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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. One term (5x or 4)
Equal
7
subtraction
monomial
2. This law combines the operations of addition and multiplication. The distribution of a common multiplier among the terms of an additive expression.
a curve - a surface or some other such object in n-dimensional space
variable
Distributive Law
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
3. LAWS FOR COMBINING NUMBERS
one characteristic in common such as similarity of appearance or purpose
variable
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
4. 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
the genus of the curve
the number formed by the two right-hand digits is divisible by 4
Place Value Concept
order of operations
5. The finiteness or not of the number of rational or integer points on an algebraic curve
base-ten number
complex number
the genus of the curve
subtraction
6. 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.
solutions
The numbers are conventionally plotted using the real part
Commutative Law of Addition
addition
7. The smallest of four sonsecutive whole numbers - the biggest of which is K+6
K+6 - K+5 - K+4 K+3.........answer is K+3
Commutative Law of Addition
The multiplication of two complex numbers is defined by the following formula:
(x-12)/40
8. The defining characteristic of a position vector is that it has
The real number a of the complex number z = a + bi
negative
T+9
magnitude and direction
9. The objects in a set have at least
difference
the number formed by the three right-hand digits is divisible by 8
polynomial
one characteristic in common such as similarity of appearance or purpose
10. More than
subtraction
subtraction
addition
C or
11. 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
Numerals
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).
Associative Law of Addition
In Diophantine geometry
12. Viewed in this way the multiplication of a complex number by i corresponds to rotating a complex number
even and the sum of its digits is divisible by 3
counterclockwise through 90
7
equation
13. Sum
(x-12)/40
Members of Elements of the Set
addition
constructing a parallelogram
14. The greatest of 3 consecutive whole numbers - the smallest of which is F
Analytic number theory
Factor of the given number
F - F+1 - F+2.......answer is F+2
addition
15. 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
Multiple of the given number
Second Axiom of Equality
addition
complex number
16. Increased by
Second Axiom of Equality
Equal
addition
variable
17. Any number that is exactly divisible by a given number is a
Second Axiom of Equality
Associative Law of Addition
Multiple of the given number
Set
18. 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
addition
C or
addition
Absolute value and argument
19. 2 -3 -4 -5 -6
constructing a parallelogram
consecutive whole numbers
the genus of the curve
counterclockwise through 90
20. The relative greatness of positive and negative numbers
F - F+1 - F+2.......answer is F+2
magnitude
monomial
subtraction
21. Less than
Numerals
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
subtraction
Base of the number system
22. 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.
Associative Law of Multiplication
Second Axiom of Equality
equation
Odd Number
23. A number is divisible by 9 if
Associative Law of Multiplication
Complex numbers
the sum of its digits is divisible by 9
(x-12)/40
24. 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.
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
Associative Law of Addition
Third Axiom of Equality
consecutive whole numbers
25. 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
Place Value Concept
algebraic number
To separate a number into prime factors
a complex number is real if and only if it equals its conjugate.
26. Plus
In Diophantine geometry
addition
K+6 - K+5 - K+4 K+3.........answer is K+3
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
27. 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)
Third Axiom of Equality
Inversive geometry
Braces
28. 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.
To separate a number into prime factors
K+6 - K+5 - K+4 K+3.........answer is K+3
Second Axiom of Equality
Commutative Law of Multiplication
29. The central problem of Diophantine geometry is to determine when a Diophantine equation has
Number fields
solutions
Associative Law of Addition
Third Axiom of Equality
30. In the Rectangular Coordinate System - the direction to the right along the horizontal line is
negative
Multiple of the given number
positive
solutions
31. 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.
Third Axiom of Equality
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.
constructing a parallelogram
32. 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
Equal
Composite Number
Associative Law of Multiplication
quadratic field
33. A number is divisible by 2 if
Commutative Law of Addition
subtraction
right-hand digit is even
positive
34. 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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35. Decreased by
Second Axiom of Equality
subtraction
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
order of operations
36. 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.
variable
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
Forth Axiom of Equality
expression
37. 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.)
addition
Equal
Number fields
Positional notation (place value)
38. A curve in the plane
an equation in two variables defines
To separate a number into prime factors
Numerals
solutions
39. 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.
Commutative Law of Addition
a complex number is real if and only if it equals its conjugate.
upward
division
40. 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
base-ten number
a curve - a surface or some other such object in n-dimensional space
The numbers are conventionally plotted using the real part
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
41. Sixteen less than number Q
Positional notation (place value)
order of operations
constant
Q-16
42. 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.
Second Axiom of Equality
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
Inversive geometry
Associative Law of Addition
43. 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.
equation
Forth Axiom of Equality
Base of the number system
Complex numbers
44. 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.
F - F+1 - F+2.......answer is F+2
rectangular coordinates
Second Axiom of Equality
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
45. This formula can be used to compute the multiplicative inverse of a complex number if it is given in
addition
Positional notation (place value)
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
rectangular coordinates
46. A number is divisible by 6 if it is
Absolute value and argument
equation
complex number
even and the sum of its digits is divisible by 3
47. Any number that la a multiple of 2 is an
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
righthand digit is 0 or 5
Even Number
subtraction
48. No short method has been found for determining whether a number is divisible by
Set
Complex numbers
Q-16
7
49. Integers greater than zero and less than 5 form a set - as follows:
addition
Associative Law of Addition
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
In Diophantine geometry
50. 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
a curve - a surface or some other such object in n-dimensional space
Natural Numbers
addition