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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 - the direction to the right along the horizontal line is
right-hand digit is even
consecutive whole numbers
positive
7
2. Sixteen less than number Q
Base of the number system
Q-16
Equal
Distributive Law
3. Product of 16 and the sum of 5 and number R
Commutative Law of Multiplication
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
16(5+R)
multiplication
4. No short method has been found for determining whether a number is divisible by
7
Associative Law of Multiplication
the number formed by the two right-hand digits is divisible by 4
equation
5. The Arabic numerals from 0 through 9 are called
expression
Digits
C or
repeated elements
6. 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
Commutative Law of Multiplication
Definition of genus
one characteristic in common such as similarity of appearance or purpose
an equation in two variables defines
7. The place value which corresponds to a given position in a number is determined by the
difference
Forth Axiom of Equality
Base of the number system
addition
8. 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.
division
Commutative Law of Addition
one characteristic in common such as similarity of appearance or purpose
K+6 - K+5 - K+4 K+3.........answer is K+3
9. 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.
Braces
a curve - a surface or some other such object in n-dimensional space
addition
10. Implies a collection or grouping of similar - objects or symbols.
Prime Number
Set
Members of Elements of the Set
equation
11. The central problem of Diophantine geometry is to determine when a Diophantine equation has
one characteristic in common such as similarity of appearance or purpose
solutions
Place Value Concept
addition
12. The number touching the variable (in the case of 5x - would be 5)
division
coefficient
Digits
magnitude
13. 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
K+6 - K+5 - K+4 K+3.........answer is K+3
Equal
addition
order of operations
14. Subtraction
monomial
difference
division
Odd Number
15. 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.
Analytic number theory
polynomial
quadratic field
right-hand digit is even
16. 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
polynomial
expression
The multiplication of two complex numbers is defined by the following formula:
In Diophantine geometry
17. If a factor of a number is prime - it is called a
algebraic number
Prime Factor
Composite Number
the number formed by the two right-hand digits is divisible by 4
18. Any number that is not a multiple of 2 is an
Odd Number
the number formed by the three right-hand digits is divisible by 8
multiplication
addition
19. A number is divisible by 3 if
algebraic number
Composite Number
its the sum of its digits is divisible by 3
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.
20. 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
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.
To separate a number into prime factors
In Diophantine geometry
21. 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.
Second Axiom of Equality
Odd Number
complex number
Algebraic number theory
22. Total
addition
Natural Numbers
subtraction
Associative Law of Addition
23. 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.
To separate a number into prime factors
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
negative
Algebraic number theory
24. 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
16(5+R)
Even Number
25. 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:
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
Prime Number
addition
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).
26. A number is divisible by 2 if
Natural Numbers
Place Value Concept
right-hand digit is even
K+6 - K+5 - K+4 K+3.........answer is K+3
27. Number T increased by 9
one characteristic in common such as similarity of appearance or purpose
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
T+9
Definition of genus
28. Integers greater than zero and less than 5 form a set - as follows:
Definition of genus
(x-12)/40
7
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
29. 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 -
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
magnitude and direction
Commutative Law of Addition
Q-16
30. The greatest of 3 consecutive whole numbers - the smallest of which is F
F - F+1 - F+2.......answer is F+2
rectangular coordinates
Composite Number
negative
31. 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
Prime Number
Equal
The real number a of the complex number z = a + bi
32. 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
In Diophantine geometry
polynomial
Prime Factor
The real number a of the complex number z = a + bi
33. 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.
variable
Forth Axiom of Equality
quadratic field
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
34. 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
To separate a number into prime factors
coefficient
Commutative Law of Addition
an equation in two variables defines
35. Remainder
repeated elements
upward
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).
subtraction
36. 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.
Third Axiom of Equality
subtraction
addition
its the sum of its digits is divisible by 3
37. One term (5x or 4)
Inversive geometry
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
monomial
magnitude
38. In the Rectangular Coordinate System - On the vertical line - direction ________ is positive
the sum of its digits is divisible by 9
consecutive whole numbers
upward
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
39. Quotient
difference
base-ten number
upward
division
40. 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.
16(5+R)
Associative Law of Addition
Complex numbers
base-ten number
41. 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.
Equal
Analytic number theory
monomial
Members of Elements of the Set
42. Sum
negative
Place Value Concept
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
addition
43. The numbers which are used for counting in our number system are sometimes called
Natural Numbers
an equation in two variables defines
the number formed by the two right-hand digits is divisible by 4
multiplication
44. Number X decreased by 12 divided by forty
division
its the sum of its digits is divisible by 3
the sum of its digits is divisible by 9
(x-12)/40
45. 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.
expression
quadratic field
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
Numerals
46. 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
magnitude and direction
algebraic number
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
Base of the number system
47. LAWS FOR COMBINING NUMBERS
subtraction
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
Positional notation (place value)
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
48. A branch of geometry studying more general reflections than ones about a line - can also be expressed in terms of complex numbers.
K+6 - K+5 - K+4 K+3.........answer is K+3
The real number a of the complex number z = a + bi
Composite Number
Inversive geometry
49. 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.
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
Composite Number
Complex numbers
Absolute value and argument
50. 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
To separate a number into prime factors
negative
In Diophantine geometry
addition