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Test your basic knowledge |
CLEP General Mathematics: Number Systems And Sets
Start Test
Study First
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. The relative greatness of positive and negative numbers
C or
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
subtraction
magnitude
2. The finiteness or not of the number of rational or integer points on an algebraic curve
the genus of the curve
K+6 - K+5 - K+4 K+3.........answer is K+3
quadratic field
Commutative Law of Addition
3. 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.
Forth Axiom of Equality
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
Absolute value and argument
Commutative Law of Multiplication
4. The smallest of four sonsecutive whole numbers - the biggest of which is K+6
In Diophantine geometry
polynomial
The real number a of the complex number z = a + bi
K+6 - K+5 - K+4 K+3.........answer is K+3
5. Number symbols
constant
multiplication
addition
Numerals
6. Addition of two complex numbers can be done geometrically by
Algebraic number theory
order of operations
Odd Number
constructing a parallelogram
7. Is called the real part of z - and the real number b is often called the imaginary part. By this convention the imaginary part is a real number - not including the imaginary unit: hence b - not bi - is the imaginary part. (Others - however call bi th
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: .
Second Axiom of Equality
subtraction
8. More than one term (5x+4 contains two)
addition
polynomial
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
Third Axiom of Equality
9. Any number that la a multiple of 2 is an
Even Number
Forth Axiom of Equality
addition
C or
10. In the Rectangular Coordinate System - On the vertical line - direction ________ is positive
Absolute value and argument
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
upward
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.
11. A curve in the plane
difference
subtraction
the number formed by the two right-hand digits is divisible by 4
an equation in two variables defines
12. Does not have an equal sign (3x+5) (2a+9b)
To separate a number into prime factors
subtraction
quadratic field
expression
13. 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
positive
the number formed by the three right-hand digits is divisible by 8
(x-12)/40
The multiplication of two complex numbers is defined by the following formula:
14. 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.
Distributive Law
Associative Law of Multiplication
In Diophantine geometry
Complex numbers
15. Sum
addition
monomial
one characteristic in common such as similarity of appearance or purpose
coefficient
16. A number is divisible by 4 if
magnitude and direction
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 two right-hand digits is divisible by 4
Multiple of the given number
17. 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
subtraction
addition
Equal
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.
18. Are used to indicate sets
Commutative Law of Multiplication
difference
coefficient
Braces
19. 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.
16(5+R)
Commutative Law of Addition
quadratic field
Prime Factor
20. The greatest of 3 consecutive whole numbers - the smallest of which is F
Analytic number theory
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
F - F+1 - F+2.......answer is F+2
even and the sum of its digits is divisible by 3
21. No short method has been found for determining whether a number is divisible by
addition
C or
positive
7
22. 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.
coefficient
The numbers are conventionally plotted using the real part
multiplication
Downward
23. The number touching the variable (in the case of 5x - would be 5)
Analytic number theory
coefficient
Number fields
right-hand digit is even
24. A letter tat represents a number that is unknown (usually X or Y)
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
16(5+R)
magnitude and direction
variable
25. 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 Multiplication
The multiplication of two complex numbers is defined by the following formula:
Distributive Law
In Diophantine geometry
26. As shown earlier - c - di is the complex conjugate of the denominator c + di.
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
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
monomial
27. One term (5x or 4)
addition
monomial
base-ten number
addition
28. In the Rectangular Coordinate System - On the vertical line - direction _______ is negative
Second Axiom of Equality
quadratic field
Downward
right-hand digit is even
29. The central problem of Diophantine geometry is to determine when a Diophantine equation has
Positional notation (place value)
Commutative Law of Addition
magnitude and direction
solutions
30. The Arabic numerals from 0 through 9 are called
Braces
Digits
16(5+R)
C or
31. 2 -3 -4 -5 -6
consecutive whole numbers
the number formed by the two right-hand digits is divisible by 4
Base of the number system
Analytic number theory
32. Are not necessary. That is - the elements of {2 - 2 - 3 - 4} are simply {2 - 3 - and 4}
addition
order of operations
repeated elements
In Diophantine geometry
33. This law combines the operations of addition and multiplication. The distribution of a common multiplier among the terms of an additive expression.
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: .
Distributive Law
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.
34. Decreased by
subtraction
magnitude
Digits
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
35. 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
The multiplication of two complex numbers is defined by the following formula:
Algebraic number theory
constant
base-ten number
36. Viewed in this way the multiplication of a complex number by i corresponds to rotating a complex number
complex number
Commutative Law of Multiplication
upward
counterclockwise through 90
37. This formula can be used to compute the multiplicative inverse of a complex number if it is given in
To separate a number into prime factors
rectangular coordinates
Numerals
positive
38. Product
polynomial
Number fields
addition
multiplication
39. The place value which corresponds to a given position in a number is determined by the
negative
the number formed by the three right-hand digits is divisible by 8
Base of the number system
algebraic number
40. 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 real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
Commutative Law of Multiplication
complex number
righthand digit is 0 or 5
41. First axiom of equality
multiplication
the sum of its digits is divisible by 9
constant
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. A number is divisible by 2 if
Commutative Law of Addition
addition
the genus of the curve
right-hand digit is even
43. The number without a variable (5m+2). In this case - 2
subtraction
Prime Factor
constant
Definition of genus
44. 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.
Associative Law of Addition
Commutative Law of Addition
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
Analytic number theory
45. In the Rectangular Coordinate System - the direction to the left along the horizontal line is
Commutative Law of Addition
Place Value Concept
negative
division
46. 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
Commutative Law of Multiplication
Absolute value and argument
In Diophantine geometry
difference
47. Subtraction
difference
(x-12)/40
Members of Elements of the Set
Q-16
48. Begin by taking out the smallest factor If the number is even - take out all the 2's first - then try 3 as a factor
To separate a number into prime factors
division
In Diophantine geometry
multiplication
49. Product of 16 and the sum of 5 and number R
addition
16(5+R)
K+6 - K+5 - K+4 K+3.........answer is K+3
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).
50. A number is divisible by 8 if
the number formed by the three right-hand digits is divisible by 8
Associative Law of Addition
F - F+1 - F+2.......answer is F+2
Associative Law of Addition