 3 - 4} are simply {2 - 3 - and 4}
Odd Number
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
repeated elements
right-hand digit is even
13. A number is divisible by 3 if
the genus of the curve
its the sum of its digits is divisible by 3
In Diophantine geometry
Commutative Law of Addition
14. An equation - or system of equations - in two or more variables defines
Commutative Law of Addition
a curve - a surface or some other such object in n-dimensional space
subtraction
Digits
15. LAWS FOR COMBINING NUMBERS
Associative Law of Addition
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
difference
addition
16. 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
Place Value Concept
Absolute value and argument
Factor of the given number
negative
17. 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
the number formed by the two right-hand digits is divisible by 4
To separate a number into prime factors
complex number
In Diophantine geometry
18. 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 elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
Second Axiom of Equality
Positional notation (place value)
an equation in two variables defines
19. 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
Algebraic number theory
In Diophantine geometry
Commutative Law of Addition
equation
20. Number T increased by 9
magnitude and direction
F - F+1 - F+2.......answer is F+2
T+9
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
21. 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.
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.
counterclockwise through 90
Analytic number theory
22. Product of 16 and the sum of 5 and number R
Forth Axiom of Equality
16(5+R)
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
Multiple of the given number
23. This law states that the sum of two or more addends is the same regardless of the order in which they are arranged. Means to change - substitute or move from place to place.
positive
Even Number
Commutative Law of Addition
coefficient
24. As shown earlier - c - di is the complex conjugate of the denominator c + di.
counterclockwise through 90
Second Axiom of Equality
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
The real number a of the complex number z = a + bi
25. Quotient
division
magnitude and direction
even and the sum of its digits is divisible by 3
rectangular coordinates
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
subtraction
Definition of genus
Place Value Concept
In Diophantine geometry
27. A letter tat represents a number that is unknown (usually X or Y)
Composite Number
Positional notation (place value)
16(5+R)
variable
28. This formula can be used to compute the multiplicative inverse of a complex number if it is given in
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
Complex numbers
rectangular coordinates
addition
29. Work on the problem of general polynomials ultimately led to the fundamental theorem of algebra -
monomial
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
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:
30. 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
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
base-ten number
variable
the sum of its digits is divisible by 9
31. 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.
Set
The multiplication of two complex numbers is defined by the following formula:
Third Axiom of Equality
Associative Law of Multiplication
32. Does not have an equal sign (3x+5) (2a+9b)
Multiple of the given number
expression
upward
In Diophantine geometry
33. 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 real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
Definition of genus
repeated elements
34. More than one term (5x+4 contains two)
To separate a number into prime factors
Composite Number
polynomial
T+9
35. Any number that is not a multiple of 2 is an
In Diophantine geometry
Even Number
Odd Number
Braces
36. G - E - M - A Grouping - Exponents - Multiply/Divide - Add/Subtract
order of operations
division
The numbers are conventionally plotted using the real part
solutions
37. Product
Absolute value and argument
multiplication
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
38. The finiteness or not of the number of rational or integer points on an algebraic curve
positive
the genus of the curve
Members of Elements of the Set
addition
39. Number symbols
righthand digit is 0 or 5
Numerals
Positional notation (place value)
Prime Factor
40. The central problem of Diophantine geometry is to determine when a Diophantine equation has
solutions
7
magnitude and direction
Factor of the given number
41. This law combines the operations of addition and multiplication. The distribution of a common multiplier among the terms of an additive expression.
F - F+1 - F+2.......answer is F+2
Distributive Law
negative
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.
42. 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
In Diophantine geometry
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.
addition
43. 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.
the genus of the curve
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.
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
44. In the Rectangular Coordinate System - the direction to the left along the horizontal line is
subtraction
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
Complex numbers
negative
45. 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.
right-hand digit is even
addition
Associative Law of Multiplication
Base of the number system
46. Viewed in this way the multiplication of a complex number by i corresponds to rotating a complex number
Commutative Law of Addition
the number formed by the three right-hand digits is divisible by 8
counterclockwise through 90
The multiplication of two complex numbers is defined by the following formula:
47. Sixteen less than number Q
Q-16
order of operations
monomial
Commutative Law of Multiplication
48. The Arabic numerals from 0 through 9 are called
Algebraic number theory
Commutative Law of Multiplication
addition
Digits
49. Total
addition
Distributive Law
Second Axiom of Equality
even and the sum of its digits is divisible by 3
50. The set of all complex numbers is denoted by
addition
a complex number is real if and only if it equals its conjugate.
the sum of its digits is divisible by 9
C or