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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. A letter tat represents a number that is unknown (usually X or Y)
quadratic field
variable
addition
polynomial
2. 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.
addition
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
Forth Axiom of Equality
Complex numbers
3. In the Rectangular Coordinate System - On the vertical line - direction _______ is negative
Second Axiom of Equality
K+6 - K+5 - K+4 K+3.........answer is K+3
Downward
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
4. Less than
the genus of the curve
subtraction
even and 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.
5. Remainder
equation
difference
subtraction
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
6. Increased by
a complex number is real if and only if it equals its conjugate.
Associative Law of Addition
addition
Multiple of the given number
7. Addition of two complex numbers can be done geometrically by
Second Axiom of Equality
Inversive geometry
constructing a parallelogram
addition
8. Decreased by
difference
a complex number is real if and only if it equals its conjugate.
subtraction
algebraic number
9. Number symbols
quadratic field
Numerals
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
magnitude
10. A number that has no factors except itself and 1 is a
multiplication
Second Axiom of Equality
Prime Number
an equation in two variables defines
11. The set of all complex numbers is denoted by
Associative Law of Addition
C or
addition
Positional notation (place value)
12. Are used to indicate sets
Place Value Concept
Braces
addition
Algebraic number theory
13. 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
expression
complex number
The real number a of the complex number z = a + bi
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
14. 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
magnitude and direction
Algebraic number theory
Braces
Place Value Concept
15. In the Rectangular Coordinate System - the direction to the right along the horizontal line is
Associative Law of Addition
division
positive
To separate a number into prime factors
16. The objects in a set have at least
Odd Number
Prime Number
Downward
one characteristic in common such as similarity of appearance or purpose
17. 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
negative
coefficient
Set
In Diophantine geometry
18. A number is divisible by 3 if
Positional notation (place value)
its the sum of its digits is divisible by 3
Inversive geometry
(x-12)/40
19. 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
addition
The multiplication of two complex numbers is defined by the following formula:
The real number a of the complex number z = a + bi
(x-12)/40
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.
Odd Number
rectangular coordinates
Complex numbers
Place Value Concept
21. Product
multiplication
addition
algebraic number
To separate a number into prime factors
22. 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.
expression
Analytic number theory
order of operations
Associative Law of Addition
23. A number that has factors other than itself and 1 is a
constant
Associative Law of Addition
Third Axiom of Equality
Composite Number
24. The central problem of Diophantine geometry is to determine when a Diophantine equation has
solutions
Equal
Absolute value and argument
Odd Number
25. A number is divisible by 2 if
Commutative Law of Multiplication
right-hand digit is even
variable
Associative Law of Addition
26. A number is divisible by 4 if
quadratic field
Commutative Law of Addition
righthand digit is 0 or 5
the number formed by the two right-hand digits is divisible by 4
27. This law combines the operations of addition and multiplication. The distribution of a common multiplier among the terms of an additive expression.
Braces
righthand digit is 0 or 5
Distributive Law
an equation in two variables defines
28. LAWS FOR COMBINING NUMBERS
Forth Axiom of Equality
upward
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
F - F+1 - F+2.......answer is F+2
29. 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
difference
Set
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
Definition of genus
30. The defining characteristic of a position vector is that it has
In Diophantine geometry
magnitude and direction
Set
Commutative Law of Addition
31. Any number that can be divided lnto a given number without a remainder is a
Positional notation (place value)
In Diophantine geometry
Natural Numbers
Factor of the given number
32. Has an equal sign (3x+5 = 14)
constructing a parallelogram
Definition of genus
coefficient
equation
33. As shown earlier - c - di is the complex conjugate of the denominator c + di.
'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.
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
polynomial
34. 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
the number formed by the two right-hand digits is divisible by 4
T+9
algebraic number
quadratic field
35. 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.
Definition of genus
addition
The real number a of the complex number z = a + bi
Associative Law of Addition
36. The Arabic numerals from 0 through 9 are called
Multiple of the given number
quadratic field
Inversive geometry
Digits
37. The relative greatness of positive and negative numbers
magnitude
the sum of its digits is divisible by 9
positive
rectangular coordinates
38. The finiteness or not of the number of rational or integer points on an algebraic curve
the number formed by the two right-hand digits is divisible by 4
the genus of the curve
difference
constructing a parallelogram
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 number formed by the three right-hand digits is divisible by 8
Equal
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
complex number
40. Number T increased by 9
T+9
complex number
order of operations
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
41. Any number that is not a multiple of 2 is an
Downward
Odd Number
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
Members of Elements of the Set
42. The complex conjugate of the complex number z = x + yi is defined to be x - yi. It is denoted or . Geometrically - is the
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43. More than one term (5x+4 contains two)
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
polynomial
Composite Number
44. The number without a variable (5m+2). In this case - 2
T+9
constructing a parallelogram
constant
Commutative Law of Multiplication
45. Integers greater than zero and less than 5 form a set - as follows:
Distributive Law
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
repeated elements
difference
46. The number touching the variable (in the case of 5x - would be 5)
base-ten number
coefficient
Odd Number
Analytic number theory
47. Product of 16 and the sum of 5 and number R
addition
positive
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
16(5+R)
48. A curve in the plane
an equation in two variables defines
subtraction
rectangular coordinates
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).
49. 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:
7
Third Axiom of Equality
Numerals
50. The numbers which are used for counting in our number system are sometimes called
addition
F - F+1 - F+2.......answer is F+2
addition
Natural Numbers