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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. More than one term (5x+4 contains two)
polynomial
Even Number
Multiple of the given number
repeated elements
2. 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.
Complex numbers
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
quadratic field
3. A number is divisible by 4 if
righthand digit is 0 or 5
Equal
In Diophantine geometry
the number formed by the two right-hand digits is divisible by 4
4. 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.
a complex number is real if and only if it equals its conjugate.
Set
The numbers are conventionally plotted using the real part
coefficient
5. 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
Factor of the given number
In Diophantine geometry
its the sum of its digits is divisible by 3
complex number
6. Sixteen less than number Q
addition
Q-16
Definition of genus
Multiple of the given number
7. 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.
rectangular coordinates
Second Axiom of Equality
quadratic field
16(5+R)
8. This law can be applied to subtraction by changing signs so that all negative signs become number signs and all signs of operation are positive.
Commutative Law of Addition
Downward
division
negative
9. Viewed in this way the multiplication of a complex number by i corresponds to rotating a complex number
the number formed by the three right-hand digits is divisible by 8
its the sum of its digits is divisible by 3
addition
counterclockwise through 90
10. A number is divisible by 3 if
Composite Number
7
Digits
its the sum of its digits is divisible by 3
11. This formula can be used to compute the multiplicative inverse of a complex number if it is given in
monomial
rectangular coordinates
magnitude
Inversive geometry
12. Decreased by
variable
magnitude
subtraction
one characteristic in common such as similarity of appearance or purpose
13. The place value which corresponds to a given position in a number is determined by the
Base of the number system
T+9
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
magnitude and direction
14. Implies a collection or grouping of similar - objects or symbols.
consecutive whole numbers
negative
Set
addition
15. More than
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
the genus of the curve
addition
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
16. Work on the problem of general polynomials ultimately led to the fundamental theorem of algebra -
To separate a number into prime factors
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
Analytic number theory
In Diophantine geometry
17. If a factor of a number is prime - it is called a
Braces
Prime Factor
Factor of the given number
addition
18. Total
an equation in two variables defines
16(5+R)
addition
magnitude
19. The smallest of four sonsecutive whole numbers - the biggest of which is K+6
Q-16
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
Definition of genus
K+6 - K+5 - K+4 K+3.........answer is K+3
20. The number without a variable (5m+2). In this case - 2
C or
constant
expression
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
21. First axiom of equality
Commutative Law of Multiplication
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
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.
22. Any number that la a multiple of 2 is an
its the sum of its digits is divisible by 3
Even Number
counterclockwise through 90
equation
23. 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.
coefficient
Complex numbers
Multiple of the given number
Commutative Law of Addition
24. A number that has no factors except itself and 1 is a
Digits
Prime Number
T+9
subtraction
25. 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
Equal
7
To separate a number into prime factors
Set
26. The objects in a set have at least
subtraction
one characteristic in common such as similarity of appearance or purpose
Composite Number
monomial
27. Any number that is not a multiple of 2 is an
base-ten number
Odd Number
negative
Associative Law of Addition
28. Plus
Base of the number system
positive
C or
addition
29. Subtraction
difference
negative
even and the sum of its digits is divisible by 3
Braces
30. 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 -
magnitude and direction
Associative Law of Addition
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex 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.
Associative Law of Addition
K+6 - K+5 - K+4 K+3.........answer is K+3
Equal
subtraction
32. Increased by
Odd Number
The numbers are conventionally plotted using the real part
addition
Complex numbers
33. 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
Commutative Law of Addition
T+9
quadratic field
34. 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.
a curve - a surface or some other such object in n-dimensional space
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
multiplication
a complex number is real if and only if it equals its conjugate.
35. 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.
Set
Definition of genus
Associative Law of Multiplication
7
36. 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
difference
the genus of the curve
its the sum of its digits is divisible by 3
37. Number T increased by 9
To separate a number into prime factors
Associative Law of Addition
a complex number is real if and only if it equals its conjugate.
T+9
38. Studies algebraic properties and algebraic objects of interest in number theory. (Thus - analytic and algebraic number theory can and do overlap: the former is defined by its methods - the latter by its objects of study.) A key topic is that of the a
Members of Elements of the Set
Algebraic number theory
Prime Factor
rectangular coordinates
39. The central problem of Diophantine geometry is to determine when a Diophantine equation has
solutions
negative
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
equation
40. The number touching the variable (in the case of 5x - would be 5)
Odd Number
coefficient
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
repeated elements
41. The greatest of 3 consecutive whole numbers - the smallest of which is F
rectangular coordinates
subtraction
In Diophantine geometry
F - F+1 - F+2.......answer is F+2
42. Does not have an equal sign (3x+5) (2a+9b)
expression
Set
Definition of genus
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).
43. Number X decreased by 12 divided by forty
Composite Number
Analytic number theory
(x-12)/40
addition
44. Product
multiplication
Commutative Law of Multiplication
even and the sum of its digits is divisible by 3
Multiple of the given number
45. The finiteness or not of the number of rational or integer points on an algebraic curve
the genus of the curve
Even Number
addition
variable
46. 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
F - F+1 - F+2.......answer is F+2
The multiplication of two complex numbers is defined by the following formula:
addition
In Diophantine geometry
47. A number is divisible by 9 if
the sum of its digits is divisible by 9
Associative Law of Addition
a curve - a surface or some other such object in n-dimensional space
Odd Number
48. 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
even and the sum of its digits is divisible by 3
Factor of the given number
subtraction
The real number a of the complex number z = a + bi
49. 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
equation
monomial
Analytic number theory
Positional notation (place value)
50. This law combines the operations of addition and multiplication. The distribution of a common multiplier among the terms of an additive expression.
Distributive Law
addition
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
constant