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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. In the Rectangular Coordinate System - On the vertical line - direction ________ is positive
F - F+1 - F+2.......answer is F+2
upward
Commutative Law of Addition
subtraction
2. In the Rectangular Coordinate System - the direction to the left along the horizontal line is
(x-12)/40
In Diophantine geometry
its the sum of its digits is divisible by 3
negative
3. 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:
magnitude
Second Axiom of Equality
Commutative Law of Addition
4. An equation - or system of equations - in two or more variables defines
Place Value Concept
Positional notation (place value)
a curve - a surface or some other such object in n-dimensional space
even and the sum of its digits is divisible by 3
5. In the Rectangular Coordinate System - the direction to the right along the horizontal line is
Factor of the given number
To separate a number into prime factors
positive
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
6. Increased by
consecutive whole numbers
positive
addition
Prime Number
7. 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.
a complex number is real if and only if it equals its conjugate.
Associative Law of Multiplication
upward
Algebraic number theory
8. In the Rectangular Coordinate System - On the vertical line - direction _______ is negative
Downward
Composite Number
Digits
an equation in two variables defines
9. First axiom of equality
repeated elements
In Diophantine geometry
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.
Definition of genus
10. 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.
one characteristic in common such as similarity of appearance or purpose
the number formed by the three right-hand digits is divisible by 8
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
Factor of the given number
11. This law combines the operations of addition and multiplication. The distribution of a common multiplier among the terms of an additive expression.
Base of the number system
base-ten number
Distributive Law
order of operations
12. Any number that is not a multiple of 2 is an
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.
an equation in two variables defines
Even Number
Odd Number
13. 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
a complex number is real if and only if it equals its conjugate.
Algebraic number theory
Digits
Absolute value and argument
14. Has an equal sign (3x+5 = 14)
polynomial
Digits
Associative Law of Addition
equation
15. The real and imaginary parts of a complex number can be extracted using the conjugate:
a complex number is real if and only if it equals its conjugate.
Set
magnitude
Commutative Law of Addition
16. 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.
C or
quadratic field
7
F - F+1 - F+2.......answer is F+2
17. Work on the problem of general polynomials ultimately led to the fundamental theorem of algebra -
Numerals
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
repeated elements
Place Value Concept
18. A number is divisible by 4 if
equation
Distributive Law
Second Axiom of Equality
the number formed by the two right-hand digits is divisible by 4
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
subtraction
rectangular coordinates
Composite Number
Positional notation (place value)
20. 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.
Complex numbers
magnitude
constructing a parallelogram
the genus of the curve
21. Plus
multiplication
Algebraic number theory
addition
Set
22. The greatest of 3 consecutive whole numbers - the smallest of which is F
F - F+1 - F+2.......answer is F+2
Numerals
Associative Law of Addition
Associative Law of Addition
23. 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.
Commutative Law of Multiplication
consecutive whole numbers
Members of Elements of the Set
Associative Law of Addition
24. Are not necessary. That is - the elements of {2 - 2 - 3 - 4} are simply {2 - 3 - and 4}
Composite Number
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
difference
repeated elements
25. Product
To separate a number into prime factors
multiplication
addition
constant
26. The number touching the variable (in the case of 5x - would be 5)
constructing a parallelogram
Commutative Law of Multiplication
monomial
coefficient
27. The relative greatness of positive and negative numbers
Third Axiom of Equality
magnitude
right-hand digit is even
variable
28. 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
Members of Elements of the Set
The real number a of the complex number z = a + bi
7
Numerals
29. 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
complex number
the sum of its digits is divisible by 9
an equation in two variables defines
solutions
30. Any number that la a multiple of 2 is an
Number fields
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
positive
Even Number
31. The numbers which are used for counting in our number system are sometimes called
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 genus of the curve
Natural Numbers
Algebraic number theory
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
the genus of the curve
base-ten number
Commutative Law of Addition
33. Addition of two complex numbers can be done geometrically by
Even Number
constructing a parallelogram
Multiple of the given number
the sum of its digits is divisible by 9
34. The objects in a set have at least
addition
one characteristic in common such as similarity of appearance or purpose
The real number a of the complex number z = a + bi
addition
35. A branch of geometry studying more general reflections than ones about a line - can also be expressed in terms of complex numbers.
Inversive geometry
quadratic field
monomial
upward
36. Quotient
division
Forth Axiom of Equality
Numerals
the genus of the curve
37. The complex conjugate of the complex number z = x + yi is defined to be x - yi. It is denoted or . Geometrically - is the
38. No short method has been found for determining whether a number is divisible by
7
coefficient
In Diophantine geometry
variable
39. The objects or symbols in a set are called Numerals - Lines - or Points
rectangular coordinates
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
Members of Elements of the Set
Numerals
40. A number that has no factors except itself and 1 is a
Members of Elements of the Set
Prime Number
a curve - a surface or some other such object in n-dimensional space
Natural Numbers
41. Are used to indicate sets
even and the sum of its digits is divisible by 3
the number formed by the two right-hand digits is divisible by 4
Braces
Associative Law of Multiplication
42. Any number that is exactly divisible by a given number is a
Complex numbers
Multiple of the given number
In Diophantine geometry
7
43. Implies a collection or grouping of similar - objects or symbols.
consecutive whole numbers
subtraction
the number formed by the three right-hand digits is divisible by 8
Set
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.
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
its the sum of its digits is divisible by 3
negative
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
45. 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.
Forth Axiom of Equality
coefficient
monomial
Prime Number
46. As shown earlier - c - di is the complex conjugate of the denominator c + di.
Composite Number
Associative Law of Multiplication
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
Base of the number system
47. A number is divisible by 2 if
Inversive geometry
righthand digit is 0 or 5
right-hand digit is even
Digits
48. A number is divisible by 5 if its
F - F+1 - F+2.......answer is F+2
righthand digit is 0 or 5
Braces
magnitude and direction
49. Does not have an equal sign (3x+5) (2a+9b)
Members of Elements of the Set
consecutive whole numbers
Odd Number
expression
50. 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.
coefficient
even and the sum of its digits is divisible by 3
monomial
The numbers are conventionally plotted using the real part