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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. 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.
monomial
the number formed by the three right-hand digits is divisible by 8
Third Axiom of Equality
a complex number is real if and only if it equals its conjugate.
2. As shown earlier - c - di is the complex conjugate of the denominator c + di.
Prime Factor
Braces
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
Commutative Law of Multiplication
3. Viewed in this way the multiplication of a complex number by i corresponds to rotating a complex number
constructing a parallelogram
Commutative Law of Addition
F - F+1 - F+2.......answer is F+2
counterclockwise through 90
4. 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
Positional notation (place value)
Associative Law of Addition
5. Are not necessary. That is - the elements of {2 - 2 - 3 - 4} are simply {2 - 3 - and 4}
order of operations
repeated elements
Digits
In Diophantine geometry
6. The finiteness or not of the number of rational or integer points on an algebraic curve
the genus of the curve
Inversive geometry
its the sum of its digits is divisible by 3
T+9
7. An equation - or system of equations - in two or more variables defines
Composite Number
a curve - a surface or some other such object in n-dimensional space
In Diophantine geometry
consecutive whole numbers
8. 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.
variable
multiplication
Forth Axiom of Equality
quadratic field
9. 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
addition
Absolute value and argument
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
Set
10. LAWS FOR COMBINING NUMBERS
In Diophantine geometry
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
expression
Prime Factor
11. 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.
repeated elements
addition
The numbers are conventionally plotted using the real part
Numerals
12. Plus
Commutative Law of Multiplication
The numbers are conventionally plotted using the real part
a complex number is real if and only if it equals its conjugate.
addition
13. Integers greater than zero and less than 5 form a set - as follows:
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
Q-16
the genus of the curve
constant
14. In the Rectangular Coordinate System - On the vertical line - direction ________ is positive
positive
upward
Composite Number
base-ten number
15. 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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16. More than
Algebraic number theory
Distributive Law
addition
right-hand digit is even
17. A number that has no factors except itself and 1 is a
Prime Number
(x-12)/40
Distributive Law
monomial
18. 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
order of operations
Base of the number system
In Diophantine geometry
constant
19. A number is divisible by 4 if
the number formed by the two right-hand digits is divisible by 4
The multiplication of two complex numbers is defined by the following formula:
7
Prime Factor
20. A branch of geometry studying more general reflections than ones about a line - can also be expressed in terms of complex numbers.
constructing a parallelogram
multiplication
Inversive geometry
The multiplication of two complex numbers is defined by the following formula:
21. A number is divisible by 3 if
Even Number
Numerals
addition
its the sum of its digits is divisible by 3
22. Remainder
7
a complex number is real if and only if it equals its conjugate.
Number fields
subtraction
23. Sum
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
addition
Complex numbers
24. Less than
(x-12)/40
subtraction
addition
T+9
25. 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
Odd Number
multiplication
algebraic number
coefficient
26. The real and imaginary parts of a complex number can be extracted using the conjugate:
solutions
the sum of its digits is divisible by 9
variable
a complex number is real if and only if it equals its conjugate.
27. 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.
coefficient
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
the number formed by the two right-hand digits is divisible by 4
In Diophantine geometry
28. First axiom of equality
consecutive whole numbers
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
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.
29. 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).
Composite Number
the genus of the curve
Braces
30. 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.
the number formed by the three right-hand digits is divisible by 8
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
Commutative Law of Multiplication
Braces
31. A curve in the plane
division
an equation in two variables defines
base-ten number
constructing a parallelogram
32. If a factor of a number is prime - it is called a
Prime Factor
The multiplication of two complex numbers is defined by the following formula:
To separate a number into prime factors
algebraic number
33. A number is divisible by 5 if its
To separate a number into prime factors
Commutative Law of Addition
righthand digit is 0 or 5
even and the sum of its digits is divisible by 3
34. One term (5x or 4)
Prime Number
monomial
Numerals
its the sum of its digits is divisible by 3
35. 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.
The multiplication of two complex numbers is defined by the following formula:
Associative Law of Addition
Commutative Law of Addition
an equation in two variables defines
36. 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.
Commutative Law of Multiplication
Definition of genus
Complex numbers
solutions
37. Subtraction
difference
positive
Prime Number
addition
38. Quotient
consecutive whole numbers
division
the number formed by the two right-hand digits is divisible by 4
The multiplication of two complex numbers is defined by the following formula:
39. The Arabic numerals from 0 through 9 are called
Digits
addition
(x-12)/40
Composite Number
40. In the Rectangular Coordinate System - On the vertical line - direction _______ is negative
righthand digit is 0 or 5
Composite Number
Downward
monomial
41. The number touching the variable (in the case of 5x - would be 5)
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
addition
righthand digit is 0 or 5
coefficient
42. No short method has been found for determining whether a number is divisible by
Odd Number
7
constant
the genus of the curve
43. A number is divisible by 8 if
Second Axiom of Equality
the number formed by the three right-hand digits is divisible by 8
Commutative Law of Multiplication
repeated elements
44. This law combines the operations of addition and multiplication. The distribution of a common multiplier among the terms of an additive expression.
F - F+1 - F+2.......answer is F+2
Complex numbers
an equation in two variables defines
Distributive Law
45. Any number that la a multiple of 2 is an
subtraction
Even Number
Number fields
Members of Elements of the Set
46. G - E - M - A Grouping - Exponents - Multiply/Divide - Add/Subtract
order of operations
one characteristic in common such as similarity of appearance or purpose
Set
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
47. 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.
16(5+R)
its the sum of its digits is divisible by 3
Associative Law of Addition
Associative Law of Multiplication
48. Any number that can be divided lnto a given number without a remainder is a
the number formed by the three right-hand digits is divisible by 8
Factor of the given number
addition
The multiplication of two complex numbers is defined by the following formula:
49. Decreased by
In Diophantine geometry
a complex number is real if and only if it equals its conjugate.
Base of the number system
subtraction
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
Members of Elements of the Set
In Diophantine geometry
quadratic field
negative