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Test your basic knowledge |
CLEP General Mathematics: Number Systems And Sets
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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. More than one term (5x+4 contains two)
Second Axiom of Equality
expression
Set
polynomial
2. 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.
Analytic number theory
division
the sum of its digits is divisible by 9
Prime Number
3. A curve in the plane
Forth Axiom of Equality
an equation in two variables defines
positive
monomial
4. Are not necessary. That is - the elements of {2 - 2 - 3 - 4} are simply {2 - 3 - and 4}
right-hand digit is even
addition
repeated elements
Downward
5. The real and imaginary parts of a complex number can be extracted using the conjugate:
addition
base-ten number
a complex number is real if and only if it equals its conjugate.
7
6. No short method has been found for determining whether a number is divisible by
Factor of the given number
upward
Members of Elements of the Set
7
7. 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
Analytic number theory
a curve - a surface or some other such object in n-dimensional space
complex number
8. If a factor of a number is prime - it is called a
Base of the number system
Prime Factor
Numerals
an equation in two variables defines
9. 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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10. Implies a collection or grouping of similar - objects or symbols.
Set
negative
repeated elements
16(5+R)
11. A number that has no factors except itself and 1 is a
K+6 - K+5 - K+4 K+3.........answer is K+3
Prime Number
its the sum of its digits is divisible by 3
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
12. In the Rectangular Coordinate System - On the vertical line - direction ________ is positive
addition
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
Complex numbers
upward
13. 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
rectangular coordinates
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
To separate a number into prime factors
difference
14. 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.
difference
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
Third Axiom of Equality
magnitude and direction
15. A number is divisible by 4 if
one characteristic in common such as similarity of appearance or purpose
division
the number formed by the two right-hand digits is divisible by 4
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
16. A number that has factors other than itself and 1 is a
Braces
expression
counterclockwise through 90
Composite Number
17. 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
the genus of the curve
Absolute value and argument
Natural Numbers
repeated elements
18. Remainder
order of operations
algebraic number
base-ten number
subtraction
19. The finiteness or not of the number of rational or integer points on an algebraic curve
a curve - a surface or some other such object in n-dimensional space
Prime Factor
C or
the genus of the curve
20. An equation - or system of equations - in two or more variables defines
The numbers are conventionally plotted using the real part
a curve - a surface or some other such object in n-dimensional space
complex number
an equation in two variables defines
21. The smallest of four sonsecutive whole numbers - the biggest of which is K+6
In Diophantine geometry
multiplication
one characteristic in common such as similarity of appearance or purpose
K+6 - K+5 - K+4 K+3.........answer is K+3
22. This law combines the operations of addition and multiplication. The distribution of a common multiplier among the terms of an additive expression.
Odd Number
quadratic field
Distributive Law
Commutative Law of Addition
23. Any number that can be divided lnto a given number without a remainder is a
Digits
constructing a parallelogram
repeated elements
Factor of the given number
24. 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.
Commutative Law of Multiplication
subtraction
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
the sum of its digits is divisible by 9
25. 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.
(x-12)/40
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
monomial
Base of the number system
26. The set of all complex numbers is denoted by
C or
The real number a of the complex number z = a + bi
Natural Numbers
quadratic field
27. Product of 16 and the sum of 5 and number R
Commutative Law of Addition
variable
Factor of the given number
16(5+R)
28. 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
order of operations
repeated elements
Place Value Concept
Commutative Law of Multiplication
29. The number touching the variable (in the case of 5x - would be 5)
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
difference
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
coefficient
30. G - E - M - A Grouping - Exponents - Multiply/Divide - Add/Subtract
Natural Numbers
order of operations
multiplication
subtraction
31. LAWS FOR COMBINING NUMBERS
Composite Number
algebraic number
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
Inversive geometry
32. Product
Downward
C or
multiplication
its the sum of its digits is divisible by 3
33. A number is divisible by 9 if
The real number a of the complex number z = a + bi
repeated elements
Factor of the given number
the sum of its digits is divisible by 9
34. 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
Prime Factor
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
counterclockwise through 90
The multiplication of two complex numbers is defined by the following formula:
35. The number without a variable (5m+2). In this case - 2
Definition of genus
Equal
Associative Law of Addition
constant
36. Decreased by
subtraction
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
Natural Numbers
Associative Law of Addition
37. A number is divisible by 2 if
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
right-hand digit is even
Third Axiom of Equality
Digits
38. Sixteen less than number Q
Q-16
Prime Factor
Definition of genus
repeated elements
39. Does not have an equal sign (3x+5) (2a+9b)
Third Axiom of Equality
order of operations
expression
Absolute value and argument
40. Number T increased by 9
rectangular coordinates
The numbers are conventionally plotted using the real part
T+9
Associative Law of Addition
41. 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.
magnitude
Commutative Law of Multiplication
Numerals
quadratic field
42. 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
Commutative Law of Addition
In Diophantine geometry
a complex number is real if and only if it equals its conjugate.
43. This law can be applied to subtraction by changing signs in such a way that all negative signs are treated as number signs rather than operational signs.That is - some of the addends can be negative numbers.
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
rectangular coordinates
Associative Law of Addition
Commutative Law of Addition
44. Total
the number formed by the three right-hand digits is divisible by 8
multiplication
division
addition
45. 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
Inversive geometry
constructing a parallelogram
Place Value Concept
46. Less than
subtraction
positive
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
47. 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.
The real number a of the complex number z = a + bi
Members of Elements of the Set
Complex numbers
righthand digit is 0 or 5
48. Addition of two complex numbers can be done geometrically by
Base of the number system
16(5+R)
constructing a parallelogram
variable
49. Viewed in this way the multiplication of a complex number by i corresponds to rotating a complex number
F - F+1 - F+2.......answer is F+2
repeated elements
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
counterclockwise through 90
50. Number X decreased by 12 divided by forty
Algebraic number theory
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
(x-12)/40
Positional notation (place value)