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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. As shown earlier - c - di is the complex conjugate of the denominator c + di.
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
Even Number
even and the sum of its digits is divisible by 3
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .

2. 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
Associative Law of Multiplication
order of operations
difference

3. Plus
Third Axiom of Equality
Forth Axiom of Equality
constructing a parallelogram
addition

4. Product of 16 and the sum of 5 and number R
Set
Positional notation (place value)
addition
16(5+R)

5. Are used to indicate sets
subtraction
Braces
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).
one characteristic in common such as similarity of appearance or purpose

6. 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
order of operations
In Diophantine geometry
To separate a number into prime factors
solutions

7. Product
constructing a parallelogram
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
solutions
multiplication

8. 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
addition
Inversive geometry
Downward

9. 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
Odd Number
magnitude and direction
constructing a parallelogram

10. Remainder
solutions
magnitude and direction
order of operations
subtraction

11. 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
magnitude
repeated elements
order of operations

12. Subtraction
K+6 - K+5 - K+4 K+3.........answer is K+3
difference
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 number formed by the three right-hand digits is divisible by 8

13. 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.
Braces
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
F - F+1 - F+2.......answer is F+2
a curve - a surface or some other such object in n-dimensional space

14. An equation - or system of equations - in two or more variables defines
subtraction
upward
a curve - a surface or some other such object in n-dimensional space
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}

15. 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.
Associative Law of Multiplication
quadratic field
positive
Natural Numbers

16. In the Rectangular Coordinate System - On the vertical line - direction ________ is positive
upward
addition
Prime Number
polynomial

17. 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
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
addition

18. 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.
Associative Law of Addition
equation
Numerals
Number fields

19. G - E - M - A Grouping - Exponents - Multiply/Divide - Add/Subtract
The multiplication of two complex numbers is defined by the following formula:
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.
C or
order of operations

20. Does not have an equal sign (3x+5) (2a+9b)
Factor of the given number
expression
its the sum of its digits is divisible by 3
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:

21. Any number that is not a multiple of 2 is an
The numbers are conventionally plotted using the real part
Odd Number
Commutative Law of Addition
Commutative Law of Multiplication

22. The Arabic numerals from 0 through 9 are called
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.
Prime Number
Digits

23. The finiteness or not of the number of rational or integer points on an algebraic curve
one characteristic in common such as similarity of appearance or purpose
subtraction
Equal
the genus of the curve

24. The defining characteristic of a position vector is that it has
upward
a complex number is real if and only if it equals its conjugate.
polynomial
magnitude and direction

25. The objects or symbols in a set are called Numerals - Lines - or Points
Members of Elements of the Set
counterclockwise through 90
polynomial
base-ten number

26. Work on the problem of general polynomials ultimately led to the fundamental theorem of algebra -
The numbers are conventionally plotted using the real part
Equal
magnitude and direction
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.

27. Any number that la a multiple of 2 is an
Even Number
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
positive
equation

28. Any number that can be divided lnto a given number without a remainder is a
Associative Law of Multiplication
The numbers are conventionally plotted using the real part
the genus of the curve
Factor of the given number

29. Number X decreased by 12 divided by forty
negative
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
(x-12)/40
Even Number

30. Number T increased by 9
magnitude
its the sum of its digits is divisible by 3
T+9
Absolute value and argument

31. Sum
addition
the sum of its digits is divisible by 9
consecutive whole numbers
repeated elements

32. 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
Prime Number
quadratic field
magnitude
Definition of genus

33. Increased by
7
Even Number
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
addition

34. Addition of two complex numbers can be done geometrically by
Downward
constructing a parallelogram
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
Third Axiom of Equality

35. Quotient
Set
division
subtraction
repeated elements

36. The number without a variable (5m+2). In this case - 2
magnitude and direction
7
constant
base-ten number

37. Total
F - F+1 - F+2.......answer is F+2
addition
magnitude and direction
Commutative Law of Multiplication

38. The set of all complex numbers is denoted by
C or
the number formed by the three right-hand digits is divisible by 8
In Diophantine geometry
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.

39. Decreased by
subtraction
a curve - a surface or some other such object in n-dimensional space
rectangular coordinates
Forth Axiom of Equality

40. A number is divisible by 9 if
Braces
the sum of its digits is divisible by 9
difference
Analytic number theory

41. The place value which corresponds to a given position in a number is determined by the
even and the sum of its digits is divisible by 3
Base of the number system
Third Axiom of Equality
Multiple of the given number

42. Implies a collection or grouping of similar - objects or symbols.
Set
In Diophantine geometry
Digits
Algebraic number theory

43. The relative greatness of positive and negative numbers
magnitude
the genus of the curve
upward
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).

44. 2 -3 -4 -5 -6
Prime Factor
Factor of the given number
Numerals
consecutive whole numbers

45. This law combines the operations of addition and multiplication. The distribution of a common multiplier among the terms of an additive expression.
solutions
T+9
Commutative Law of Addition
Distributive Law

46. Sixteen less than number Q
Q-16
subtraction
The real number a of the complex number z = a + bi
a curve - a surface or some other such object in n-dimensional space

47. Viewed in this way the multiplication of a complex number by i corresponds to rotating a complex number
an equation in two variables defines
counterclockwise through 90
Forth Axiom of Equality
solutions

48. 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
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
quadratic field
Place Value Concept
Odd Number

49. More than
the genus of the curve
constant
addition
constructing a parallelogram

50. The objects in a set have at least
an equation in two variables defines
subtraction
K+6 - K+5 - K+4 K+3.........answer is K+3
one characteristic in common such as similarity of appearance or purpose