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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.
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.
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. Any number that is not a multiple of 2 is an
Downward
an equation in two variables defines
Odd Number
righthand digit is 0 or 5
2. 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.
Absolute value and argument
Complex numbers
magnitude and direction
right-hand digit is even
3. As shown earlier - c - di is the complex conjugate of the denominator c + di.
monomial
addition
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
Associative Law of Addition
4. Total
addition
In Diophantine geometry
Members of Elements of the Set
Forth Axiom of Equality
5. The number touching the variable (in the case of 5x - would be 5)
coefficient
Prime Factor
expression
righthand digit is 0 or 5
6. The greatest of 3 consecutive whole numbers - the smallest of which is F
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).
In Diophantine geometry
F - F+1 - F+2.......answer is F+2
addition
7. One term (5x or 4)
repeated elements
coefficient
monomial
quadratic field
8. Are used to indicate sets
coefficient
C or
Digits
Braces
9. 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
16(5+R)
even and the sum of its digits is divisible by 3
Positional notation (place value)
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
10. More than
addition
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
Third Axiom of Equality
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
11. 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
Digits
right-hand digit is even
Equal
constant
12. Number T increased by 9
T+9
Associative Law of Multiplication
Inversive geometry
Base of the number system
13. A number is divisible by 4 if
the number formed by the two right-hand digits is divisible by 4
Equal
subtraction
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
14. 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.
Q-16
The numbers are conventionally plotted using the real part
monomial
Absolute value and argument
15. Number X decreased by 12 divided by forty
To separate a number into prime factors
(x-12)/40
Q-16
constructing a parallelogram
16. The central problem of Diophantine geometry is to determine when a Diophantine equation has
Absolute value and argument
Second Axiom of Equality
solutions
magnitude and direction
17. A number is divisible by 9 if
Positional notation (place value)
Third Axiom of Equality
constructing a parallelogram
the sum of its digits is divisible by 9
18. 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
Definition of genus
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
Equal
Associative Law of Multiplication
19. Number symbols
T+9
Numerals
the sum of its digits is divisible by 9
positive
20. Any number that la a multiple of 2 is an
Even Number
Associative Law of Addition
Natural Numbers
Commutative Law of Multiplication
21. Remainder
subtraction
(x-12)/40
addition
the genus of the curve
22. 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
Positional notation (place value)
the genus of the curve
The real number a of the complex number z = a + bi
algebraic number
23. The defining characteristic of a position vector is that it has
T+9
magnitude and direction
Digits
Commutative Law of Multiplication
24. Work on the problem of general polynomials ultimately led to the fundamental theorem of algebra -
Prime Number
addition
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
Even Number
25. LAWS FOR COMBINING NUMBERS
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).
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.
addition
26. 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.)
Commutative Law of Addition
C or
Number fields
addition
27. A number is divisible by 5 if its
Algebraic number theory
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
righthand digit is 0 or 5
Second Axiom of Equality
28. Decreased by
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
(x-12)/40
subtraction
Complex numbers
29. 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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30. Consists of all numbers of the form - where a and b are rational numbers and d is a fixed rational number whose square root is not rational.
the number formed by the three right-hand digits is divisible by 8
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
quadratic field
Equal
31. The set of all complex numbers is denoted by
The multiplication of two complex numbers is defined by the following formula:
C or
The numbers are conventionally plotted using the real part
its the sum of its digits is divisible by 3
32. The finiteness or not of the number of rational or integer points on an algebraic curve
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
Commutative Law of Addition
the genus of the curve
Distributive Law
33. Plus
even and the sum of its digits is divisible by 3
Composite Number
Set
addition
34. 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
Inversive geometry
its the sum of its digits is divisible by 3
Place Value Concept
subtraction
35. An equation - or system of equations - in two or more variables defines
a curve - a surface or some other such object in n-dimensional space
right-hand digit is even
16(5+R)
solutions
36. 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
The multiplication of two complex numbers is defined by the following formula:
Natural Numbers
even and the sum of its digits is divisible by 3
subtraction
37. Any number that can be divided lnto a given number without a remainder is a
order of operations
Definition of genus
Factor of the given number
multiplication
38. The relative greatness of positive and negative numbers
magnitude
Absolute value and argument
Commutative Law of Addition
Algebraic number theory
39. 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
the genus of the curve
the number formed by the two right-hand digits is divisible by 4
In Diophantine geometry
Place Value Concept
40. Are not necessary. That is - the elements of {2 - 2 - 3 - 4} are simply {2 - 3 - and 4}
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
K+6 - K+5 - K+4 K+3.........answer is K+3
multiplication
repeated elements
41. Integers greater than zero and less than 5 form a set - as follows:
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
In Diophantine geometry
Equal
Even Number
42. 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.
Commutative Law of Addition
addition
negative
Third Axiom of Equality
43. In the Rectangular Coordinate System - On the vertical line - direction _______ is negative
addition
base-ten number
Downward
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
44. 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
Commutative Law of Multiplication
Absolute value and argument
(x-12)/40
addition
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.
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
Associative Law of Addition
Algebraic number theory
the number formed by the three right-hand digits is divisible by 8
46. More than one term (5x+4 contains two)
polynomial
multiplication
subtraction
The numbers are conventionally plotted using the real part
47. 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.
upward
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
48. The place value which corresponds to a given position in a number is determined by the
monomial
Base of the number system
Set
upward
49. 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
solutions
complex number
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
difference
50. In the Rectangular Coordinate System - the direction to the left along the horizontal line is
positive
negative
constant
addition
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