College Algebra - Putting It All Together |51
Questions| With Correct Answers.
1). Natural numbers
Ans: Sometimes referred to as the "counting numbers"
1, 2, 3, 4, 5,...
2). Intergers
Ans: Include the natural numbers, their opposites, and 0
..., -2, -1, 0, 1, 2,...
3). Rational numbers
Ans: Include integers; all fractions p/q, where p and q are integers with q not = 0; all
repeating and all terminating decimals
1/2, -3, 128/6, -0.335, 0,
0.25 = 1/4, 0.33 cont. = 1/3
4). Irrational numbers
Ans: Can be written as nonrepeating, nonterminating decimals; cannot be a rational
number; if a square root of a positive integer is not an integer, it is an irrational number
pi, root 2, -root 5, ^3 root 7, pi^4
5). Real numbers
Ans: Any number that can be expressed in standard (decimal) form
Include the rational numbers and irrational numbers
pi, root 7, -4/7, 0, -10, 1.237
0.6 cont. = 2/3, 1000, root 15, -root 5
6). Order of operations
Ans: Using the following order of operations, perform all calculations within
parentheses, square roots, and absolute value bars and above and below fraction bars.
Then perform any remaining calculations.
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, 1. Evaluate all exponents. Then do any negation after evaluating exponents.
2. Do all multiplication and division from left to right.
3. Do all addition and subtraction from left to right.
-4squared minus 12 divide 2 = -16 - 12 divide 2 - 2
= -16 - 6 - 2
= -22 - 2
= -24
2 + 4squared / 3 - 3 time 5 = 2 + - 15
= 18 / -12
= -
7). Mean, or average
Ans: To find the mean, or average, of n numbers, divide their sum by n.
The mean of the four numbers -3, 5, 6, 9 is
-3 + 5 + 6 + = 4.25.
8). Median
Ans: The median of a sorted list of numbers equals the value that is located in the
middle of the list. Half the data are greater than or equal to the median, and half the data
are less than or equal to the median.
The median of 2, 3, 6, 9, 11 is 6, the middle data item.
The median of 2, 3, 6, 9 is the average of the two middle values: 3 and 6. Therefore the
median is:
3 + = 4.5.
9). Relation, domain, and range
Ans: A relation is a set of ordered pairs (x, y). The set of x-values is called the domain,
and the set of y-values is called the range.
The relation S = {(1,3), (2,5), (1,6)} has domain D = {1,2} and range R = {3, 5, 6}.
10). Distance formula
Ans: The distance between (x1, y1) and (x2, y2) is
d = root over all (x2 - x1)squared + (y2 - y1)squared.
The distance between (2, -1) and (-1, 3) is d = root over all (-1 - 2)squared + (3 -
(-1))squared = 5.
11). Midpoint formula
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Questions| With Correct Answers.
1). Natural numbers
Ans: Sometimes referred to as the "counting numbers"
1, 2, 3, 4, 5,...
2). Intergers
Ans: Include the natural numbers, their opposites, and 0
..., -2, -1, 0, 1, 2,...
3). Rational numbers
Ans: Include integers; all fractions p/q, where p and q are integers with q not = 0; all
repeating and all terminating decimals
1/2, -3, 128/6, -0.335, 0,
0.25 = 1/4, 0.33 cont. = 1/3
4). Irrational numbers
Ans: Can be written as nonrepeating, nonterminating decimals; cannot be a rational
number; if a square root of a positive integer is not an integer, it is an irrational number
pi, root 2, -root 5, ^3 root 7, pi^4
5). Real numbers
Ans: Any number that can be expressed in standard (decimal) form
Include the rational numbers and irrational numbers
pi, root 7, -4/7, 0, -10, 1.237
0.6 cont. = 2/3, 1000, root 15, -root 5
6). Order of operations
Ans: Using the following order of operations, perform all calculations within
parentheses, square roots, and absolute value bars and above and below fraction bars.
Then perform any remaining calculations.
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, 1. Evaluate all exponents. Then do any negation after evaluating exponents.
2. Do all multiplication and division from left to right.
3. Do all addition and subtraction from left to right.
-4squared minus 12 divide 2 = -16 - 12 divide 2 - 2
= -16 - 6 - 2
= -22 - 2
= -24
2 + 4squared / 3 - 3 time 5 = 2 + - 15
= 18 / -12
= -
7). Mean, or average
Ans: To find the mean, or average, of n numbers, divide their sum by n.
The mean of the four numbers -3, 5, 6, 9 is
-3 + 5 + 6 + = 4.25.
8). Median
Ans: The median of a sorted list of numbers equals the value that is located in the
middle of the list. Half the data are greater than or equal to the median, and half the data
are less than or equal to the median.
The median of 2, 3, 6, 9, 11 is 6, the middle data item.
The median of 2, 3, 6, 9 is the average of the two middle values: 3 and 6. Therefore the
median is:
3 + = 4.5.
9). Relation, domain, and range
Ans: A relation is a set of ordered pairs (x, y). The set of x-values is called the domain,
and the set of y-values is called the range.
The relation S = {(1,3), (2,5), (1,6)} has domain D = {1,2} and range R = {3, 5, 6}.
10). Distance formula
Ans: The distance between (x1, y1) and (x2, y2) is
d = root over all (x2 - x1)squared + (y2 - y1)squared.
The distance between (2, -1) and (-1, 3) is d = root over all (-1 - 2)squared + (3 -
(-1))squared = 5.
11). Midpoint formula
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