I. Grade Level: 10II. Grading Period: 3rd QuarterIII. Learning Competency: Construct a box plot from a set of dataIV. Topic: Application of QuartilesV. Activity:

Which Drug is Better?

A hospital has been trying out two new pain relieving drugs. Patients taking drugs were asked to record how many hours it was before any pain recurred. The results are summarized below:

Drugs

Recurrence Times (Hours)

A 6 7 10

7 11

5 8 10

6 7 11

B 3 12

5 10

2 13

9 15

3 6 14

The hospital’s problem is to decide which of the drugs is preferable.

What is the mean recurrence time for each drug? What is the median recurrence time for each drug? What is the first quartile for each drug? What is the third quartile for each drug? Does the mean, median, first and second quartile give you a sufficient

information to recommend which drug to use?

VI. Discussion:A more useful method of analysis using the quartiles of a set of data is called

a box plot or a box and whisker diagram. This plot makes it easy to see how the data is distributed along a number line. Bet of all, a box plot is easy to make. As an example, we will construct a box plot for the given data: 10, 5, 12, 9, 14, 12, 12, 6, 4, 7, 10 and 11.

The step in constructing a box plot is as follows:

1. Find the median and the first and third quadrant of the data set.For our set of data: 10, 5 12, 9, 14, 12, 12, 6, 4, 7, 10 and 11Median = 101st quartile = 6.25

3rd quartile = 12

2. Find the lower and upper outliers these are the lowest and highest number in the data set. In our example the lower and upper outliers are 4 and 14

3. Draw a number line. And mark the median, the first and second quartile and the outliers.

Outlier 1st Quartile

Median 3rd Quartile Outlier

4. Draw a box connecting the quartiles. Connect the outliers to the box by drawing a horizontal line.

Looking at the box plot we can visualize the distribution of numbers in any set of data. You can easily see, for example, whether the numbers in the data set bunch more in the first quartile by looking at the size of the box in the left.

VII. AssessmentLook at the figure below then answer the following question.

1. The median of the data set presented by the box plot isa. 5 b. 6.25 c. 9.25 d. 10.5

2. The first quartile of the data set presented by the box plot isa. 5 b. 6.25 c. 9.25 d. 10.5

3. The second quartile is ata. 5 b. 6.25 c. 9.25 d. 10.5

4. Which of the following number is an outlier?a. 6.5 b. 10.25 c. 8 d. 6

5. Which statement best describe the data set presented by the box plota. There are more numbers located in the third quartile.b. There are more numbers located in the first quartile.c. The median divides the data set into two equal parts.d. The upper and lower outliers has equal length.

VIII. AuthorMarvin Y. Arce Mamerto P. Sanita Jr.Teacher I Teacher ISan Julian-Sta. Maria High School San Julian-Sta. Maria High School

I. Grade Level: 10II. Grading Period: 2nd QuarterIII. Learning Competency: Derive the distance formula between two

points on the plane.IV. Topic: The Distance FormulaV. Activity:

Peter walks from his home to school He takes the route as given in the figure to the left. His house is located at Apitong Street, designated as (-3, 4) on the coordinate map, Cacal street is designated as (5, 4) and the school as (5, -4). Each unit distance is equivalent to 10 meters.

1. How far is Apitong Street from Cacal Street? Use the coordinates of each.

2. How far is Cacal Street from the School? Use the coordinates of each.

3. If a segment is drawn from the coordinate of Apitong St. and the School, what type of figure is formed?

4. What theorem can you use to find the length of the segment connecting the coordinates of Apitong St. and the School?

5. How far is Peter’s house from the school?

VI. DiscussionTo find the distance between two points on a plane, the distance formula is

to be used. The formula is derived using the Pythagorean Theorem. To find the distance d between two points P1 (x1, y1) and P2 (x2, y2), we use:

d=√(x2−x1 )2+( y2− y1)2

We will now try to solve the problem in the activity using the distance formula. The coordinate of Peter’s house at Apitong Street is (-3, 4). We will let this be P1. The coordinate of Peter’s school is (5, -2) we will let this be P2. We the substitute the coordinates of P1 and P2 in the equation:

d=√(x2−x1 )2+( y2− y1)2 where x1 = -3, y1 = 4, x2 = 5 and y2 = -2

¿√ (5−(−3))2+(−2−4 )2

Apitong St. Cacal St.

School

10 m.

10 m.

¿√ (8 )2+36 ¿√64+36 ¿√100=10units

Since each unit distance is equal to 10 meters, the distance of Peter’s House to his school is 10 x 10 = 100 meters.

VII. AssessmentEncircle the letter of the correct answer.

1. Find the distance of the segment joining (2, -3) and (-1, -2)a. √10 b. 10 c. √5 d. 5

2. How far is (-1, 6) to (6, -5)?a. 170 b. √170 c. 70 d. √70

3. The point (5,4) lies on a circle. What is the length of the radius of this circle if the center is located at (3,2)?a. 2√2 b. 8 c. 2√10 d. 2√5

4. The length of segment AB is √40 units. If the coordinate of A is (7,1), while B is (x, -3), what are the values of x?a. 12 & 2 b. -12 & 2 c. -12 & -2 d. 12 & -2

5. Find the values of y if (4, y) is 10 units from the point (-2, -1)a. 9 & 7 b. -9 & -7 c. 9 & -7 d. -7 & 9

VIII. Author

Corazon K. BartolomeEduardo Cojuangco National Vocational High School

I. Grade Level: 10II. Grading Period: 1st QuarterIII. Learning Competency: Find the sum of a terms of a given geometric

sequenceIV. Topic: Sum of Terms of Finite Geometric SequenceV. Activity:

The King’s Challenge

One day by playing a game of chess, the king challenged you with a question: How many grains of rice will there be if we will put one grain on the first square, then two grains on the second, then four grains on the third, 8 on the fourth and so on until the last square?

1. How many grains of rice will there be in the 8th

square?2. How many grains of rice will there be on the 16th square?3. Is there a pattern we could use in order to find the number of grains of rice

for the remaining squares? Write it using the notation for number sequence.

4. How many grains of rice will there be on the 64th square?5. Can you manually compute the total amount of rice in the chess board? Why

or why not?

VI. DiscussionA geometric sequence is in the form a, ar, ar2, ar3, ar4, …, arn-1,

where r is the common ratio and arn-1 is the nth term. Therefore the sum of the terms is a + ar + ar2 + ar3 + ar4 + … + arn-1. But using this formula is quite hard for sequence with many terms. we can use the formula for the sum of terms of a finite geometric sequence.

Sn=a (1−r n)1−r

We will now solve the activity above by following these simple steps in finding the sum of terms of a geometric sequence:

1. Identify the first term in the sequence, a. In the activity above a = 1.2. Identify the common ratio, r. Since the grains of rice is doubled for each

succeeding squares r = 2.

Where:Sn = sum of the terms of the sequence n = number of terms in the sequence a = the first term r = common ratio

3. Identify the number of terms, n. A chessboard has 64 squares, therefore n = 64.

4. Use the formula the find the sum.

Sn=a (1−r n)1−r

a = 1, r = 2 and n = 6418446744073709551616

¿ 1(1−264)

1−2

¿ 1−18,446,744,073,709,551,616−1

¿ −18,446,744,073,709,551,615−1

¿18,446,744,073,709,551,615

VII. AssessmentEncircle the letter of the correct answer.

1. What is the sum of the first eight terms of the geometric sequence 5, 15, 45, ... ?

a. 320 b. 5,465 c. 16,400 d. 32,8002. What is the sum of the first nine terms of the geometric sequence 20, 10,

5, ... ? Give your answer as a decimal correct to 1 decimal place.a. 39.9 b. 40 c. 59.9 d. 79.8

3. The sum of the first 5 terms of a geometric sequence, whose common ratio

is 12 , is

152

. What is the first term of the sequence?

a. 4 b. 5 c. 6 d. 74. How many terms of the geometric sequence 2, 8, 32, 128,... are required to

give a sum of 174,762?a. 8 b. 9 c. 10 d. 11

5. The sum of the first two terms of a Geometric Progression is 36 and the product of the first and third terms is 9 times the second term. Find the sum of the first 8 terms.

a. 348081

b. 328081

c. 368081

d. 388081

I. Grade Level: 9II. Grading Period: 1st QuarterIII. Learning Competency: Solve problem involving quadratic equationsIV. Topic: Application of Quadratic EquationsV. Activity:

Baseball SuperstarA baseball player hits a ball straight up in the air. The height (h) in feet of the

ball after t seconds is given by the formula: h = -16t2 + 64t + 4. Fill the table of values below, then answer the given questions.

t 0 1 1.75 2 2.25 3 4h

1. On a sheet of graph paper carefully graph the ordered pairs you calculated above. Plot h on the vertical axis, and t on the horizontal axis.

2. What are the coordinates of the highest point on the graph?3. Use the given formula to find the height of the ball after ½ second.4. Use your graph to approximate the height of the ball after ½ second. How

does this compare with your calculated value?5. Suppose that someone catches the ball at a height of 4 feet just before it

strikes the ground. At what time was the ball caught?

VI. DiscussionQuadratic functions have many applications in our daily life. Like in our

activity, quadratic equation is used in projectile motions. If you throw a ball it will go up into the air, slowing down as it goes, then come down again and a quadratic equation tells you where it will be.

Example, if a ball is thrown straight up, from 3 meters above the ground, with a velocity of 14 m/s. When does it hit the ground?

To solve this, we must assume that there is no resistance and considered the following things:

The height starts at 3 m The ball travels upward at 14 m/s or 14t

Gravity pulls the ball down, changing is speed by - 12at2. The negative

sign denotes that acceleration due to gravity is downward and a = 9.81 m/s2. Simplifying this we will have -4.905t2 or 5t2.

Adding the following will give us the height of the ball after its flight. Therefore h = -5t2 + 14t + 3. Since when the ball hit the ground h = 0. We now have a quadratic equation:

-5t2 + 14t + 3 = 0To solve the problem, we must compute the roots of the equation.

5t2 - 14t - 3 = 0 We transform the equation in standard form.5t2 - 14t - 3 = 0 multiply 5 by -3 and find the factor the prouct whose

sum is -14. (-15 and the factors are 1 and -15).5t2 – 15t + t – 3 = 0 Rewrite the middle term into the factor of the

product.5t(t – 3) + (t – 3) = 0 Factor by grouping.(5t + 1)(t – 3) = 0 The roots of the equation are -1/5 and 3.

Since for 5t + 1 = 0 time is negative we discard it and accept t = 3. The ball will hit the ground after 3 seconds.

VII. AssessmentSelect the letter of the correct answer.

1. A motorboat makes a round trip on a river 56 miles upstream and 56 miles downstream, maintaining the constant speed 15 miles per hour relative to the water. The entire trip up and back takes 7.5 hours. What is the speed of the current?

a. 1 mile/h b. 2 mi/h c. 3 mi/h d. 4 mi/h2. A ball is launched upward at 48 ft/s from a platform that is 100 ft. high. Find

the maximum height the ball reaches.a. 133 feet b. 134 feet c. 135 feet d. 136 feet

3. How long will the ball in problem 2 reach the maximum height?a. 1.5 sec. b. 2 sec. c. 2.5 sec. d. 3 sec.

4. A farmer has 1000 feet of fencing and a very big field. She can enclose a rectangular area with dimensions x ft and 500 – x ft. What is the largest rectangular area she can create?

a. 62,500 ft2 b. 250,000 ft2 c. 1,000 ft2 d. 500 ft2

5. Bob made a quilt that is 4 cm x 5 cm. He has 10 cm2 of fabric to create a border around the quilt. How wide should he make the border to use all the fabric? (The border must be the same width on all four sides and let x be the side of the border.)

a. 2 cm. b. 1.5 cm. c. 1 cm. d. 0.5 cm.

VIII. AuthorFrancisco P. SerdeñolaEduardo Cojuangco Technical Vocational High School