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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. Number symbols
magnitude and direction
magnitude
Numerals
Absolute value and argument
2. 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
a complex number is real if and only if it equals its conjugate.
Equal
constructing a parallelogram
even and the sum of its digits is divisible by 3
3. Remainder
Downward
Members of Elements of the Set
subtraction
the number formed by the three right-hand digits is divisible by 8
4. Any number that can be divided lnto a given number without a remainder is a
a complex number is real if and only if it equals its conjugate.
Factor of the given number
the number formed by the three right-hand digits is divisible by 8
a curve - a surface or some other such object in n-dimensional space
5. 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
Absolute value and argument
addition
Prime Factor
Place Value Concept
6. Any number that la a multiple of 2 is an
Even Number
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
repeated elements
division
7. The greatest of 3 consecutive whole numbers - the smallest of which is F
solutions
right-hand digit is even
F - F+1 - F+2.......answer is F+2
Prime Number
8. As shown earlier - c - di is the complex conjugate of the denominator c + di.
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
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).
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
Inversive geometry
9. 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 -
Distributive Law
Commutative Law of Addition
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
a curve - a surface or some other such object in n-dimensional space
10. The set of all complex numbers is denoted by
a complex number is real if and only if it equals its conjugate.
Prime Factor
constructing a parallelogram
C or
11. This law combines the operations of addition and multiplication. The distribution of a common multiplier among the terms of an additive expression.
Odd Number
Forth Axiom of Equality
Distributive Law
base-ten number
12. Number T increased by 9
T+9
Second Axiom of Equality
Base of the number system
algebraic number
13. The central problem of Diophantine geometry is to determine when a Diophantine equation has
addition
Associative Law of Addition
solutions
the number formed by the two right-hand digits is divisible by 4
14. The number touching the variable (in the case of 5x - would be 5)
coefficient
F - F+1 - F+2.......answer is F+2
Algebraic number theory
rectangular coordinates
15. 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
polynomial
Absolute value and argument
Q-16
coefficient
16. 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
positive
Forth Axiom of Equality
the number formed by the two right-hand digits is divisible by 4
Definition of genus
17. 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.
Second Axiom of Equality
To separate a number into prime factors
Base of the number system
Commutative Law of Addition
18. The objects or symbols in a set are called Numerals - Lines - or Points
Members of Elements of the Set
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.
one characteristic in common such as similarity of appearance or purpose
Positional notation (place value)
19. G - E - M - A Grouping - Exponents - Multiply/Divide - Add/Subtract
order of operations
addition
16(5+R)
K+6 - K+5 - K+4 K+3.........answer is K+3
20. Sixteen less than number Q
a complex number is real if and only if it equals its conjugate.
Q-16
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
Digits
21. Integers greater than zero and less than 5 form a set - as follows:
F - F+1 - F+2.......answer is F+2
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
Inversive geometry
Composite Number
22. 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.
addition
quadratic field
the number formed by the two right-hand digits is divisible by 4
Q-16
23. An equation - or system of equations - in two or more variables defines
F - F+1 - F+2.......answer is F+2
Even Number
a curve - a surface or some other such object in n-dimensional space
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
24. Viewed in this way the multiplication of a complex number by i corresponds to rotating a complex number
Inversive geometry
multiplication
counterclockwise through 90
Base of the number system
25. A letter tat represents a number that is unknown (usually X or Y)
variable
K+6 - K+5 - K+4 K+3.........answer is K+3
Place Value Concept
quadratic field
26. 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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27. Increased by
Prime Number
consecutive whole numbers
addition
solutions
28. 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
addition
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.
addition
29. The smallest of four sonsecutive whole numbers - the biggest of which is K+6
positive
right-hand digit is even
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
K+6 - K+5 - K+4 K+3.........answer is K+3
30. 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
Q-16
complex number
multiplication
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
31. A number that has factors other than itself and 1 is a
multiplication
Set
Composite Number
quadratic field
32. Total
Distributive Law
addition
Associative Law of Addition
Place Value Concept
33. 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
addition
magnitude and direction
quadratic field
To separate a number into prime factors
34. 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.
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:
Factor of the given number
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
35. A number that has no factors except itself and 1 is a
Multiple of the given number
the sum of its digits is divisible by 9
Prime Number
rectangular coordinates
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.
Multiple of the given number
Associative Law of Multiplication
7
Numerals
37. A number is divisible by 4 if
polynomial
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
rectangular coordinates
the number formed by the two right-hand digits is divisible by 4
38. A number is divisible by 8 if
Positional notation (place value)
Commutative Law of Addition
the number formed by the three right-hand digits is divisible by 8
7
39. Less than
Analytic number theory
Distributive Law
subtraction
Prime Factor
40. Sum
addition
an equation in two variables defines
polynomial
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
41. The defining characteristic of a position vector is that it has
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
Forth Axiom of Equality
magnitude and direction
42. More than
Members of Elements of the Set
Prime Factor
complex number
addition
43. More than one term (5x+4 contains two)
Prime Number
Associative Law of Multiplication
polynomial
Equal
44. 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.
Third Axiom of Equality
addition
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
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).
45. 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:
Inversive geometry
Commutative Law of Addition
the genus of the curve
46. The place value which corresponds to a given position in a number is determined by the
variable
Base of the number system
Inversive geometry
a complex number is real if and only if it equals its conjugate.
47. Quotient
Complex numbers
addition
coefficient
division
48. 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:
one characteristic in common such as similarity of appearance or purpose
complex number
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).
Algebraic number theory
49. 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
Inversive geometry
Base of the number system
Associative Law of Multiplication
50. 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
Associative Law of Multiplication
its the sum of its digits is divisible by 3
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
Positional notation (place value)