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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. Integers greater than zero and less than 5 form a set - as follows:
equation
Third Axiom of Equality
C or
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}

2. In the Rectangular Coordinate System - the direction to the left along the horizontal line is
Distributive Law
negative
The real number a of the complex number z = a + bi
order of operations

3. 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.
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).
monomial
expression
Associative Law of Addition

4. Are used to indicate sets
Base of the number system
Commutative Law of Multiplication
Braces
In Diophantine geometry

5. 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
Commutative Law of Multiplication
Place Value Concept
16(5+R)
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .

6. Subtraction
difference
Positional notation (place value)
the genus of the curve
F - F+1 - F+2.......answer is F+2

7. Number T increased by 9
K+6 - K+5 - K+4 K+3.........answer is K+3
Base of the number system
T+9
Third Axiom of Equality

8. G - E - M - A Grouping - Exponents - Multiply/Divide - Add/Subtract
polynomial
Equal
right-hand digit is even
order of operations

9. 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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10. 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.
constant
a curve - a surface or some other such object in n-dimensional space
Third Axiom of Equality
K+6 - K+5 - K+4 K+3.........answer is K+3

11. The set of all complex numbers is denoted by
Downward
algebraic number
C or
division

12. 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
Q-16
The real number a of the complex number z = a + bi
base-ten number
variable

13. The place value which corresponds to a given position in a number is determined by the
Base of the number system
Q-16
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.
To separate a number into prime factors

14. Number symbols
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
The multiplication of two complex numbers is defined by the following formula:
right-hand digit is even
Numerals

15. 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.
addition
Absolute value and argument
rectangular coordinates
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.

16. 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
Complex numbers
algebraic number
7
repeated elements

17. A number is divisible by 8 if
one characteristic in common such as similarity of appearance or purpose
addition
the number formed by the three right-hand digits is divisible by 8
constructing a parallelogram

18. In the Rectangular Coordinate System - the direction to the right along the horizontal line is
division
Commutative Law of Multiplication
positive
The numbers are conventionally plotted using the real part

19. 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
In Diophantine geometry
solutions
Equal
7

20. The numbers which are used for counting in our number system are sometimes called
its the sum of its digits is divisible by 3
Associative Law of Addition
Prime Number
Natural Numbers

21. A number that has factors other than itself and 1 is a
Composite Number
Digits
one characteristic in common such as similarity of appearance or purpose
(x-12)/40

22. If a factor of a number is prime - it is called a
Prime Factor
Algebraic number theory
Commutative Law of Addition
Second Axiom of Equality

23. One term (5x or 4)
Second Axiom of Equality
a complex number is real if and only if it equals its conjugate.
monomial
consecutive whole numbers

24. This law combines the operations of addition and multiplication. The distribution of a common multiplier among the terms of an additive expression.
addition
Distributive Law
the number formed by the two right-hand digits is divisible by 4
Absolute value and argument

25. First axiom of equality
The multiplication of two complex numbers is defined by the following formula:
subtraction
C or
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.

26. The smallest of four sonsecutive whole numbers - the biggest of which is K+6
Multiple of the given number
K+6 - K+5 - K+4 K+3.........answer is K+3
Complex numbers
the genus of the curve

27. Any number that is exactly divisible by a given number is a
Composite Number
addition
Multiple of the given number
Downward

28. 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
addition
subtraction
Factor of the given number

29. 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
Factor of the given number
order of operations
Commutative Law of Addition
Absolute value and argument

30. A number is divisible by 6 if it is
base-ten number
even and the sum of its digits is divisible by 3
solutions
Analytic number theory

31. 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.
an equation in two variables defines
F - F+1 - F+2.......answer is F+2
addition
Complex numbers

32. A number is divisible by 3 if
its the sum of its digits is divisible by 3
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
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.

33. Plus
the genus of the curve
addition
Equal
16(5+R)

34. 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.
rectangular coordinates
Definition of genus
expression
Commutative Law of Addition

35. 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.
Second Axiom of Equality
Complex numbers
Prime Factor
Numerals

36. 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.
In Diophantine geometry
Associative Law of Multiplication
K+6 - K+5 - K+4 K+3.........answer is K+3
coefficient

37. 2 -3 -4 -5 -6
positive
consecutive whole numbers
Place Value Concept
rectangular coordinates

38. A curve in the plane
subtraction
K+6 - K+5 - K+4 K+3.........answer is K+3
an equation in two variables defines
difference

39. Number X decreased by 12 divided by forty
addition
The real number a of the complex number z = a + bi
the sum of its digits is divisible by 9
(x-12)/40

40. Any number that can be divided lnto a given number without a remainder is a
constant
Associative Law of Addition
subtraction
Factor of the given number

41. Decreased by
multiplication
C or
the number formed by the three right-hand digits is divisible by 8
subtraction

42. 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 -
Definition of genus
one characteristic in common such as similarity of appearance or purpose
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
16(5+R)

43. Product
multiplication
Set
a complex number is real if and only if it equals its conjugate.
subtraction

44. If two equal quantities are divided by the same quantity - the resulting quotients are equal. If equals are divided by equals - the results are equal.
7
To separate a number into prime factors
Forth Axiom of Equality
repeated elements

45. Does not have an equal sign (3x+5) (2a+9b)
righthand digit is 0 or 5
difference
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
expression

46. 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
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).
Multiple of the given number
right-hand digit is even

47. Work on the problem of general polynomials ultimately led to the fundamental theorem of algebra -
an equation in two variables defines
C or
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.

48. The finiteness or not of the number of rational or integer points on an algebraic curve
the genus of the curve
Members of Elements of the Set
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
Factor of the given number

49. The Arabic numerals from 0 through 9 are called
even and the sum of its digits is divisible by 3
Digits
the sum of its digits is divisible by 9
Place Value Concept

50. 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.)
complex number
16(5+R)
Second Axiom of Equality
Number fields