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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. 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.
Commutative Law of Addition
Complex 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).
Equal
2. Any number that can be divided lnto a given number without a remainder is a
Forth Axiom of Equality
Factor of the given number
order of operations
upward
3. 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.
Commutative Law of Addition
multiplication
difference
Second Axiom of Equality
4. 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.
rectangular coordinates
Commutative Law of Multiplication
subtraction
repeated elements
5. Are used to indicate sets
quadratic field
Prime Factor
Braces
Set
6. A letter tat represents a number that is unknown (usually X or Y)
16(5+R)
Absolute value and argument
Third Axiom of Equality
variable
7. Is any complex number that is a solution to some polynomial equation with rational coefficients; for example - every solution x of (say) is an algebraic number. Fields of algebraic numbers are also called algebraic number fields - or shortly number f
a curve - a surface or some other such object in n-dimensional space
Q-16
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
algebraic number
8. The set of all complex numbers is denoted by
C or
In Diophantine geometry
addition
negative
9. The number touching the variable (in the case of 5x - would be 5)
Downward
one characteristic in common such as similarity of appearance or purpose
coefficient
The multiplication of two complex numbers is defined by the following formula:
10. The place value which corresponds to a given position in a number is determined by the
counterclockwise through 90
a curve - a surface or some other such object in n-dimensional space
Base of the number system
Factor of the given number
11. 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 elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
the sum of its digits is divisible by 9
Third Axiom of Equality
Prime Factor
12. Viewed in this way the multiplication of a complex number by i corresponds to rotating a complex number
counterclockwise through 90
Commutative Law of Multiplication
To separate a number into prime factors
division
13. In the Rectangular Coordinate System - On the vertical line - direction _______ is negative
Downward
upward
addition
T+9
14. Any number that is exactly divisible by a given number is a
addition
Multiple of the given number
Prime Number
7
15. 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
Q-16
quadratic field
To separate a number into prime factors
Composite Number
16. If a factor of a number is prime - it is called a
The real number a of the complex number z = a + bi
Prime Factor
expression
Base of the number system
17. The greatest of 3 consecutive whole numbers - the smallest of which is F
consecutive whole numbers
F - F+1 - F+2.......answer is F+2
repeated elements
Odd Number
18. No short method has been found for determining whether a number is divisible by
7
even and the sum of its digits is divisible by 3
quadratic field
expression
19. 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.
Positional notation (place value)
magnitude and direction
Braces
quadratic field
20. A number is divisible by 5 if its
repeated elements
righthand digit is 0 or 5
variable
Members of Elements of the Set
21. 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.
base-ten number
The numbers are conventionally plotted using the real part
Braces
Natural Numbers
22. Does not have an equal sign (3x+5) (2a+9b)
C or
expression
Downward
the number formed by the two right-hand digits is divisible by 4
23. LAWS FOR COMBINING NUMBERS
quadratic field
repeated elements
T+9
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
24. In the Rectangular Coordinate System - the direction to the left along the horizontal line is
The real number a of the complex number z = a + bi
Prime Factor
negative
Complex numbers
25. 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.
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
expression
Associative Law of Addition
the sum of its digits is divisible by 9
26. Any number that is not a multiple of 2 is an
To separate a number into prime factors
Odd Number
algebraic number
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
27. This formula can be used to compute the multiplicative inverse of a complex number if it is given in
Downward
In Diophantine geometry
rectangular coordinates
equation
28. More than one term (5x+4 contains two)
(x-12)/40
algebraic number
polynomial
Composite Number
29. A number is divisible by 2 if
In Diophantine geometry
right-hand digit is even
positive
Factor of the given number
30. Quotient
division
Multiple of the given number
subtraction
Factor of the given number
31. Product of 16 and the sum of 5 and number R
consecutive whole numbers
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
16(5+R)
Natural Numbers
32. 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 -
Digits
Definition of genus
righthand digit is 0 or 5
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
33. A branch of geometry studying more general reflections than ones about a line - can also be expressed in terms of complex numbers.
Downward
Inversive geometry
coefficient
Natural Numbers
34. Increased by
Q-16
addition
the genus of the curve
quadratic field
35. First axiom of equality
Commutative Law of Addition
quadratic field
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.
addition
36. Remainder
difference
quadratic field
subtraction
variable
37. The central problem of Diophantine geometry is to determine when a Diophantine equation has
Inversive geometry
Set
solutions
righthand digit is 0 or 5
38. The objects or symbols in a set are called Numerals - Lines - or Points
addition
Members of Elements of the Set
Analytic number theory
addition
39. 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
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
Set
Equal
Commutative Law of Multiplication
40. Sixteen less than number Q
righthand digit is 0 or 5
addition
In Diophantine geometry
Q-16
41. A number is divisible by 6 if it is
Prime Factor
an equation in two variables defines
even and the sum of its digits is divisible by 3
the number formed by the three right-hand digits is divisible by 8
42. In the Rectangular Coordinate System - On the vertical line - direction ________ is positive
Factor of the given number
right-hand digit is even
upward
expression
43. The Arabic numerals from 0 through 9 are called
addition
16(5+R)
subtraction
Digits
44. Implies a collection or grouping of similar - objects or symbols.
Set
Prime Number
C or
F - F+1 - F+2.......answer is F+2
45. A number that has factors other than itself and 1 is a
Composite Number
complex number
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
addition
46. These are emphasised in a complex number's polar form and it turns out notably that the operations of addition and multiplication take on a very natural geometric character when complex numbers are viewed as position vectors:
Set
constructing a parallelogram
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).
polynomial
47. Sum
Prime Number
addition
constructing a parallelogram
division
48. 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
Associative Law of Addition
quadratic field
Commutative Law of Addition
49. 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.
the genus of the curve
Commutative Law of Addition
constructing a parallelogram
Third Axiom of Equality
50. The smallest of four sonsecutive whole numbers - the biggest of which is K+6
Inversive geometry
Algebraic number theory
Commutative Law of Addition
K+6 - K+5 - K+4 K+3.........answer is K+3