Algebra Part 2 Unit 1

Evaluate the infinite series if it has a sum

-12

Use inscribed rectangles to approximate the area under f(x) = -x2 + 7 for the -2 ≤ x ≤ 0 and rectangle width 0.5.

10.25 units^2

The sequence -5, -2, 1, 4, ... , 25 has 11 terms. Evaluate the related series.

110

Find the 14th term of the sequence 10, 18, 26, 34, ....

114

Find the next three terms in the sequence 1, 2, 4, 8, ....

16, 32, 64

The sequence -14, -9, -4, 1, ... , 41 has 12 terms. Evaluate the related series.

162

Find the missing terms of the geometric sequence 480, ___, ___, ___, 12.288, .... (Hint: The geometric mean of the first and fifth terms is the third term.)

192, 76.8, 30.72

The table gives data about municipal waste collected and recycled by type. Find P(paper | not recycled).

31.7%

Use the frequency table to find P(2 or 3 children).

42%

The table lists the results of a survey of the students at a community college. Suppose a student is selected at random. Find P(male | student takes physiology).

43/83

Ms. Chin collected data about how long students in two of her classes spent doing homework. This table shows the result. Suppose a student from her third or fourth period class is selected at random.

5/23

Evaluate the series

5461/16,384

For the sum find the number of terms, the first term, and the last term. Then evaluate the series.

6 terms, 25, 0; 75

Use the frequency table to find P(0 - 2 children).

68%

The probability that a city bus is ready for service when needed is 85%. The probability that a city bus is ready for service and has a working radio is 64%. Find the probability that a bus chosen at random has a working radio given that it is ready for service.

75.3%

Evaluate the series 3 + 9 + 15 + 21 + 27 + ... to the 16th term.

768

Find the arithmetic mean an of the terms

91/60

Describe the pattern 1, 2/3, 3/5, 4/7, 5/9, ....

Add 1 to the numerator and 2 to the denominator of the previous number.

A spinner is divided into eight equally-sized areas. The central angle for pink is 90°, for teal is 225°, and for blue is 45°. Which is the correct frequency table for this spinner?

Color Frequency Probability Pink 2 1/4 Teal 5 5/8 Blue 1 1/8

5, 7, 11, 15, 21 is an infinite series.

False

A situation may not be described by more than one sample space.

False

If x is at the 63rd percentile, then 37% of the data are less than or equal to x.

False

The missing term of the arithmetic sequence 13, __, 27 is 21.

False; 20

The sum of a geometric series containing five terms, a common ratio of 3, and a first term of 1/2 is 62.5.

False; 60.5

The sequence 3, 6, 9, 12 is geometric.

False; This sequence is an arithmetic sequence.

A box-and-whisker plot is a method of displaying data that uses quartiles to form the center box and the minimum and maximum values to form the whiskers.

True

A frequency table is a list of the outcomes in a sample space and the number of times each outcome occurs.

True

A percentile is a number from 0 to 100 which can be associated with x to indicate the percent of the data that are less than or equal to x.

True

If 10% of a group ate sandwiches two days in a row, and 40% of the group had a sandwich on the first day, this means that 25% of the group that ate a first sandwich had a second.

True

Inscribed rectangles are completely under the curve.

True

The area approximated by circumscribed rectangles is greater than the area under the curve.

True

The mode of the set 2, 3, 3, 4, 5, 8, 9, 10 is 3.

True

The next three terms of the sequence 1, 3, 5, 7, ... are 9, 11, 13.

True

What is the first step in finding the median in a set of data?

Write the numbers in order from least to greatest.

Write the explicit formula for the sequence with a1 = 120 and r = 0.3. Then generate the first five terms.

an = 120 • 0.3n - 1; 120, 36, 10.8, 3.24, 0.972

Write an explicit formula for the sequence

an=n+1/n^2+3; 15/199

Decide whether the formula an = -4n(n - 1) is explicit or recursive. Then find the first five terms of the sequence.

explicit; 0, -8, -24, -48, -80

What does the dot at 47 represent?

lower quartile

Find the mean, the median, and mode of the set of values. 17, 19, 22, 9, 18, 13, 24, 6, 25

mean: 17, median: 18, no mode

Make a box-and-whisker plot for the set of values. 5.2, 9.2, 5.2, 3.2, 3.2, 7.2, 6.2, 8.2, 5.2, 4.2, 5.2, 6.2, 9.2, 9.2, 8.2

minimum=3.2; maximum=9.2; Q1=5.2; Q2=6.2; Q3=8.2

Identify the sequence 4, 6, 10, 18, ... as arithmetic, geometric, or neither. Then find the next two terms.

neither; 34, 66

Tell whether 3, 10, 17, 24, ... , 73 is a sequence or a series. Then tell whether it is finite or infinite.

sequence, finite

Is the sequence 5.1, 10.5, 15.9, 21.3, ... arithmetic? If so, identify the common difference.

yes, 5.4