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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. In the Rectangular Coordinate System - the direction to the left along the horizontal line is
negative
Natural Numbers
Definition of genus
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.

2. Are not necessary. That is - the elements of {2 - 2 - 3 - 4} are simply {2 - 3 - and 4}
The multiplication of two complex numbers is defined by the following formula:
righthand digit is 0 or 5
repeated elements
The real number a of the complex number z = a + bi

3. The objects or symbols in a set are called Numerals - Lines - or Points
Composite Number
Members of Elements of the Set
Braces
Complex numbers

4. The finiteness or not of the number of rational or integer points on an algebraic curve
the genus of the curve
16(5+R)
Multiple of the given number
even and the sum of its digits is divisible by 3

5. A number that has factors other than itself and 1 is a
solutions
Composite Number
righthand digit is 0 or 5
even and the sum of its digits is divisible by 3

6. The smallest of four sonsecutive whole numbers - the biggest of which is K+6
To separate a number into prime factors
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).
K+6 - K+5 - K+4 K+3.........answer is K+3
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}

7. As shown earlier - c - di is the complex conjugate of the denominator c + di.
quadratic field
Commutative Law of Addition
Prime Factor
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.

8. Does not have an equal sign (3x+5) (2a+9b)
Commutative Law of Multiplication
subtraction
the number formed by the two right-hand digits is divisible by 4
expression

9. If a factor of a number is prime - it is called a
Prime Factor
Commutative Law of Addition
an equation in two variables defines
addition

10. One term (5x or 4)
Even Number
righthand digit is 0 or 5
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
monomial

11. Addition of two complex numbers can be done geometrically by
Associative Law of Addition
constructing a parallelogram
a curve - a surface or some other such object in n-dimensional space
In Diophantine geometry

12. 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.
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
Third Axiom of Equality
Forth Axiom of Equality
K+6 - K+5 - K+4 K+3.........answer is K+3

13. 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
right-hand digit is even
addition
Absolute value and argument
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.

14. 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
multiplication
addition
base-ten number

15. A branch of geometry studying more general reflections than ones about a line - can also be expressed in terms of complex numbers.
consecutive whole numbers
Absolute value and argument
Inversive geometry
monomial

16. 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:
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).
consecutive whole numbers
subtraction
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.

17. A curve in the plane
Q-16
Number fields
a curve - a surface or some other such object in n-dimensional space
an equation in two variables defines

18. 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
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
In Diophantine geometry
monomial
Braces

19. Remainder
subtraction
Members of Elements of the Set
multiplication
Digits

20. A number is divisible by 8 if
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
expression
Associative Law of Addition
the number formed by the three right-hand digits is divisible by 8

21. Less than
subtraction
16(5+R)
(x-12)/40
Base of the number system

22. This formula can be used to compute the multiplicative inverse of a complex number if it is given in
Forth Axiom of Equality
an equation in two variables defines
rectangular coordinates
monomial

23. This law combines the operations of addition and multiplication. The distribution of a common multiplier among the terms of an additive expression.
Associative Law of Addition
Even Number
subtraction
Distributive Law

24. The Arabic numerals from 0 through 9 are called
a complex number is real if and only if it equals its conjugate.
righthand digit is 0 or 5
Digits
Downward

25. More than one term (5x+4 contains two)
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
the sum of its digits is divisible by 9
polynomial
C or

26. A number that has no factors except itself and 1 is a
positive
magnitude
Prime Number
negative

27. 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.
polynomial
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
Associative Law of Addition
Commutative Law of Addition

28. Number X decreased by 12 divided by forty
difference
variable
(x-12)/40
Digits

29. The relative greatness of positive and negative numbers
Odd Number
addition
magnitude
Inversive geometry

30. Total
Downward
an equation in two variables defines
addition
Natural Numbers

31. Work on the problem of general polynomials ultimately led to the fundamental theorem of algebra -
C or
Second Axiom of Equality
order of operations
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.

32. 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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33. 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.
equation
Prime Factor
base-ten number

34. The defining characteristic of a position vector is that it has
positive
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
the sum of its digits is divisible by 9
magnitude and direction

35. Any number that is exactly divisible by a given number is a
variable
The numbers are conventionally plotted using the real part
Multiple of the given number
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:

36. The central problem of Diophantine geometry is to determine when a Diophantine equation has
solutions
Number fields
Set
subtraction

37. In the Rectangular Coordinate System - On the vertical line - direction ________ is positive
Positional notation (place value)
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
Natural Numbers
upward

38. 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.
T+9
Commutative Law of Multiplication
Natural Numbers
The multiplication of two complex numbers is defined by the following formula:

39. The numbers which are used for counting in our number system are sometimes called
Natural Numbers
Downward
C or
addition

40. 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.
upward
solutions
Numerals
Complex numbers

41. A letter tat represents a number that is unknown (usually X or Y)
Numerals
In Diophantine geometry
variable
Commutative Law of Multiplication

42. No short method has been found for determining whether a number is divisible by
Prime Factor
7
division
consecutive whole numbers

43. 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.
Second Axiom of Equality
magnitude
Q-16
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.

44. Decreased by
T+9
subtraction
Associative Law of Addition
addition

45. 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.
quadratic field
division
Q-16
Associative Law of Addition

46. 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
the number formed by the three right-hand digits is divisible by 8
In Diophantine geometry
a curve - a surface or some other such object in n-dimensional space
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.

47. The greatest of 3 consecutive whole numbers - the smallest of which is F
magnitude and direction
F - F+1 - F+2.......answer is F+2
Positional notation (place value)
Commutative Law of Addition

48. A number is divisible by 4 if
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
the number formed by the two right-hand digits is divisible by 4
difference
7

49. The number touching the variable (in the case of 5x - would be 5)
Forth Axiom of Equality
polynomial
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).
coefficient

50. Product of 16 and the sum of 5 and number R
(x-12)/40
Q-16
16(5+R)
C or