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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. Does not have an equal sign (3x+5) (2a+9b)
expression
magnitude and direction
Commutative Law of Addition
addition
2. Product of 16 and the sum of 5 and number R
right-hand digit is even
an equation in two variables defines
16(5+R)
Prime Factor
3. 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.
subtraction
In Diophantine geometry
variable
Commutative Law of Addition
4. Product
multiplication
Multiple of the given number
Even Number
Associative Law of Addition
5. Any number that can be divided lnto a given number without a remainder is a
complex number
Factor of the given number
monomial
To separate a number into prime factors
6. A number is divisible by 8 if
right-hand digit is even
expression
the number formed by the three right-hand digits is divisible by 8
The multiplication of two complex numbers is defined by the following formula:
7. 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.
Complex numbers
Factor of the given number
complex number
monomial
8. A number that has no factors except itself and 1 is a
the genus of the curve
Prime Number
Associative Law of Multiplication
Second Axiom of Equality
9. A number is divisible by 9 if
the sum of its digits is divisible by 9
addition
Associative Law of Multiplication
multiplication
10. 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
base-ten number
rectangular coordinates
subtraction
11. The defining characteristic of a position vector is that it has
the number formed by the three right-hand digits is divisible by 8
magnitude and direction
order of operations
Distributive Law
12. No short method has been found for determining whether a number is divisible by
algebraic number
base-ten number
7
the number formed by the three right-hand digits is divisible by 8
13. The Arabic numerals from 0 through 9 are called
Digits
C or
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
7
14. A number is divisible by 2 if
Associative Law of Multiplication
polynomial
addition
right-hand digit is even
15. A number is divisible by 6 if it is
even and the sum of its digits is divisible by 3
Complex numbers
subtraction
Composite Number
16. Any number that la a multiple of 2 is an
F - F+1 - F+2.......answer is F+2
Multiple of the given number
In Diophantine geometry
Even Number
17. In the Rectangular Coordinate System - On the vertical line - direction _______ is negative
Commutative Law of Multiplication
T+9
Downward
Natural Numbers
18. 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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19. Quotient
division
base-ten number
Prime Factor
Definition of genus
20. In the Rectangular Coordinate System - the direction to the right along the horizontal line is
equation
magnitude
positive
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
21. The numbers which are used for counting in our number system are sometimes called
Numerals
Forth Axiom of Equality
Natural Numbers
Composite Number
22. 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
algebraic number
K+6 - K+5 - K+4 K+3.........answer is K+3
Absolute value and argument
the genus of the curve
23. The relative greatness of positive and negative numbers
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
even and the sum of its digits is divisible by 3
addition
magnitude
24. 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
The real number a of the complex number z = a + bi
quadratic field
difference
Factor of the given number
25. A number is divisible by 3 if
its the sum of its digits is divisible by 3
In Diophantine geometry
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
Composite Number
26. The number without a variable (5m+2). In this case - 2
constant
magnitude and direction
K+6 - K+5 - K+4 K+3.........answer is K+3
Place Value Concept
27. Addition of two complex numbers can be done geometrically by
Factor of the given number
division
constructing a parallelogram
order of operations
28. Are not necessary. That is - the elements of {2 - 2 - 3 - 4} are simply {2 - 3 - and 4}
repeated elements
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
constructing a parallelogram
Algebraic number theory
29. 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.
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.
Members of Elements of the Set
multiplication
Second Axiom of Equality
30. A number that has factors other than itself and 1 is a
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
Equal
Composite Number
difference
31. LAWS FOR COMBINING NUMBERS
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
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
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
32. G - E - M - A Grouping - Exponents - Multiply/Divide - Add/Subtract
order of operations
Braces
upward
In Diophantine geometry
33. 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
subtraction
In Diophantine geometry
solutions
Associative Law of Multiplication
34. 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
an equation in two variables defines
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
Odd Number
35. Number symbols
Numerals
(x-12)/40
consecutive whole numbers
Forth Axiom of Equality
36. The base which is most commonly used is ten - and the system with ten as a base is called the decimal system (decem is the Latin word for ten). Any number is assumed - unless indicated - to be a
Braces
Absolute value and argument
expression
base-ten number
37. 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.
In Diophantine geometry
Commutative Law of Multiplication
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
upward
38. This law combines the operations of addition and multiplication. The distribution of a common multiplier among the terms of an additive expression.
Distributive Law
Digits
addition
the sum of its digits is divisible by 9
39. The objects or symbols in a set are called Numerals - Lines - or Points
Digits
Members of Elements of the Set
its the sum of its digits is divisible by 3
division
40. 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
the number formed by the three right-hand digits is divisible by 8
complex number
7
Positional notation (place value)
41. 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.
The numbers are conventionally plotted using the real part
Positional notation (place value)
Q-16
Complex numbers
42. 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.
Set
Prime Factor
Associative Law of Addition
Prime Number
43. Plus
repeated elements
addition
Associative Law of Addition
upward
44. The finiteness or not of the number of rational or integer points on an algebraic curve
addition
addition
Multiple of the given number
the genus of the curve
45. Remainder
order of operations
subtraction
counterclockwise through 90
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
46. Increased by
addition
monomial
magnitude
Place Value Concept
47. 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).
equation
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
Second Axiom of Equality
48. More than one term (5x+4 contains two)
Place Value Concept
Commutative Law of Addition
polynomial
multiplication
49. 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
addition
(x-12)/40
complex number
magnitude
50. 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
positive
Equal
Prime Number
a complex number is real if and only if it equals its conjugate.