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Test your basic knowledge |
CLEP General Mathematics: Number Systems And Sets
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Subjects
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clep
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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. Decreased by
division
In Diophantine geometry
Inversive geometry
subtraction
2. A number is divisible by 2 if
Commutative Law of Addition
To separate a number into prime factors
In Diophantine geometry
right-hand digit is even
3. 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
Natural Numbers
To separate a number into prime factors
Multiple of the given number
Second Axiom of Equality
4. The greatest of 3 consecutive whole numbers - the smallest of which is F
F - F+1 - F+2.......answer is F+2
Distributive Law
the sum of its digits is divisible by 9
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.
5. A branch of geometry studying more general reflections than ones about a line - can also be expressed in terms of complex numbers.
Commutative Law of Addition
Braces
order of operations
Inversive geometry
6. If a factor of a number is prime - it is called a
the sum of its digits is divisible by 9
Complex numbers
Prime Factor
Positional notation (place value)
7. 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.
right-hand digit is even
The multiplication of two complex numbers is defined by the following formula:
Even Number
8. A number that has no factors except itself and 1 is a
addition
Forth Axiom of Equality
Prime Number
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
9. G - E - M - A Grouping - Exponents - Multiply/Divide - Add/Subtract
F - F+1 - F+2.......answer is F+2
addition
order of operations
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).
10. Integers greater than zero and less than 5 form a set - as follows:
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
right-hand digit is even
its the sum of its digits is divisible by 3
11. 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
Second Axiom of Equality
Definition of genus
constant
consecutive whole numbers
12. A number that has factors other than itself and 1 is a
subtraction
Composite Number
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.
a curve - a surface or some other such object in n-dimensional space
13. As shown earlier - c - di is the complex conjugate of the denominator c + di.
the number formed by the three right-hand digits is divisible by 8
Second Axiom of Equality
addition
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
14. 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
its the sum of its digits is divisible by 3
monomial
Q-16
In Diophantine geometry
15. A number is divisible by 6 if it is
even and the sum of its digits is divisible by 3
righthand digit is 0 or 5
F - F+1 - F+2.......answer is F+2
Definition of genus
16. Are not necessary. That is - the elements of {2 - 2 - 3 - 4} are simply {2 - 3 - and 4}
repeated elements
solutions
Commutative Law of Addition
righthand digit is 0 or 5
17. Are used to indicate sets
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).
Braces
equation
constant
18. 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.
Natural Numbers
Complex numbers
monomial
Third Axiom of Equality
19. 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)
magnitude
expression
The numbers are conventionally plotted using the real part
20. The smallest of four sonsecutive whole numbers - the biggest of which is K+6
Second Axiom of Equality
Base of the number system
Digits
K+6 - K+5 - K+4 K+3.........answer is K+3
21. The relative greatness of positive and negative numbers
magnitude
Second Axiom of Equality
quadratic field
complex number
22. The central problem of Diophantine geometry is to determine when a Diophantine equation has
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.
solutions
Commutative Law of Addition
23. Less than
subtraction
Digits
Even Number
constant
24. 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
Numerals
repeated elements
The real number a of the complex number z = a + bi
Distributive Law
25. The number without a variable (5m+2). In this case - 2
constant
Prime Factor
Forth Axiom of Equality
Inversive geometry
26. 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.
The numbers are conventionally plotted using the real part
order of operations
Analytic number theory
Members of Elements of the Set
27. Total
solutions
addition
C or
the number formed by the two right-hand digits is divisible by 4
28. Sum
Number fields
addition
subtraction
Members of Elements of the Set
29. 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
Algebraic number theory
base-ten number
Complex numbers
constructing a parallelogram
30. 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.
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
subtraction
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).
The numbers are conventionally plotted using the real part
31. A number is divisible by 8 if
the number formed by the two right-hand digits is divisible by 4
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
the number formed by the three right-hand digits is divisible by 8
upward
32. Product
even and the sum of its digits is divisible by 3
repeated elements
expression
multiplication
33. Implies a collection or grouping of similar - objects or symbols.
Commutative Law of Multiplication
its the sum of its digits is divisible by 3
an equation in two variables defines
Set
34. Work on the problem of general polynomials ultimately led to the fundamental theorem of algebra -
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
Algebraic number theory
Numerals
35. The set of all complex numbers is denoted by
difference
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
C or
constant
36. Does not have an equal sign (3x+5) (2a+9b)
a curve - a surface or some other such object in n-dimensional space
addition
expression
Number fields
37. 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.
subtraction
right-hand digit is even
upward
38. 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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39. 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.
Set
Associative Law of Addition
quadratic field
F - F+1 - F+2.......answer is F+2
40. The place value which corresponds to a given position in a number is determined by the
Base of the number system
addition
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
Second Axiom of Equality
41. The numbers which are used for counting in our number system are sometimes called
Third Axiom of Equality
Associative Law of Addition
Natural Numbers
Place Value Concept
42. More than one term (5x+4 contains two)
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
a complex number is real if and only if it equals its conjugate.
polynomial
consecutive whole numbers
43. 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:
Associative Law of Addition
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
44. Remainder
counterclockwise through 90
In Diophantine geometry
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
subtraction
45. The objects or symbols in a set are called Numerals - Lines - or Points
repeated elements
The real number a of the complex number z = a + bi
order of operations
Members of Elements of the Set
46. The finiteness or not of the number of rational or integer points on an algebraic curve
Third Axiom of Equality
right-hand digit is even
the genus of the curve
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
47. Any number that is not a multiple of 2 is an
7
algebraic number
Odd Number
equation
48. 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
Third Axiom of Equality
addition
Downward
49. In the Rectangular Coordinate System - On the vertical line - direction ________ is positive
variable
addition
upward
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
50. 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 real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
In Diophantine geometry
Third Axiom of Equality
Associative Law of Addition
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