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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. Sum
addition
division
Number fields
The absolute value (or modulus or magnitude) of a complex number z = x + yi is

2. The greatest of 3 consecutive whole numbers - the smallest of which is F
The real number a of the complex number z = a + bi
subtraction
Positional notation (place value)
F - F+1 - F+2.......answer is F+2

3. No short method has been found for determining whether a number is divisible by
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
Factor of the given number
addition
7

4. Integers greater than zero and less than 5 form a set - as follows:
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
addition
repeated elements
The real number a of the complex number z = a + bi

5. 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.
The numbers are conventionally plotted using the real part
complex number
counterclockwise through 90
addition

6. More than one term (5x+4 contains two)
The multiplication of two complex numbers is defined by the following formula:
Members of Elements of the Set
polynomial
Commutative Law of Addition

7. One term (5x or 4)
monomial
Associative Law of Multiplication
Equal
Natural Numbers

8. The relative greatness of positive and negative numbers
repeated elements
Forth Axiom of Equality
magnitude
Inversive geometry

9. 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.
subtraction
Commutative Law of Multiplication
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).
complex number

10. 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.
division
quadratic field
Natural Numbers
Number fields

11. A curve in the plane
Natural Numbers
an equation in two variables defines
quadratic field
Associative Law of Addition

12. The number touching the variable (in the case of 5x - would be 5)
a curve - a surface or some other such object in n-dimensional space
Digits
Associative Law of Addition
coefficient

13. 2 -3 -4 -5 -6
consecutive whole numbers
subtraction
T+9
Associative Law of Addition

14. The place value which corresponds to a given position in a number is determined by the
Base of the number system
Digits
righthand digit is 0 or 5
Composite Number

15. The finiteness or not of the number of rational or integer points on an algebraic curve
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
the genus of the curve
7
Prime Number

16. A letter tat represents a number that is unknown (usually X or Y)
counterclockwise through 90
division
variable
magnitude and direction

17. Product of 16 and the sum of 5 and number R
repeated elements
16(5+R)
right-hand digit is even
Absolute value and argument

18. The real and imaginary parts of a complex number can be extracted using the conjugate:
right-hand digit is even
a complex number is real if and only if it equals its conjugate.
Associative Law of Addition
the genus of the curve

19. 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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20. A number is divisible by 4 if
the number formed by the two right-hand digits is divisible by 4
subtraction
subtraction
Associative Law of Addition

21. The objects in a set have at least
one characteristic in common such as similarity of appearance or purpose
constructing a parallelogram
Commutative Law of Multiplication
Digits

22. 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).
Digits
its the sum of its digits is divisible by 3
The real number a of the complex number z = a + bi

23. The central problem of Diophantine geometry is to determine when a Diophantine equation has
polynomial
order of operations
solutions
Composite Number

24. Decreased by
magnitude and direction
base-ten number
subtraction
Definition of genus

25. If a factor of a number is prime - it is called a
Multiple of the given number
Members of Elements of the Set
subtraction
Prime Factor

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 -
equation
a complex number is real if and only if it equals its conjugate.
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
Second Axiom of Equality

27. A number is divisible by 2 if
The numbers are conventionally plotted using the real part
right-hand digit is even
K+6 - K+5 - K+4 K+3.........answer is K+3
rectangular coordinates

28. 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.
an equation in two variables defines
monomial
Associative Law of Multiplication
16(5+R)

29. A number that has factors other than itself and 1 is a
addition
base-ten number
Third Axiom of Equality
Composite Number

30. Has an equal sign (3x+5 = 14)
division
T+9
multiplication
equation

31. 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
Definition of genus
consecutive whole numbers
Multiple of the given number

32. First axiom of equality
the sum of its digits is divisible by 9
right-hand digit is even
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.
difference

33. 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 real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
The numbers are conventionally plotted using the real part
Algebraic number theory

34. 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.
F - F+1 - F+2.......answer is F+2
subtraction
Prime Factor
Complex numbers

35. Any number that can be divided lnto a given number without a remainder is a
Factor of the given number
Members of Elements of the Set
equation
Multiple of the given number

36. In the Rectangular Coordinate System - On the vertical line - direction _______ is negative
Downward
Inversive geometry
Composite Number
addition

37. 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.
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
16(5+R)
Associative Law of 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.

38. 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
Factor of the given number
equation
In Diophantine geometry
subtraction

39. 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
Third Axiom of Equality
F - F+1 - F+2.......answer is F+2
C or
To separate a number into prime factors

40. G - E - M - A Grouping - Exponents - Multiply/Divide - Add/Subtract
Algebraic number theory
order of operations
(x-12)/40
Even Number

41. This formula can be used to compute the multiplicative inverse of a complex number if it is given in
Members of Elements of the Set
rectangular coordinates
quadratic field
order of operations

42. 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 number formed by the two right-hand digits is divisible by 4
the number formed by the three right-hand digits is divisible by 8
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
Third Axiom of Equality

43. 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
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
Members of Elements of the Set
coefficient
Equal

44. 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
Second Axiom of Equality
addition
Complex numbers

45. A number is divisible by 3 if
C or
its the sum of its digits is divisible by 3
magnitude
Prime Number

46. Any number that is exactly divisible by a given number is a
Associative Law of Addition
addition
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
Multiple of the given number

47. A number is divisible by 9 if
the sum of its digits is divisible by 9
polynomial
Algebraic number theory
Even Number

48. The number without a variable (5m+2). In this case - 2
base-ten number
division
Commutative Law of Addition
constant

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
16(5+R)
Equal
Analytic number theory

50. Less than
subtraction
Prime Number
Complex numbers
Associative Law of Addition