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CLEP General Mathematics: Number Systems And Sets

Subjects : clep, math

Instructions:

Answer 50 questions in 15 minutes.
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Match each statement with the correct term.
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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. Increased by
addition
Prime Factor
Braces
Numerals

2. An equation - or system of equations - in two or more variables defines
F - F+1 - F+2.......answer is F+2
Odd Number
a curve - a surface or some other such object in n-dimensional space
T+9

3. Decreased by
polynomial
one characteristic in common such as similarity of appearance or purpose
the genus of the curve
subtraction

4. 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
complex number
Forth Axiom of Equality
In Diophantine geometry
Downward

5. 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:
expression
negative
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).
Base of the number system

6. A number that has factors other than itself and 1 is a
the genus of the curve
Composite Number
Associative Law of Addition
addition

7. 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
To separate a number into prime factors
constructing a parallelogram
Prime Number
T+9

8. 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 -
16(5+R)
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.
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:

9. More than one term (5x+4 contains two)
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
Prime Number
polynomial
addition

10. Does not have an equal sign (3x+5) (2a+9b)
In Diophantine geometry
Equal
Members of Elements of the Set
expression

11. Any number that can be divided lnto a given number without a remainder is a
subtraction
addition
Numerals
Factor of the given number

12. 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
Factor of the given number
Multiple of the given number
subtraction
complex number

13. Product
multiplication
The real number a of the complex number z = a + bi
Even Number
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .

14. Sum
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
the genus of the curve
addition
upward

15. The Arabic numerals from 0 through 9 are called
magnitude and direction
Inversive geometry
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
Digits

16. The finiteness or not of the number of rational or integer points on an algebraic curve
Prime Factor
a complex number is real if and only if it equals its conjugate.
the genus of the curve
magnitude

17. 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
coefficient
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
solutions

18. The smallest of four sonsecutive whole numbers - the biggest of which is K+6
division
Prime Number
K+6 - K+5 - K+4 K+3.........answer is K+3
In Diophantine geometry

19. Number T increased by 9
negative
T+9
The real number a of the complex number z = a + bi
Associative Law of Addition

20. Sixteen less than number Q
algebraic number
righthand digit is 0 or 5
right-hand digit is even
Q-16

21. Any number that la a multiple of 2 is an
the number formed by the two right-hand digits is divisible by 4
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.
The multiplication of two complex numbers is defined by the following formula:
Even Number

22. Integers greater than zero and less than 5 form a set - as follows:
right-hand digit is even
Absolute value and argument
Composite Number
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}

23. LAWS FOR COMBINING NUMBERS
Analytic number theory
T+9
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
Algebraic number theory

24. 2 -3 -4 -5 -6
addition
Digits
consecutive whole numbers
Multiple of the given number

25. 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
The real number a of the complex number z = a + bi
Q-16
Place Value Concept
right-hand digit is even

26. The place value which corresponds to a given position in a number is determined by the
Members of Elements of the Set
Algebraic number theory
consecutive whole numbers
Base of the number system

27. 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.
addition
Complex numbers
Number fields
polynomial

28. Less than
positive
Second Axiom of Equality
subtraction
Complex numbers

29. A number is divisible by 9 if
the sum of its digits is divisible by 9
equation
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
Place Value Concept

30. 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.
Digits
The real number a of the complex number z = a + bi
Downward
Commutative Law of Multiplication

31. As shown earlier - c - di is the complex conjugate of the denominator c + di.
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
Absolute value and argument
complex number
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.

32. Are used to indicate sets
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).
Braces
Associative Law of Addition
magnitude

33. A branch of geometry studying more general reflections than ones about a line - can also be expressed in terms of complex numbers.
Complex numbers
Inversive geometry
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
Definition of genus

34. One term (5x or 4)
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
Positional notation (place value)
To separate a number into prime factors
monomial

35. The real and imaginary parts of a complex number can be extracted using the conjugate:
To separate a number into prime factors
a complex number is real if and only if it equals its conjugate.
Absolute value and argument
division

36. The greatest of 3 consecutive whole numbers - the smallest of which is F
Inversive geometry
F - F+1 - F+2.......answer is F+2
Complex numbers
the number formed by the three right-hand digits is divisible by 8

37. A number is divisible by 6 if it is
counterclockwise through 90
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
even and the sum of its digits is divisible by 3
one characteristic in common such as similarity of appearance or purpose

38. 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.
Composite Number
coefficient
Analytic number theory
In Diophantine geometry

39. 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.
Positional notation (place value)
Commutative Law of Multiplication
Associative Law of Addition
the sum of its digits is divisible by 9

40. 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
Positional notation (place value)
a complex number is real if and only if it equals its conjugate.
addition
Place Value Concept

41. 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
Associative Law of Multiplication
In Diophantine geometry
monomial
the number formed by the two right-hand digits is divisible by 4

42. 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
Absolute value and argument
magnitude
magnitude and direction
algebraic number

43. Work on the problem of general polynomials ultimately led to the fundamental theorem of algebra -
positive
righthand digit is 0 or 5
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
7

44. 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
Absolute value and argument
one characteristic in common such as similarity of appearance or purpose
Commutative Law of Addition
order of operations

45. 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.
upward
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
Factor of the given number
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.

46. 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
Positional notation (place value)
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
upward
Second Axiom of Equality

47. Total
order of operations
Numerals
the number formed by the three right-hand digits is divisible by 8
addition

48. Number symbols
Q-16
F - F+1 - F+2.......answer is F+2
rectangular coordinates
Numerals

49. A curve in the plane
solutions
T+9
an equation in two variables defines
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.

50. Viewed in this way the multiplication of a complex number by i corresponds to rotating a complex number
coefficient
repeated elements
counterclockwise through 90
Commutative Law of Addition