ALGEBRA & FUNCTIONS

SATDATA ANALYSIS, STATISTICS & PROBABILITY

CHECKPOINT REVIEW # 6EXERCISE 1, Page152.Which of the following changes to the number 372 would increase its value by more than 50%?

Switching the hundreds digit and the units digit.Switching the tens digit and the units digit.Adding 2 to the hundreds digit.Adding 1 to the hundreds digit.Adding 150.

572CHECKPOINT REVIEW # 6

EXERCISE 2, Page 152.Mitch and Dennis are running a 6000-meter race. If they start at the same time, and Mitch runs at a constant speed of 1200 meters per minute and Dennis runs at a constant speed of 1120 meters per minute, how many meters will Dennis have to run after Mitch crosses the finish line?

80240400480600

CHECKPOINT REVIEW # 6RateTimeDistanceMitch1200t6000Dennis1120t?RateTimeDistanceMitch1200t6000Dennis1120t?5 mins5 mins1120*5=56006000 - 5600CHECKPOINT REVIEW # 6EXERCISE 3, Page 152.

The figure above shows part of the graph y = 2x. What is the area of the shaded rectangle?

21325684168

Height = y = 2 (4) = 16Area = 2 (16)CHECKPOINT REVIEW # 6EXERCISE 4, Page 153.

In the figure above, O is the center of a circle with radius 8 and the length of arc AB is 4. What is the perimeter of triangle AOB?8 + 16 + 881624

88CHECKPOINT REVIEW # 6EXERCISE 5, Page 153.If the slope of line L is 1 / 3 and points ( 3, 9 ) and ( 6, p) are on line L, what is the value of p?

AVERAGESSolve AVERAGE questions by using the following formula:

If the average of six numbers is 12, what is the sum of the six numbers? ___________________NEVER average two averages. Instead find the average of the combined group of numbers.Choosing your own numbers to plug in work well on many average questions.

72Arithmetic mean!!!!AVERAGES: Put It TogetherEXERCISE 1, Page 155.The average of - 6 and y is 0. What is y ?

1860- 6- 18

AVERAGES: Put It TogetherEXERCISE 2, Page 155.The average of 14 numbers is 52. A fifteenth number is added to the set, and the average is still 52. What is the fifteenth number ?

5352150It cannot be determined from the information given.

AVERAGES: Put It TogetherEXERCISE 2, Page 155.

Let y denote the 15th number.

AVERAGES: Put It TogetherEXERCISE 3, Page 155.While out for a run, two joggers with an average age of 55 are joined by three more joggers. If the average age of the group of five joggers is 43, what is the average age of the three new joggers ?

3233343540

AVERAGES: Put It TogetherEXERCISE 3, Page 155.

MEDIAN AND MODEThe MEDIAN of a group of numbers is the middle number, when the numbers are FIRST arranged in order ( LARGEST to SMALLEST or SMALLEST to LARGEST).The MODE of a group of numbers is the number OR WORD ( CATEGORICAL VARIABLES ) that appears most frequently.On median and mode problems, always arrange first.Consider the following set of numbers: 3, 10, 6, 9, 4, 9, 5, 9, 3.

What is the median ? ____________________What is the mode ? ____________________

SORT FIRST: 3, 3, 4, 5, 6, 9, 9, 9, 0 6 9ABOUT THE MEDIAN ARRANGE FIRST.Use the formula to locate the MEDIAN but always consider the sample size.When the sample size is an ODD NUMBER, the formula above gives you the MEDIAN right away.EXAMPLE: Find the median for 2, 3, 5, 6, 7, 8, 12, 12, 13.( n + 1 )/ 2= 10 / 2 = 5When the sample size is an EVEN NUMBER, the formula above gives you the location but not the MEDIAN, you will need to find the average of two numbers.EXAMPLE: Find the median for 2, 3, 5, 6, 7, 8, 12, 12.( n + 1 )/ 2= 9 / 2 = 4.5

MEDIAN AND MODE: Put It TogetherEXERCISE 1, Page 157.The Hilltop High School basketball team has played 7 games so far this season. Once they scored in the 40s, once they scored in the 60s, twice in 70s, and three times in the 80s. The median score is:6365In the 60sIn the 70sIn the 80s40, 60, 70, 70, 80, 80, 80MEDIAN AND MODE: Put It TogetherEXERCISE 2, Page 157.At summer camp, the median age of the campers is 12. If there are 9 campers, which of the following must be true:

At least one of the campers is 12.If there is an 11-year-old camper, there is also a 13 year old.The mode of the campers ages is 12.

None.I only.I and II only.I and III only.I, II, and III.

TRUE!!!FALSE!!!FALSE!!!SAMPLE SIZE ODD NUMBER, THE MEDIAN IS THE MIDDLE NUMBERTHERES NO ENOUGH INFORMATION TO SAY SO.THERES NO ENOUGH INFORMATION TO SAY SO.MEDIAN AND MODE: Put It TogetherEXERCISE 3, Page 157.The average of 3 integers, x, y, and z is equal to the median of x, y, and z. If x > y > z > 0, which of the following must be true?

PROBABILITYProbability of an event happening =

If you flip two ordinary coins, what is the probability that both coins will come up heads or both coins will come up tails?

List the possible outcomes ____________________________List the # ways the event ( both heads or both tails ) can happen ______What is the probability that both coins will come up heads or both coins will come up tails? ________________________THE SUM OF ALL THE PROBABILITIES ALWAYS EQUALS 1.

HH, HT, TH, TTHH, TT2 / 4 = 1 /2PROBABILITYGEOMETRIC PROBABILITY QUESTIONS. Solve geometric probability questions by dividing a specific area by the area of the whole region.

The figure above is comprised of 12 1 inch and 2 inch rectangular cells. If a point is chosen at random from within the figure, what is the probability that the point will be in the shaded region?

What is the area of each cell? ______________What is the area of the entire figure ? _____________What is the area of the shaded region ? _____________________Whats the probability ( likelihood ) that the point will be in the shaded region ? _________________________

2 sq. in24 sq. in6 sq. in1 / 442PROBABILITY: Put It TogetherEXERCISE 1, Page 159.A bag contains only $1, $5, and $10 poker chips. The probability of randomly drawing a $1 chip is 1 / 2, and the probability of randomly drawing a $5 chip is 1 / 4. If there are four $10 chips in the same bag, how many chips in total are in the bag?

2824201816

PROBABILITY: Put It TogetherEXERCISE 2, Page 159.

Refer to the figure of tiles above. The smallest tiles have dimensions 1 x 1. The next largest tiles have dimensions 1 x 2. The largest tile has dimensions 1 x 3. A dart is thrown at the tiles. Any spot has an equal chance of getting hit by the dart. What is the probability that the dart lands on one of the tiles with dimensions 1 x 2 ?1 / 31 / 52 / 54 / 95 / 9

Total area: 3 x 3 = 93322Target area: 2 x 2 = 4

PROBABILITY: Put It TogetherEXERCISE 3, Page 159.If m is chosen at random from the set {2, 7, 8} and n is chosen at random from the set {3, 10}, what is the probability that the product of m and n is divisible by 4 ?

COMBINATIONSCOMBINATION questions ask you to determine the number of different possibilities that can occur in a given situation. You can solve in one of two ways:Look at the answer choices. List all possible combinations in an organized way.Use the FUNDAMENTAL PRINCIPLE OF COUNTING when the number of combinations is too large to list. This is, multiply the number of ways each event can occur.COMBINATIONS; Build Your AnswerAt a diner, a customer wants to order a soup and sandwich for lunch. If there are 3 different varieties of soup and 4 different types of sandwiches on the menu, how many different soup and sandwich combinations are possible?

46111218COMBINATIONS: Put It TogetherEXERCISE 1, Page 161.Maria is travelling from Amesville to Shore Harbor to Smithtown. If there are three different roads she can take from Amesville to Shore Harbor, and 6 different roads she can take from Share Harbor to Smithtown, how many different routes for the trip are possible ?

1812863COMBINATIONS: Put It TogetherEXERCISE 2, Page 161.The digits 2, 5, 3, and 7 each appear in a four-digit number n that is greater than 3000. How many differrent possible values exist for n ?

812182436

Combinations starting with 36 x 3GRAPHS & CHARTSBefore diving into the question, take a second to interpret the information presented.

GRAPHS & CHARTS: Put It TogetherEXERCISE 1, Page 163.

According to the graph above, if there are 20,000 fans at the game who are under the age of 30, how many fans are over 50 ?

4,2506,0006,5007,0007,500

UNDER 3012% X + 28%X = 20,000X = 50,000OVER 5012% ( 50,000 )GRAPHS & CHARTS: Put It TogetherEXERCISE 2, Page 163.

The scatterplot above gives information about 5 different package deliveries. Which point represents the package delivery with the slowest average speed ?

ABCDE

CHECKPOINT REVIEW # 7EXERCISE 1, Page 164.If a packaging machine packs 120 boxes every 3 hours, how many hours would it take the same machine to pack 280 boxes ?

2.54567

CHECKPOINT REVIEW # 7EXERCISE 2, Page 164.Points A ( 0, 4 ) and B ( -3, 0 ) are located on the coordinate plane. What is the area of the triangle enclosed by the line connecting these two points, the x axis, and the y - axis ?

BASE = 3HEIGHT = 4CHECKPOINT REVIEW # 7EXERCISE 3, Page 164.

In the figure above, lines, m, n, and l intersect to form a triangle. If m and n are not perpendicular, which of the following CANNOT be the value of a ?

2728293060

90o CHECKPOINT REVIEW # 7EXERCISE 4, Page 165.

The table above contains the results of a quiz given in Mrs. Nalbandians class. There were four additional students, not shown, who took the quiz. If their average score was 5.5, what was the average score of the nine students who took the quiz ?

5.9566.46.957

=32

CHECKPOINT REVIEW # 7EXERCISE 5, Page 165.A pair of dice is rolled. If the 6 faces of each die are numbered with a different integer from 1 to 6, what is the probability that the product of the two faces showing will be 6 ?

1 / 361 / 182 / 211 / 91 / 6

ADDITIONAL EXERCISEThe sum of 1, x, x2 & x3 equals 60. Find the average of x, x2, x3 & x4.

9x10x12x14x15x