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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. Any number that is not a multiple of 2 is an
Commutative Law of Addition
Odd Number
To separate a number into prime factors
Third Axiom of Equality
2. 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}
algebraic number
Q-16
one characteristic in common such as similarity of appearance or purpose
3. 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
16(5+R)
Positional notation (place value)
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.
Prime Factor
4. 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
magnitude
Commutative Law of Addition
the sum of its digits is divisible by 9
Absolute value and argument
5. 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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6. A branch of geometry studying more general reflections than ones about a line - can also be expressed in terms of complex numbers.
T+9
multiplication
the number formed by the two right-hand digits is divisible by 4
Inversive geometry
7. 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
magnitude
the sum of its digits is divisible by 9
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
The multiplication of two complex numbers is defined by the following formula:
8. Sum
addition
Multiple of the given number
K+6 - K+5 - K+4 K+3.........answer is K+3
division
9. Has an equal sign (3x+5 = 14)
equation
Composite Number
an equation in two variables defines
K+6 - K+5 - K+4 K+3.........answer is K+3
10. A number is divisible by 9 if
the sum of its digits is divisible by 9
variable
polynomial
complex number
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.
Factor of the given number
subtraction
Place Value Concept
The numbers are conventionally plotted using the real part
12. 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
Prime Factor
repeated elements
Number fields
Equal
13. A letter tat represents a number that is unknown (usually X or Y)
T+9
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
Third Axiom of Equality
variable
14. As shown earlier - c - di is the complex conjugate of the denominator c + di.
variable
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
a complex number is real if and only if it equals its conjugate.
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
15. The objects in a set have at least
Multiple of the given number
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
one characteristic in common such as similarity of appearance or purpose
division
16. 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
C or
algebraic number
magnitude and direction
Prime Number
17. Number T increased by 9
Positional notation (place value)
T+9
Prime Factor
Forth Axiom of Equality
18. The place value which corresponds to a given position in a number is determined by the
negative
Base of the number system
Associative Law of Addition
F - F+1 - F+2.......answer is F+2
19. The defining characteristic of a position vector is that it has
magnitude and direction
the number formed by the three right-hand digits is divisible by 8
variable
difference
20. Plus
Members of Elements of the Set
addition
constructing a parallelogram
Inversive geometry
21. Increased by
multiplication
addition
subtraction
Prime Factor
22. More than
addition
Positional notation (place value)
base-ten number
complex number
23. A number is divisible by 5 if its
Complex numbers
Even Number
righthand digit is 0 or 5
algebraic number
24. 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.
Members of Elements of the Set
C or
Associative Law of Addition
positive
25. 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
Prime Factor
Commutative Law of Addition
Analytic number theory
Place Value Concept
26. Addition of two complex numbers can be done geometrically by
Number fields
constructing a parallelogram
Associative Law of Addition
the genus of the curve
27. Number X decreased by 12 divided by forty
Number fields
Members of Elements of the Set
(x-12)/40
T+9
28. Any number that is exactly divisible by a given number is a
Multiple of the given number
difference
K+6 - K+5 - K+4 K+3.........answer is K+3
equation
29. 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
Positional notation (place value)
the genus of the curve
addition
30. Product of 16 and the sum of 5 and number R
coefficient
16(5+R)
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
constructing a parallelogram
31. 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
difference
coefficient
counterclockwise through 90
32. In the Rectangular Coordinate System - On the vertical line - direction _______ is negative
7
Downward
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
consecutive whole numbers
33. Quotient
division
K+6 - K+5 - K+4 K+3.........answer is K+3
subtraction
upward
34. The relative greatness of positive and negative numbers
Set
Analytic number theory
magnitude
Place Value Concept
35. 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.
Natural Numbers
repeated elements
Second Axiom of Equality
quadratic field
36. 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.
Analytic number theory
Factor of the given number
Associative Law of Multiplication
K+6 - K+5 - K+4 K+3.........answer is K+3
37. G - E - M - A Grouping - Exponents - Multiply/Divide - Add/Subtract
order of operations
subtraction
Digits
F - F+1 - F+2.......answer is F+2
38. Any number that la a multiple of 2 is an
Prime Factor
Commutative Law of Multiplication
Even Number
Third Axiom of Equality
39. 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 -
the number formed by the two right-hand digits is divisible by 4
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
polynomial
Place Value Concept
40. The numbers which are used for counting in our number system are sometimes called
solutions
Natural Numbers
coefficient
Commutative Law of Addition
41. One term (5x or 4)
Absolute value and argument
monomial
Equal
(x-12)/40
42. The number without a variable (5m+2). In this case - 2
Associative Law of Addition
upward
constant
Analytic number theory
43. In the Rectangular Coordinate System - On the vertical line - direction ________ is positive
multiplication
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
upward
the genus of the curve
44. 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.
7
C or
monomial
Commutative Law of Addition
45. A number that has factors other than itself and 1 is a
Complex numbers
multiplication
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
Composite Number
46. Remainder
positive
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.
subtraction
righthand digit is 0 or 5
47. This law combines the operations of addition and multiplication. The distribution of a common multiplier among the terms of an additive expression.
Prime Factor
monomial
Distributive Law
quadratic field
48. 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.
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
In Diophantine geometry
complex number
Base of the number system
49. The objects or symbols in a set are called Numerals - Lines - or Points
addition
the genus of the curve
Commutative Law of Addition
Members of Elements of the Set
50. Does not have an equal sign (3x+5) (2a+9b)
equation
Q-16
expression
multiplication