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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.
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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. In the Rectangular Coordinate System - the direction to the left along the horizontal line is
even and the sum of its digits is divisible by 3
righthand digit is 0 or 5
negative
a curve - a surface or some other such object in n-dimensional space
2. The Arabic numerals from 0 through 9 are called
Digits
Associative Law of Addition
expression
addition
3. 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
Odd Number
Complex numbers
addition
4. A number is divisible by 9 if
addition
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).
Analytic number theory
the sum of its digits is divisible by 9
5. Plus
Odd Number
Inversive geometry
addition
Commutative Law of Addition
6. This law combines the operations of addition and multiplication. The distribution of a common multiplier among the terms of an additive expression.
negative
F - F+1 - F+2.......answer is F+2
The real number a of the complex number z = a + bi
Distributive Law
7. The finiteness or not of the number of rational or integer points on an algebraic curve
the genus of the curve
Downward
magnitude and direction
the sum of its digits is divisible by 9
8. 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.
positive
addition
Second Axiom of Equality
multiplication
9. Any number that is not a multiple of 2 is an
Digits
Odd Number
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
Associative Law of Addition
10. A number is divisible by 4 if
Second Axiom of Equality
the number formed by the two right-hand digits is divisible by 4
Downward
Positional notation (place value)
11. 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
Natural Numbers
Place Value Concept
Odd Number
a complex number is real if and only if it equals its conjugate.
12. Are used to indicate sets
solutions
Distributive Law
Braces
the number formed by the three right-hand digits is divisible by 8
13. Sum
Multiple of the given number
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
In Diophantine geometry
addition
14. 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
algebraic number
order of operations
Braces
15. A letter tat represents a number that is unknown (usually X or Y)
addition
equation
variable
positive
16. The real and imaginary parts of a complex number can be extracted using the conjugate:
Numerals
Forth Axiom of Equality
a complex number is real if and only if it equals its conjugate.
Composite Number
17. G - E - M - A Grouping - Exponents - Multiply/Divide - Add/Subtract
Distributive Law
order of operations
repeated elements
Members of Elements of the Set
18. 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
the genus of the curve
base-ten number
To separate a number into prime factors
subtraction
19. A number is divisible by 6 if it is
monomial
even and the sum of its digits is divisible by 3
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
C or
20. 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
addition
The numbers are conventionally plotted using the real part
Associative Law of Addition
21. 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
the genus of the curve
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).
subtraction
22. Does not have an equal sign (3x+5) (2a+9b)
T+9
base-ten number
expression
its the sum of its digits is divisible by 3
23. Work on the problem of general polynomials ultimately led to the fundamental theorem of algebra -
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
7
counterclockwise through 90
Set
24. 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.
addition
Definition of genus
16(5+R)
Associative Law of Addition
25. 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
Third Axiom of Equality
addition
Even Number
26. As shown earlier - c - di is the complex conjugate of the denominator c + di.
Algebraic number theory
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
order of operations
In Diophantine geometry
27. Less than
subtraction
F - F+1 - F+2.......answer is F+2
algebraic number
order of operations
28. Number T increased by 9
polynomial
expression
the sum of its digits is divisible by 9
T+9
29. Decreased by
subtraction
Downward
equation
Forth Axiom of Equality
30. No short method has been found for determining whether a number is divisible by
7
Prime Factor
subtraction
To separate a number into prime factors
31. If a factor of a number is prime - it is called a
Q-16
Inversive geometry
Braces
Prime Factor
32. 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.
7
one characteristic in common such as similarity of appearance or purpose
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
an equation in two variables defines
33. A number that has no factors except itself and 1 is a
Prime Number
counterclockwise through 90
solutions
even and the sum of its digits is divisible by 3
34. Any number that la a multiple of 2 is an
Even Number
Numerals
an equation in two variables defines
counterclockwise through 90
35. The number without a variable (5m+2). In this case - 2
Commutative Law of Multiplication
constant
monomial
Algebraic number theory
36. 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
Multiple of the given number
Algebraic number theory
T+9
a complex number is real if and only if it equals its conjugate.
37. Sixteen less than number Q
Q-16
expression
base-ten number
Place Value Concept
38. The central problem of Diophantine geometry is to determine when a Diophantine equation has
quadratic field
solutions
positive
Third Axiom of Equality
39. A number that has factors other than itself and 1 is a
constructing a parallelogram
Members of Elements of the Set
Composite Number
Associative Law of Addition
40. First axiom of equality
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.
7
upward
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).
41. 2 -3 -4 -5 -6
addition
K+6 - K+5 - K+4 K+3.........answer is K+3
consecutive whole numbers
The numbers are conventionally plotted using the real part
42. 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
(x-12)/40
Base of the number system
Positional notation (place value)
magnitude and direction
43. 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.
The multiplication of two complex numbers is defined by the following formula:
Associative Law of Multiplication
F - F+1 - F+2.......answer is F+2
counterclockwise through 90
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.
Commutative Law of Addition
righthand digit is 0 or 5
Set
addition
45. Product of 16 and the sum of 5 and number R
16(5+R)
multiplication
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
coefficient
46. The defining characteristic of a position vector is that it has
Set
K+6 - K+5 - K+4 K+3.........answer is K+3
magnitude and direction
multiplication
47. 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
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
consecutive whole numbers
the number formed by the three right-hand digits is divisible by 8
In Diophantine geometry
48. Number symbols
expression
C or
K+6 - K+5 - K+4 K+3.........answer is K+3
Numerals
49. 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.
division
variable
Commutative Law of Multiplication
Downward
50. 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
Set
Commutative Law of Addition
Third Axiom of Equality
The real number a of the complex number z = a + bi
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