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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. Sum
The multiplication of two complex numbers is defined by the following formula:
constant
addition
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
2. The number of digits in an integer indicates its rank; that is - whether it is 'in the hundreds -' 'in the thousands -' etc. The idea of ranking numbers in terms of tens - hundreds - thousands - etc. - is based on the
difference
Place Value Concept
subtraction
(x-12)/40
3. Integers greater than zero and less than 5 form a set - as follows:
quadratic field
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
Inversive geometry
Natural Numbers
4. The numbers which are used for counting in our number system are sometimes called
Natural Numbers
complex number
division
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
5. The central problem of Diophantine geometry is to determine when a Diophantine equation has
7
Commutative Law of Addition
solutions
division
6. If a factor of a number is prime - it is called a
Third Axiom of Equality
Second Axiom of Equality
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
Prime Factor
7. Any number that is not a multiple of 2 is an
Associative Law of Multiplication
In Diophantine geometry
solutions
Odd Number
8. Total
The numbers are conventionally plotted using the real part
rectangular coordinates
repeated elements
addition
9. 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 elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
Associative Law of Addition
Third Axiom of Equality
10. No short method has been found for determining whether a number is divisible by
7
algebraic number
counterclockwise through 90
rectangular coordinates
11. 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
Multiple of the given number
algebraic number
Third Axiom of Equality
The multiplication of two complex numbers is defined by the following formula:
12. The number touching the variable (in the case of 5x - would be 5)
Commutative Law of Multiplication
coefficient
Complex numbers
variable
13. A number that has no factors except itself and 1 is a
Prime Number
positive
Inversive geometry
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
14. 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 -
(x-12)/40
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
counterclockwise through 90
15. 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:
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).
Prime Number
constructing a parallelogram
Inversive geometry
16. 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
Second Axiom of Equality
Equal
a complex number is real if and only if it equals its conjugate.
17. A number that has factors other than itself and 1 is a
Composite Number
subtraction
right-hand digit is even
variable
18. The greatest of 3 consecutive whole numbers - the smallest of which is F
Associative Law of Addition
coefficient
F - F+1 - F+2.......answer is F+2
algebraic number
19. The place value which corresponds to a given position in a number is determined by the
Base of the number system
Odd Number
Prime Number
a curve - a surface or some other such object in n-dimensional space
20. 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
quadratic field
Definition of genus
addition
Commutative Law of Multiplication
21. Number symbols
Numerals
repeated elements
F - F+1 - F+2.......answer is F+2
quadratic field
22. Addition of two complex numbers can be done geometrically by
even and the sum of its digits is divisible by 3
constructing a parallelogram
Q-16
Multiple of the given number
23. In the Rectangular Coordinate System - On the vertical line - direction _______ is negative
Downward
T+9
the number formed by the two right-hand digits is divisible by 4
an equation in two variables defines
24. A number is divisible by 6 if it is
subtraction
even and the sum of its digits is divisible by 3
Distributive Law
constructing a parallelogram
25. LAWS FOR COMBINING NUMBERS
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.
Commutative Law of Addition
Prime Factor
26. The objects or symbols in a set are called Numerals - Lines - or Points
base-ten number
Members of Elements of the Set
F - F+1 - F+2.......answer is F+2
Numerals
27. 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.
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
addition
Associative Law of Addition
Third Axiom of Equality
28. 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
Associative Law of Multiplication
T+9
Prime Factor
29. A letter tat represents a number that is unknown (usually X or Y)
(x-12)/40
the number formed by the three right-hand digits is divisible by 8
addition
variable
30. 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
the sum of its digits is divisible by 9
difference
In Diophantine geometry
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
31. Work on the problem of general polynomials ultimately led to the fundamental theorem of algebra -
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
Second Axiom of Equality
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
the number formed by the three right-hand digits is divisible by 8
32. 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
Analytic number theory
Associative Law of Addition
the number formed by the three right-hand digits is divisible by 8
Positional notation (place value)
33. The real and imaginary parts of a complex number can be extracted using the conjugate:
Commutative Law of Addition
order of operations
a complex number is real if and only if it equals its conjugate.
Definition of genus
34. More than one term (5x+4 contains two)
counterclockwise through 90
Downward
Multiple of the given number
polynomial
35. A number is divisible by 3 if
Positional notation (place value)
The multiplication of two complex numbers is defined by the following formula:
Commutative Law of Addition
its the sum of its digits is divisible by 3
36. This formula can be used to compute the multiplicative inverse of a complex number if it is given in
rectangular coordinates
even and the sum of its digits is divisible by 3
Q-16
To separate a number into prime factors
37. 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
order of operations
Absolute value and argument
the number formed by the two right-hand digits is divisible by 4
Set
38. A number is divisible by 5 if its
righthand digit is 0 or 5
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
Inversive geometry
the genus of the curve
39. Remainder
polynomial
subtraction
Associative Law of Addition
The real number a of the complex number z = a + bi
40. 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
solutions
Braces
7
41. The objects in a set have at least
one characteristic in common such as similarity of appearance or purpose
Natural Numbers
Inversive geometry
addition
42. 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.
monomial
Complex numbers
Definition of genus
base-ten number
43. Number T increased by 9
order of operations
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
difference
T+9
44. As shown earlier - c - di is the complex conjugate of the denominator c + di.
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.
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
F - F+1 - F+2.......answer is F+2
45. 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.
Multiple of the given number
order of operations
Commutative Law of Addition
difference
46. The set of all complex numbers is denoted by
Associative Law of Addition
rectangular coordinates
Algebraic number theory
C or
47. 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.)
Number fields
Prime Factor
T+9
constant
48. 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.
Associative Law of Addition
Forth Axiom of Equality
Odd Number
order of operations
49. G - E - M - A Grouping - Exponents - Multiply/Divide - Add/Subtract
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
Downward
rectangular coordinates
order of operations
50. A number is divisible by 4 if
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
the number formed by the two right-hand digits is divisible by 4
7
C or