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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. A number is divisible by 5 if its
righthand digit is 0 or 5
Even Number
upward
Definition of genus
2. If a factor of a number is prime - it is called a
Odd Number
Prime Factor
Positional notation (place value)
Braces
3. Viewed in this way the multiplication of a complex number by i corresponds to rotating a complex number
variable
negative
counterclockwise through 90
right-hand digit is even
4. 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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5. 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.
addition
Algebraic number theory
Distributive Law
6. 2 -3 -4 -5 -6
magnitude
The real number a of the complex number z = a + bi
consecutive whole numbers
solutions
7. 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
Q-16
Second Axiom of Equality
In Diophantine geometry
multiplication
8. Sixteen less than number Q
Q-16
Numerals
subtraction
an equation in two variables defines
9. 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
To separate a number into prime factors
Digits
addition
The real number a of the complex number z = a + bi
10. A number is divisible by 2 if
right-hand digit is even
polynomial
Commutative Law of Multiplication
F - F+1 - F+2.......answer is F+2
11. A number is divisible by 8 if
a complex number is real if and only if it equals its conjugate.
Equal
the number formed by the three right-hand digits is divisible by 8
Q-16
12. 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
division
addition
constant
13. 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.)
coefficient
rectangular coordinates
7
Number fields
14. Any number that is exactly divisible by a given number is a
Commutative Law of Addition
Multiple of the given number
Second Axiom of Equality
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
15. A number is divisible by 9 if
Prime Number
Complex numbers
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
the sum of its digits is divisible by 9
16. Implies a collection or grouping of similar - objects or symbols.
Set
Analytic number theory
algebraic number
Odd Number
17. 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
Complex numbers
subtraction
one characteristic in common such as similarity of appearance or purpose
Definition of genus
18. Plus
equation
solutions
addition
positive
19. 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
counterclockwise through 90
Associative Law of Addition
In Diophantine geometry
20. 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
Third Axiom of Equality
Place Value Concept
The real number a of the complex number z = a + bi
magnitude
21. 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
The numbers are conventionally plotted using the real part
Base of the number system
C or
22. 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.
multiplication
The real number a of the complex number z = a + bi
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
rectangular coordinates
23. 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 multiplication of two complex numbers is defined by the following formula:
Analytic number theory
monomial
Positional notation (place value)
24. In the Rectangular Coordinate System - On the vertical line - direction _______ is negative
polynomial
K+6 - K+5 - K+4 K+3.........answer is K+3
Downward
magnitude and direction
25. Addition of two complex numbers can be done geometrically by
order of operations
constructing a parallelogram
consecutive whole numbers
the genus of the curve
26. 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:
addition
order of operations
Distributive Law
27. In the Rectangular Coordinate System - On the vertical line - direction ________ is positive
Commutative Law of Addition
upward
Set
positive
28. The relative greatness of positive and negative numbers
16(5+R)
F - F+1 - F+2.......answer is F+2
magnitude
Algebraic number theory
29. The number touching the variable (in the case of 5x - would be 5)
coefficient
positive
Odd Number
even and the sum of its digits is divisible by 3
30. Total
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
Braces
addition
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
31. Does not have an equal sign (3x+5) (2a+9b)
quadratic field
righthand digit is 0 or 5
T+9
expression
32. The real and imaginary parts of a complex number can be extracted using the conjugate:
a complex number is real if and only if it equals its conjugate.
Even Number
equation
subtraction
33. Studies algebraic properties and algebraic objects of interest in number theory. (Thus - analytic and algebraic number theory can and do overlap: the former is defined by its methods - the latter by its objects of study.) A key topic is that of the a
division
righthand digit is 0 or 5
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
Algebraic number theory
34. A branch of geometry studying more general reflections than ones about a line - can also be expressed in terms of complex numbers.
Inversive geometry
addition
In Diophantine geometry
the sum of its digits is divisible by 9
35. The smallest of four sonsecutive whole numbers - the biggest of which is K+6
K+6 - K+5 - K+4 K+3.........answer is K+3
multiplication
Third Axiom of Equality
subtraction
36. A number is divisible by 4 if
constructing a parallelogram
the number formed by the two right-hand digits is divisible by 4
Odd Number
difference
37. 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.
rectangular coordinates
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
Q-16
The numbers are conventionally plotted using the real part
38. 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
constructing a parallelogram
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
rectangular coordinates
39. LAWS FOR COMBINING NUMBERS
constructing a parallelogram
equation
subtraction
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
40. A number that has factors other than itself and 1 is a
Positional notation (place value)
equation
Composite Number
the genus of the curve
41. Any number that la a multiple of 2 is an
algebraic number
The numbers are conventionally plotted using the real part
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
Even Number
42. This law combines the operations of addition and multiplication. The distribution of a common multiplier among the terms of an additive expression.
expression
Distributive Law
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
(x-12)/40
43. Quotient
Commutative Law of Addition
addition
subtraction
division
44. Number X decreased by 12 divided by forty
complex number
Complex numbers
(x-12)/40
addition
45. Subtraction
Set
Composite Number
difference
F - F+1 - F+2.......answer is F+2
46. In the Rectangular Coordinate System - the direction to the right along the horizontal line is
In Diophantine geometry
the number formed by the three right-hand digits is divisible by 8
division
positive
47. A number that has no factors except itself and 1 is a
K+6 - K+5 - K+4 K+3.........answer is K+3
the number formed by the three right-hand digits is divisible by 8
Prime Number
Distributive Law
48. This formula can be used to compute the multiplicative inverse of a complex number if it is given in
rectangular coordinates
The numbers are conventionally plotted using the real part
Equal
the genus of the curve
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
multiplication
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
complex number
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
50. The place value which corresponds to a given position in a number is determined by the
Base of the number system
Natural Numbers
a complex number is real if and only if it equals its conjugate.
upward