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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. 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.
Members of Elements of the Set
Commutative Law of Multiplication
solutions
Second Axiom of Equality
2. 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
a curve - a surface or some other such object in n-dimensional space
the number formed by the two right-hand digits is divisible by 4
upward
Definition of genus
3. Number T increased by 9
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
T+9
Definition of genus
negative
4. 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
even and the sum of its digits is divisible by 3
(x-12)/40
Equal
In Diophantine geometry
5. Plus
Equal
Associative Law of Addition
The multiplication of two complex numbers is defined by the following formula:
addition
6. Any number that is not a multiple of 2 is an
Odd Number
T+9
The real number a of the complex number z = a + bi
repeated elements
7. Any number that can be divided lnto a given number without a remainder is a
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).
Factor of the given number
difference
The real number a of the complex number z = a + bi
8. This formula can be used to compute the multiplicative inverse of a complex number if it is given in
even and the sum of its digits is divisible by 3
rectangular coordinates
addition
monomial
9. Total
Distributive Law
addition
Associative Law of Addition
constructing a parallelogram
10. This law combines the operations of addition and multiplication. The distribution of a common multiplier among the terms of an additive expression.
Associative Law of Multiplication
Distributive Law
Third Axiom of Equality
Prime Number
11. 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.
Complex numbers
In Diophantine geometry
Positional notation (place value)
Forth Axiom of Equality
12. A number is divisible by 9 if
addition
an equation in two variables defines
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
the sum of its digits is divisible by 9
13. Product
magnitude
multiplication
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
Number fields
14. Are used to indicate sets
Odd Number
Braces
the sum of its digits is divisible by 9
Associative Law of Multiplication
15. A branch of geometry studying more general reflections than ones about a line - can also be expressed in terms of complex numbers.
Place Value Concept
constructing a parallelogram
Inversive geometry
addition
16. In the Rectangular Coordinate System - the direction to the right along the horizontal line is
positive
Commutative Law of Addition
its the sum of its digits is divisible by 3
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
17. 2 -3 -4 -5 -6
a curve - a surface or some other such object in n-dimensional space
Associative Law of Addition
monomial
consecutive whole numbers
18. In the Rectangular Coordinate System - On the vertical line - direction _______ is negative
Commutative Law of Addition
The numbers are conventionally plotted using the real part
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
Downward
19. 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
Absolute value and argument
Prime Factor
Associative Law of Addition
constant
20. Subtraction
difference
negative
Downward
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.
21. A number that has factors other than itself and 1 is a
Composite Number
addition
the number formed by the three right-hand digits is divisible by 8
Definition of genus
22. The numbers which are used for counting in our number system are sometimes called
Natural Numbers
Q-16
Even Number
Number fields
23. A curve in the plane
Prime Number
the sum of its digits is divisible by 9
variable
an equation in two variables defines
24. The objects or symbols in a set are called Numerals - Lines - or Points
Members of Elements of the Set
constant
a complex number is real if and only if it equals its conjugate.
equation
25. Decreased by
Composite Number
subtraction
the sum of its digits is divisible by 9
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
26. Does not have an equal sign (3x+5) (2a+9b)
C or
addition
expression
quadratic field
27. An equation - or system of equations - in two or more variables defines
its the sum of its digits is divisible by 3
Commutative Law of Addition
Factor of the given number
a curve - a surface or some other such object in n-dimensional space
28. The central problem of Diophantine geometry is to determine when a Diophantine equation has
solutions
a curve - a surface or some other such object in n-dimensional space
C or
addition
29. A number is divisible by 2 if
equation
Definition of genus
right-hand digit is even
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
30. The defining characteristic of a position vector is that it has
its the sum of its digits is divisible by 3
magnitude and direction
Braces
base-ten number
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.
magnitude and direction
Associative Law of Addition
Downward
Equal
32. 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.
subtraction
Odd Number
Commutative Law of Addition
Associative Law of Addition
33. The sum of two complex numbers A and B - interpreted as points of the complex plane - is the point X obtained by building a parallelogram three of whose vertices are O - A and B. Equivalently - X is the point such that the triangles with vertices O -
Distributive Law
Third Axiom of Equality
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
Commutative Law of Multiplication
34. 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.
magnitude
Natural Numbers
C or
Associative Law of Addition
35. More than
addition
expression
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
one characteristic in common such as similarity of appearance or purpose
36. A number is divisible by 3 if
Natural Numbers
constant
algebraic number
its the sum of its digits is divisible by 3
37. The smallest of four sonsecutive whole numbers - the biggest of which is K+6
Prime Number
positive
K+6 - K+5 - K+4 K+3.........answer is K+3
Complex numbers
38. In the Rectangular Coordinate System - On the vertical line - direction ________ is positive
Algebraic number theory
upward
Prime Number
positive
39. The number without a variable (5m+2). In this case - 2
constant
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
subtraction
consecutive whole numbers
40. Product of 16 and the sum of 5 and number R
addition
addition
the genus of the curve
16(5+R)
41. Less than
subtraction
Downward
K+6 - K+5 - K+4 K+3.........answer is K+3
the number formed by the three right-hand digits is divisible by 8
42. 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.
Positional notation (place value)
Base of the number system
base-ten number
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
43. If a factor of a number is prime - it is called a
Prime Number
expression
addition
Prime Factor
44. Viewed in this way the multiplication of a complex number by i corresponds to rotating a complex number
counterclockwise through 90
Third Axiom of Equality
coefficient
addition
45. The number touching the variable (in the case of 5x - would be 5)
coefficient
constructing a parallelogram
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
positive
46. Any number that la a multiple of 2 is an
Number fields
Third Axiom of Equality
Members of Elements of the Set
Even Number
47. A number is divisible by 8 if
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
the number formed by the three right-hand digits is divisible by 8
order of operations
Forth Axiom of Equality
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.)
equation
Number fields
base-ten number
Members of Elements of the Set
49. First axiom of equality
Q-16
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.
7
Members of Elements of the Set
50. 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.
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
Inversive geometry
repeated elements
Analytic number theory