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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. The number touching the variable (in the case of 5x - would be 5)
coefficient
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
the sum of its digits is divisible by 9
Base of the number system

2. Product of 16 and the sum of 5 and number R
the number formed by the two right-hand digits is divisible by 4
Absolute value and argument
16(5+R)
Analytic number theory

3. 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.
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
negative
Complex numbers
Definition of genus

4. 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
Set
even and the sum of its digits is divisible by 3
quadratic field
Absolute value and argument

5. LAWS FOR COMBINING NUMBERS
Positional notation (place value)
variable
7
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.

6. Does not have an equal sign (3x+5) (2a+9b)
Algebraic number theory
K+6 - K+5 - K+4 K+3.........answer is K+3
expression
Third Axiom of Equality

7. The defining characteristic of a position vector is that it has
negative
quadratic field
Inversive geometry
magnitude and direction

8. 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
positive
an equation in two variables defines
magnitude and direction
Place Value Concept

9. The central problem of Diophantine geometry is to determine when a Diophantine equation has
Downward
solutions
rectangular coordinates
Braces

10. The greatest of 3 consecutive whole numbers - the smallest of which is F
F - F+1 - F+2.......answer is F+2
Distributive Law
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
Numerals

11. The smallest of four sonsecutive whole numbers - the biggest of which is K+6
Numerals
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
addition
K+6 - K+5 - K+4 K+3.........answer is K+3

12. Any number that is not a multiple of 2 is an
The multiplication of two complex numbers is defined by the following formula:
difference
the number formed by the two right-hand digits is divisible by 4
Odd Number

13. Any number that is exactly divisible by a given number is a
repeated elements
Forth Axiom of Equality
Multiple of the given number
Distributive Law

14. 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.
C or
monomial
Analytic number theory
the number formed by the three right-hand digits is divisible by 8

15. Any number that can be divided lnto a given number without a remainder is a
constructing a parallelogram
Distributive Law
Factor of the given number
Q-16

16. The real and imaginary parts of a complex number can be extracted using the conjugate:
Equal
a complex number is real if and only if it equals its conjugate.
equation
To separate a number into prime factors

17. 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.)
an equation in two variables defines
addition
Number fields
Braces

18. An equation - or system of equations - in two or more variables defines
Commutative Law of Multiplication
magnitude
a curve - a surface or some other such object in n-dimensional space
Prime Factor

19. Total
(x-12)/40
7
negative
addition

20. 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
The real number a of the complex number z = a + bi
one characteristic in common such as similarity of appearance or purpose
Algebraic number theory

21. 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.
division
one characteristic in common such as similarity of appearance or purpose
Commutative Law of Multiplication
The absolute value (or modulus or magnitude) of a complex number z = x + yi is

22. Sum
Positional notation (place value)
the sum of its digits is divisible by 9
addition
Numerals

23. Quotient
division
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
polynomial
Digits

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.
(x-12)/40
Composite Number
Associative Law of Addition
addition

25. Number symbols
Inversive geometry
Numerals
Complex numbers
Analytic number theory

26. 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
Algebraic number theory
solutions
The real number a of the complex number z = a + bi
Positional notation (place value)

27. 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
Composite Number
To separate a number into prime factors
a curve - a surface or some other such object in n-dimensional space
one characteristic in common such as similarity of appearance or purpose

28. 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.
Place Value Concept
magnitude and direction
difference
Third Axiom of Equality

29. G - E - M - A Grouping - Exponents - Multiply/Divide - Add/Subtract
subtraction
In Diophantine geometry
order of operations
Commutative Law of Addition

30. 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
base-ten number
Positional notation (place value)
Analytic number theory
The numbers are conventionally plotted using the real part

31. A number that has no factors except itself and 1 is a
algebraic number
Prime Number
equation
Positional notation (place value)

32. 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:
division
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).
the genus of the curve
Set

33. 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
Braces
In Diophantine geometry
its the sum of its digits is divisible by 3
Number fields

34. A number that has factors other than itself and 1 is a
polynomial
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.
Composite Number
rectangular coordinates

35. No short method has been found for determining whether a number is divisible by
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).
7
subtraction
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}

36. 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.
Third Axiom of Equality
its the sum of its digits is divisible by 3
The numbers are conventionally plotted using the real part
equation

37. In the Rectangular Coordinate System - the direction to the right along the horizontal line is
positive
In Diophantine geometry
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
quadratic field

38. Plus
subtraction
addition
consecutive whole numbers
Associative Law of Multiplication

39. 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.
Forth Axiom of Equality
Commutative Law of Multiplication
even and the sum of its digits is divisible by 3
constructing a parallelogram

40. 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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41. Viewed in this way the multiplication of a complex number by i corresponds to rotating a complex number
Associative Law of Multiplication
Complex numbers
algebraic number
counterclockwise through 90

42. In the Rectangular Coordinate System - On the vertical line - direction _______ is negative
Downward
difference
negative
Absolute value and argument

43. Number X decreased by 12 divided by forty
Even Number
Q-16
subtraction
(x-12)/40

44. One term (5x or 4)
The multiplication of two complex numbers is defined by the following formula:
Commutative Law of Addition
Second Axiom of Equality
monomial

45. A number is divisible by 9 if
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
constructing a parallelogram
consecutive whole numbers
the sum of its digits is divisible by 9

46. The objects or symbols in a set are called Numerals - Lines - or Points
Positional notation (place value)
Members of Elements of the Set
the genus of the curve
The real number a of the complex number z = a + bi

47. The relative greatness of positive and negative numbers
Base of the number system
negative
upward
magnitude

48. If a factor of a number is prime - it is called a
Prime Factor
the sum of its digits is divisible by 9
The multiplication of two complex numbers is defined by the following formula:
subtraction

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
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
a complex number is real if and only if it equals its conjugate.
Associative Law of Addition
In Diophantine geometry

50. Has an equal sign (3x+5 = 14)
Positional notation (place value)
magnitude
equation
division