SUMMATIVE TEST 2
A. Refer to the given situation below and find the value of the indicated measure of
position.
The owner of a Parque Café recorded the number of customers who came into
their café each hour a day. The results were
2, 3, 4, 7, 8, 9, 10, 12, 13, 14, 15, 16, 17, 18, 19, 20, 20, 21, 22
1.
P30 = ________
6.
P25 = ________
2.
Q2 = _________
7.
Upper Quartile = ________
3.
D7 = _________
8.
Lower Quartile = _______
4.
P45 = _________
9. Interquartile range = ______
5.
D6 = __________
10. P80 = _______
B. The selected grade 10 students were weighed by their MAPEH teacher in order for
him to identify their weight in kilograms. Out of curiosity he wanted that the
information be interpreted by the school statistician. With the help and guidance
of a Math teacher they came up with the table of distribution specified below. Let
us together help our MAPEH teacher by answering the questions that follow. But
before that, we have to complete first the table by filling in the value of the Lower
Boundary(LB).
The Weight of Selected Grade 10 in Kilogram.
Weight
Lower
Cumulative
Boundary(LB)
Frequency(<cf)
Frequency(f)
61-65
8
50
56-60
7
42
51-55
4
35
46 -50
6
31
41-45
11
25
36-40
9
14
31 -35
5
5
Calculate the following (Show your Solution )
1. Q 2
2. D 9
3. D 4
4. P 40
5. P 80
NAME:______________
PERFORMANCE TASK NO.2
MATH 10/4TH QUARTER
SCORE:___________
A non-profit organization is planning to provide assistance to the student-residents in your
barangay. The organization needs information regarding the target population. You are asked to
prepare a frequency distribution of the grade level of the student-residents in your barangay
whose age is 3 - 25 years old in order to determine their grade level, the basis will be their ages.
WHAT TO DO:
1. Collect the data on the ages of student-residents in your barangay and their gradelevel.
2. Prepare a tabular list of the age and grade level collected.
3. The class interval of the frequency class table is 3.
4. List the lower class limit and the lower class boundary.
5. Get the sum of the frequency column and check against the total number of observations.
Based on the frequency distribution constructed:
1. How many school kits are estimated to be prepared for the elementary studentresidents?______________
2. How many school kits are estimated to be prepared for the Junior and Senior high
school student-residents?________________
3. How many school kits are estimated to be prepared for the college studentresidents?__________________
4. If an elementary school kit cost Php 210.00 each, what is the estimate amount needed
for the provision of the school kits?___________________
5. If the Junior and Senior High school kit costs Php 300.00 each, what is the estimated
amount needed for the provision of the school kits?_____________________
6. If a College school kits costs Php 400 each, what is the estimated amount needed for the
provision of the school kits?_________________________
7. What is the total amount needed for the provision of the school kits for the studentresidents of your barangay?__________________
8. If the non-profit organization has 27 current contributing members, how much would
each member contribute for the purchase of the school kits?____________________
9. Compute the median represented by the frequency table
A. Q2=_______
B. D5 =_______
III. P50=__________
10.
As a receiver of the assistance, how would you show appreciation of the received school
kits?____________
RUBRICS
CRITERIA
EXCELLENT (5)
GOOD (4)
FAIR (3)
POOR (2)
Table of
frequency
distribution
The table is
complete with
reasonable and
accurate
intervals, correct
calculation of the
frequencies,
correct
summation of
cumulative
frequencies and
correct lower
boundary.
The table is
complete with
some
unreasonable
intervals, some
incorrect
cumulation of
frequencies,
incorrect
summation of
the cumulative
frequencies and
lower
boundaries.
The table is
complete with
some
unreasonable
intervals,
incorrect
calculation of
frequencies,
incorrect
summation of
cumulative
frequencies and
lower
boundaries.
The table is
not complete
and consists
of incorrect
data
Solutions
to the given
problems
With correct
solution and
accurate process
and presentation
of answers to the
given problem
With some
incorrect
solution but
accurate answer
to the follow-up
questions.
With incorrect
solution but
responded to
the given
problem.
With
incorrect
solution.
NOTE: WRITE YOUR FREQUECY DISTRIBUTION TABLE AT THE BACK OF THIS PAG
NAME:______________
PERFORMANCE TASK NO 1
MATH 10/4TH QUARTER
SCORE:___________
Directions; Read and analyze the given problem.
Calculate P25 and Q1 and interpret your answer.
During the ECQ and MGCQ, Aurora Provincial Government distributed packs of relief goods
among the affected families as shown in the table below.
Number of Families
1150–1154
1145 –1149
1140 –1144
1135 – 1139
1130 – 1134
Packs of Relief Goods
Received
5
4
2
3
6
Rubric for Checking
Equivalent
Score
2
3
4
5
Criteria
Solve the problem but not able to give the correct answer
Able to make a complete and correct frequency distribution table with
inaccurate answer
Able to make a complete and correct frequency distribution table with
accurate answer
Able to make a complete and correct frequency distribution table with
accurate answer and correct interpretation
RODRIGO D. PALMERO MEMORIAL NATIONAL HIGH SCHOOL
BANNAWAG, MARIA AURORA, AURORA
SUMMATIVE TEST 3
MATH 10/4TH QUARTER
NAME:______________
SCORE:___________
MELCs: Formulates statistical mini –research. M10SP - IVf-g-1
PART 1. WRITTEN WORKS. Encircle the letter of the correct answer.
1. What is the process used to collect and analyze information to increase our understanding
of a topic or issue?
A. Analysis of Data
C. Research
B. Hypothesis
D. Sampling Method
2. Which of the following refers to the process extracting from the given data relevant information
from which numerical description can be formed?
A. Analysis of Data
C. Interpretation of Data
B. Collection of Data
D. Organization of Data
3.What is a statement that can be tested by a scientific research?
A. Conclusions
C. Recommendations
B. Hypothesis
D. Statement of the Problem
4. If the confidence level of 95% , what is the margin of error (%) ?
A. 1
C. 5
B. 2
D. 4
5.What do you call the part where the researcher’s task is to draw conclusions from the analyzed data?
A. Analysis of Data
C. Interpretation of Data
B. Collection of Data
D. Organization of Data
6. The following are the main components of any title page of research except:
A. The name of the researcher/s
B. The name of the school of the researcher/s
C. The title of the research
D. The researcher/s address
7.Which of the following is the broad overview of the questions that will be addressed in a given
area research?
A. Background of the study
C. Definition of Terms
B. Conclusions
D. Statement of the Problem
8. What do you call the data that are taken from previous recorded data?
A. External Data
C. Primary Data
B. Internal Data
D. Secondary Data
9.It serves as a space for materials that help clarify your research.
A. Appendices
C. Generalization
B. Conclusions
D. Recommendations
10. It is defined as the critical suggestion regarding the best course of action in a certain issue:
A. Recommendations
B. Hypothesis
C. Conclusion
D. Background of the study
11. Which is true about a mini-research?
A. Mini-research is a two-step process.
B. Mini-research always answer questions in measures of position.
C. Formulation and presentation of mini-research is similar to standard research.
D. Formulation and presentation of mini-research is different to standard research.
12. Which is NOT included in the presentation of methodology?
A. method
B. results
C. instrument
D. analysis tools
13. Which types of variables are most appropriate for a statistical mini-research which involves
measures of position?
A. nominal and ordinal
C. Either A or B
B. interval and ratio
D. Neither A nor B
14. Which variable is most appropriate for a statistical mini-research which involves measures of position?
A. grades in Math
C. street of residence
B. favorite color
D. degree of willingness to be vaccinated
15. The arrangement of the common parts of a research paper is _____________________.
A. Title Page, Problem, Methodology, Results and Discussion, Conclusion
B. Title Page, Problem, Results and Discussion, Methodology, Conclusion
C. Title Page, Methodology, Problem, Conclusion, Results and Discussion
D. Title Page, Conclusion, Methodology, Problem, Results and Discussion
PART 2: PERFROMANCE TASK
1. Conduct a mini-research about the topic that you are interested in. Ask yourself the question,
what do you want to know?
2. Include research questions involving measures of positions and percentile rank;
3. Follow the sample presented in the module(FORMULATING STATISTICAL RESEARCH) including
how each part is presented;
Specifically, your mini-research must have:
- Title Page
- The Problem
- Methodology
- Results and Discussion
- Conclusions
4. Present your output in letter-sized bond paper (short, 8.5”x11”) with margins of 1 inch on each side.
You can submit printed, typewritten or handwritten outputs. When submitting printed output, use
Courier New sized 12 font.
Rating Checklist for your Output
1. The Problem (5 points)
✓ Chosen variable(s) is/are appropriate and practical for statistical mini-research.(2 points)
✓ There are research questions involving measures of position and percentile rank. (2 points)
✓ There is discussion about the chosen variable(s). (1 point)
2. Methodology (5 points)
✓ Appropriate method was used. (1 point)
✓ The sampling and number of respondents are discussed. (1 point)
✓ Number of respondents is around 40 or more. (1 point)
✓ Data gathering and/or alternative is discussed. (1 point)
✓ Appropriate data analysis tools are specified. (1 point)
3. Results and Discussions (10 points)
✓ Frequency distribution is correctly constructed. (3 points)
✓ Measures of positions are accurately calculated. (2 points)
✓ Percentile ranks are accurately calculated. (2 points)
✓ Calculated values are interpreted accordingly. (2 point)
✓ Tables and figures are properly labeled. (1 point)
4. Conclusions (5 points)
✓ Conclusions answer the research questions. (3 points)
✓ Number of conclusion statements is equal to the number of research questions. (2 points)
5. Others (5 points)
✓ There is a prescribed title page. (2 points)
✓ The research paper is neatly/legibly accomplished. (2 points)
✓ There is an appendix for raw data. (1 point)
NAME:______________
SUMMATIVE TEST 4
MATH 10/4TH QUARTER
SCORE:___________
Encircle the letter of the correct answer.
1. In a 50 item test, Phoebe got a score of 30 which is the third Quartile, this means
_________________________.
A. She got the lowest score..
B. She surpassed 75% of her classmates.
C. Her score is higher than 25% of her classmates
D. 75% of the class did not pass the test.
2. In a 40 item test, the passing mark is the 3rd quartile, What does it imply?
A . The student should answer at least 20 items correctly to pass the test.15
B . The student should answer at least 30 items correctly to pass the test.
C . The student should answer at most 20 items correctly to pass the test.
D. The student should answer at most 30 items correctly to pass the test
3. Ashely got 45 in her 50-item test in Mathematics. The percentile rank of her score is 90% This
means ______________.
A. She answered 90% of the items correctly.
B. She answered 45% of the items correctly.
C. She answered 45% of the items wrong.
D. She answered 90% of the items wrong.
4. If you received a score of 85 on a mathematics test and this score is greater than or equal to the
scores of 80% of the students taking the test, what will be your percentile rank?
A. 75%
B. 80%
C. 85%
D. 90%
5. In a 60 item test, Carlson scored 48. His score has a percentile rank of 70%, what does it
mean?
A. He is 30% better than other test takers.
B. He is 70% better than other test takers.
C. His score is greater than or equal to 30% of the other test takers.
D. His score is lower than or equal to to 70 % of the other test takers
6. Which of the following is NOT suitable to use to describe data in parts or divisions?
A. mean
B. median
C. quartile
D. percentile
7. Which measure is used to help you analyze research data in 10 parts?
A. mean
B. quartile
C. decile
D. percentile
8. Mr. Guanzon’s business is booming. He wants to describe his sales in four parts. Which should Mr.
Guanzon use to describe his business sales?
A. mean
B. quartile
C. decile
D. percentile
9. Which of the following measures help you to describe the data the finest divisions?
A. mean
B. quartile
C. decile
D. percentile
10. Which of the following is true about any statistic?
A. It is arbitrary.
B. It summarizes data.
C. It is exact at all times.
D. It depends upon the view of the researcher.
11. When do we treat data as grouped?
A. If it is small
B. If it is large
C. Both A & B
D. Neither A nor B
12. Which of the following statements is not true?
A. Statistics in not an exact science.
B. Young researchers must use methods comfortable to them.
C. There are natural and comfortable presentations of research data.
D. There are no hard rules in choosing the class size in making a frequency distribution table
13. Benny’s percentile rank in General Scholastic Aptitude of NCAE is 85. Academic Track test has 155
items. There were 1,289,364 takers when Benny took the test. Which of the following statements is true?
A. Benny answered correctly 115 items in Academic Track test.
B. Benny’s score is less than or equal to around 1,095,959 takers.
C. Benny’s score is greater than or equal to around 1,095,959 takers.
D. Benny answered correctly 115 items in Academic Track test and his score is greater than or
equal to around 1,095,959 takers.
For items 14-20, refer to the data below. The data are daily allowance (in pesos) of students of
Grade 10-Diligence.
14
12
35
25
0
5
46
27
5
6
15
21
2
9
20
40
7
14
31
28
3
5
25
51
15
6
39
21
10
9
40
20
5
7
40
25
3
7
53
32
14. How many class intervals are there if the class size is 11?
A. 3
B. 4
C. 5
D. 6
15. What is the upper limit of the highest class when the class size is 11?
A. 53
B. 54
C. 55
D. 56
16. Which of the following can we use to determine the median, the upper 20% and lower 20% of the data?
A. decile
B. percentile
C. A or B
D. Neither A nor B
17. What is the highest daily allowance included in the bottom 25%?
A. 5
B. 6
C. 7
D. 9
18. Which amount separates the distribution into two equal parts?
A. 12
B. 14
C. 15
D. 20
19. Which of the following is a relevant conclusion if you calculated 28 as
3rd quartile?
A. Php 28 is lower than 30 allowance values.
B. Php 28 is greater than 29 allowance values.
C. Php 28 is greater than 30 allowance values.
D. Php 28 is greater than to at most 10 allowance values.
20. Dexter’s daily allowance is Php 12. Describe Dexter’s allowance with regards to rest of the students.
A. Dexter has higher daily allowance than 17 other students.
B. Dexter has lower daily allowance than at most 17 other students.
C. Dexter has higher daily allowance than at most 13 other students.
D. Dexter has higher daily allowance than at most 16 other student
NAME:______________
PERFORMANCE TASK 4
MATH 10/4TH QUARTER
SCORE:___________
Directions: Use appropriate measure of position to interpret and analyze the following data. Make a
conclusion about the bottom third of the data.
Monthly Family income(in pesos) No. of Families
40,000 and above
6
35,000 – 39,999
11
30,000- 34,999
15
25,000 - 29,999
13
20,000 – 24,999
16
15,000 – 19,999
21
10,000 – 14,999
46
5,000 – 9,999
49
4,999 – and below
36
Present your solution in a separate sheet if paper.
Rubrics for your Output
Score Descriptors
10
Formulas used are correct. Calculations are accurate and conclusion is
relevant.
8
There are errors in the formula used. Calculations are accurate and
conclusion is relevant.
6
Formulas used are correct. Calculations are accurate. Conclusion is
irrelevant and/or off
4
Two of the characteristics (correct formulas, accurate calculation, and
relevant conclusion) are missing in the presentation.
2
All of the characteristics are missing in the presentation.
NAME:______________
SUMMATIVE TEST 2
MATH 7/4TH QUARTER
SCORE:_____
Encircle the letter of the correct answer.
1.
2.
It refers to the number of times an observation occurs or appears in a data set.
A. Class interval
C. Frequency
B. Class limits
D. Range
It is used to present data in the most systematic and organized manner.
A. chart
C. picture
B. graph
D. table
3.
It is the tabular method of organizing data.
A. frequency distribution table C. multiplication table
B. logarithmic table
D. trigonometric table
4.
It is the difference between the highest and the lowest values.
A. boundary
C. limit
B. interval
D. range
5.
Which of the following is/ are properties of an effective table?
I.
The date of the survey is indicated.
II.
The source of the data is no longer identified.
III.
The title clearly states the personality of the researcher.
IV.
The data are arranged systematically in columns and properly labeled.
A. I and III
C. I and IV
B. II and III
D. III and IV
For items 6-10.
Pelmar opened a pack of marbles. He found out that there are 15 red, 10 blue, 7 orange, 7 yellow, 13 green,
and 8 purple marbles.
A.
Color
Frequency
Color
Frequency
red
15
red
15
green
10
green
13
blue
7
blue
10
purple
13
purple
8
orange
7
orange
7
yellow
8
yellow
7
B.
D.
Color
7.
C.
Frequency
Color
Frequency
red
7
red
15
green
7
blue
10
blue
8
orange
7
purple
10
yellow
7
orange
13
green
8
yellow
15
purple
13
Which of the following is the appropriate title for the distribution table?
A
Frequency Distribution Table of Marbles
B.
Frequency Distribution Table of Colors
C.
Frequency Distribution Table of Pelmar’s Marbles.
D.
Frequency Distribution Table of Red, Blue, Yellow, Orange, Green, and Marbles
8.
What is the total number of marbles?
A.50
C. 58
B.55
D. 60
9.
Which color has the highest number of marbles?
A. blue
C. red
B. green
D. yellow
10. Which color has the least number of marbles?
A. blue
C. red
B. green
D. yellow
11.
What is the pictorial representation of a statistical data?
A. Diagram
C. Table
B. Graph
D. Textual
12.
What graph is used to show the relation of a part to the whole?
A. Bar Graph C. Line Graph
B. Histogram
13.
D. Pie Chart
What graph is illustrated below?
A Survey of the Daily Allowance of
50 Grade 7 Students
1
10
5
₱30
₱35
₱40
Daily Allowance
A. Bar Graph
B. Histogram
Number of Students
20
12
3
₱45
₱50
C. Line Graph
D. Pie Chart
Students
Number of tudents
14. What kind of graph is illustrated below?
Yearly Enrollment of Grade 7 Students
240
230
220
210
200
190
180
230
220
215
210
200
2015
2016
2017
2018
2019
Years
15.
A. Bar Graph
C. Line Graph
B. Histogram
D. Pie Chart
Which of the graphs is used to present data that indicate trends over a period of time?
A. Bar Graph
B. Histogram
C. Line Graph
D. Pie Chart
For questions 16 – 20, refer to the illustration below.
Favorite Sports of 205 Boys in Grade 7 Classes
70
60
50
40
60
50
40
30
25
30
20
10
0
Volleyball
Basketball
Softball
Sepak TakrawSwimming
Favorite Sports
What two quantities are compared in the graph of the Grade 7 Classes?
A.
Number of Boys and Hobbies
B.
Number of Boys and Favorite Sports
C.
Number of Boys and Favorite Talents
D.
Number of Boys and Favorite Game Shows
17.
How many boys are interested in Softball?
A. 20
B. 30
C. 40
D. 50
18. Which sport is the most favored?
A. Basketball
C. Softball
B. Sepak Takraw
D. Volleyball
19. Which sport ranks second in interest?
A. Basketball
C. Softball
B. Sepak Takraw
D. Volleyball
20. Which sport is the least favored?
A. Sepak Takraw
C. Swimming
B. Softball
D. Volleyball
16.
PERFORMANCE TASK 1
MATH 7/4TH QUARTER
SCORE:___________
NAME:______________
Create a bar graph and line graph
Do It This Way:
1.
2.
3.
The table below shows a survey result of the daily allowance of 45 Grade 7 students.
Construct a vertical bar graph and line graph showing the result of this survey.
Copy the given table and write the answer on your answer sheet.
Daily Allowance
Number of Students
₱ 30
12
₱ 35
8
₱ 40
18
₱ 45
4
₱ 50
3
Total
45
PERFORMANCE TASK 2
MATH 7/4TH QUARTER
Challenge Yourself!
Find at least 15 kinds of plants in your surroundings. Measure the height of
each in inches and record the result. From the data gathered, make a frequency
distribution table then create a histogram and an ogive graph. Use a separate sheet
of graphing paper for the graph.
PERFORMANCE TASK 3
MATH 7/4TH QUARTER
Let’s Find Out: Uses of Mean, Median and Mode in Real Life
Let’s Do It This Way: Give one (1) use of mean, median and mode in real life. Write the answer at
the back of this paper. The given below is your guide.
Mean
Median
Mode
It helps teachers to see It is used to find
It is used to find the
the average marks of the middle age from most saleable shoe size
the students.
the class students.
in a department store.
PERFORMANCE TASK 4
MATH 7/4TH QUARTER
NAME:______________
SCORE:___________
Collect your electric bill for the whole year. Record the bill for the corresponding month on the table. Make a table in
your answer sheet as shown below.
MONTH
January
February
March
April
May
June
July
August
September
October
November
December
ELECTRIC BILL
1. What is the mean, median and mode of your electric bill?
2. In what month does your bill has the least consumed electricity?
3. If you were ask to budget the money for electric bill in a year, what measures
of central tendency are you going to use?
4.
What solution can you suggest to your parents to lessen your bill in electricity?
Rubrics for Grading:
10
8
6
4
DATA
All data was
All data was
Data was
Included little
QUALITY
complete and complete and incomplete.
or no relevant
accurately
not accurately Some data
data. Data
labeled using
labeled using
was not
was not
appropriate
appropriate
labeled using
labeled using
unit of
unit of
appropriate
appropriate
measures
measures
units of
unit of
measure
measure
DATA
Identified and Identified
Only
Trends were
ANALYSIS
described
valid trends
identified
missing.
trends and
and made
obvious
Obvious
made
appropriate
trends not
trends were
appropriate
conclusions
fully
overlooked.
conclusions
based on the
supported by
based on the
data
the data
data
IDEAS
Every Idea
Almost every
More than
Some ideas
was related to idea was
half of the
were not
the topic
related to the ideas were
related to the
topic
related to the topic
topic
NAME:______________
SUMMATIVE TEST 3
MATH 7/4TH QUARTER
SCORE:_____
Encircle the letter of the correct answer.
1. What is the most stable and useful measure of central tendency?
A. mean
B. median
C. mode
D. range
2. When the data has extreme scores, what is the best measure of average?
A. mean
B. median
C. mode
D. range
For numbers 3 – 5,
The list gives the ages of students enrolled in swimming classes.
4 3 4 5 6 7 8 30
5 9 11 5 7 8 6 7
3. What is the median age of the students enrolled in swimming classes?
A. 6.5
B. 7
C. 7.5
D. 8
4. Which of the following describes the distribution?
A. unimodal
B. bimodal
C. trimodal
D. no mode
5. What is the mean age of the students?
A. 6.21
B. 7.34
C. 7.81
D. 8
For numbers 6-10 ,
Using the data on scores of 40 students in a mathematics test, answer the questions that follow.
scores
Frequency (f)
Cumulative frequency (cf)
95-99
1
40
90-94
4
39
85-89
3
32
80-84
7
25
75-79
7
18
70-74
9
9
65-69
2
7
60-64
1
6
55-59
2
4
50-54
2
2
45-49
2
N=40
6. What is the size of the class interval of the given frequency distribution
table?
A. 5
B. 6
C. 7
D. 8
7. What is the median class of the scores of 40 students in a mathematics
test?
A. 60-64
B. 65-69
C. 70-74
D. 75-79
8. What is the modal class of the scores of 40 students in a mathematics
test?
A. 75-79
B. 70-74
C. 65-69
D. 60-64
9. What is the median of the set of data?
A. 74.50
B. 75.60
C. 76
D. 76.50
10. What is the mode of the set of data?
A. 73.40
B. 73.60
C. 74.10
D. 75
11. Vic’s scores in three unit tests are 92, 87 and 88. What must his score be on the fourth test to get an average of
90?
A. 90
B. 91
C. 92
D. 93
12. What is the median score of 50 students if 10 of them got 23, 3 got 25, 6 of them got 28, another 6 got 30, 12
got 33, and the rest got 35?
A. 35
B. 33
C. 28
D. 25
13. If the heights in centimeters of a group of students are 180, 180, 173, 170 and
167, what is the mean height of these students?
A. 170
B. 173
C. 174
D. 180
14. A group of 13 real estate were asked how many houses they had sold in the past month. Find the mode.
Number of household
0
1
2
total
A. 0
B. 2
C. 6
D. 13
15. A friend of yours has 20 minutes to get to her after-school job. Despite her best efforts, she is frequently late
and has been tracking how long it takes (in minutes) to get there.
Determine the median. Her recorded times are as follows:
{18, 20, 22, 27, 16, 23, 25, 26, 19, 28}.
A. 21
B. 22.5
C. 23
D. 25
NAME:______________
SUMMATIVE TEST 4
MATH 7/4TH QUARTER
SCORE:_____
Encircle the letter of the correct answer.
1. What is the most reliable measure of variability?
A. range
C. average deviation
B. variance
D. standard deviation
2. If the range of a set of scores is 14 and the lowest score is 7, what is the highest score?
A. 21
B. 24
C. 14
D. 7
3. If the range of the set of scores is 14, and the highest score is 31, what is the lowest score?
A. 25
B. 23
C. 17
D. 9
4. Which of the following is the formula in finding the average deviation?
A. H – L
∑(x − 𝑥̅)2 / 𝑁
B. √
C. ∑(x − 𝑥̅)2 / 𝑁
D. ∑|𝑥−𝑥̅| / 𝑁
5 . What is the simplest measure of variability?
A. variance
C. standard deviation
B. range
D. average deviation
6. The following data represents the hours worked over a eight week period:
36, 40, 40, 42, 40, 50, 40, and 44. Calculate the range for this set of data.
A. 36
C. 14
B. 40
D. 50
7. Find the mean deviation of the following set of scores: 5, 6, 7, 7, 8, 8
A. 1.5
C. 0.83
B. 0.5
D. 0.89
8. The variance for a given set of data is 25 . Calculate the standard deviation.
A. 8
C. 2.56
B. 6.25
D. 5
9. The following are the scores you shot in five rounds of golf:
70, 80, 75, 75, and 80. The variance is:
A. 3.74
C. 70
B. 196
D. 14
10. This measures of variability tells you how far, on average, all values are from
the middle.
A. standard deviation
C. Range
B. variance
D. Mean deviation
11. A face shield vendor records the number of pieces he sells daily from Monday to Saturday and obtains the
following figures: 23, 18, 27,30,43 and 78.
What is the range of the given set of data?
A. 58
B. 60
C. 62
D. 64
12. What is the variance if Rodrigo obtains the following scores in his 5-item quizzes: 5, 4,3,6 and 2?
A. 3.5
B. 3
C. 2.5
D. 2
For items 13-15 refer to the problem below.
Ages of permanent employees in a Thermo-scanner factory in Pasig City.
Ages(X)
No. of employees (f)
40-44
8
35-39
10
30-34
12
25-29
4
20-24
6
N=40
13. What is the range of the given data?
A. 27
B. 25
C. 20
D. 30
14. What is the value of the variance?
A. 43.27
B. 53.27
C. 63.27
D. 33.27
15. What is the value of the standard deviation?
A. 3.58
B. 4.58
C. 2.58
D. 6.58
Study the table below, and answer the questions that follow.
The IQs of 5 members of 2 families A and B are:
Family A
108
112
127
118
113
Family B
120
110
118
120
110
16. What can you say about the mean IQ of both families?
A. The mean IQ of Family A is greater than the Mean IQ of Family B.
B. The mean IQs of two families are equal.
C. The mean IQ of Family B is greater than the mean IQ of Family A.
D. None of the above
17. What is the range of the IQ of Family A?
A. 19
B. 20
C.18
D. 21
18. What is the range of the IQ of family B?
A. 9
B. 6
C. 11
D. 10
19. How can you compare the range of the IQ’s of the two families?
A. The range of Family A is less than the range of Family B
B. The range of Family B is less than the range of Family A
C. The range of both families are equal
D. All of the above
20. Which of the two families has consistent IQ?
A. Both
B. Family A
C. Family B
D. None of them
NAME:______________
SUMMATIVE TEST 2
MATH 9/4TH QUARTER
SCORE:_____
DIRECTION: Read and understand each item and choose the letter of your answer.
(Items 1 -4): Refer to the figure below.
1.Which of the following refers to the angle R shown in the figure?
A. angle of elevation
C. complementary angle
B. angle of depression
D. supplementary angle
2. Side i in the figure above is referred to as what?
A. horizontal line
C. reference line
B. line of sight
D. vertical line
3.Using the concept of right angles, what is side a with angle R as the reference
angle?
A. adjacent line
C. hypotenuse
B. horizontal line
D. opposite line
4. If the measure of side a = 17 and r = 7m , what is the measurement of?
A. 22.38⁰
B. 24.38⁰
C. 60.38⁰
D. 65.68⁰
(Items 5 -10): Refer to the figure below.
5.What is the measurement of ∠O if o = 12 and l= 36?
A. 18.43º
B. 19.47º
C. 70.52º
D. 71.65º
6.What is the measurement of l if the angle of elevation is 25° and the horizontal
line measures 34 ft ?
A. 37.51 ft
B. 39.05 ft
C. 72.91 ft
D. 80.45 ft
7.Solve for o if g measures 12cm. and ∠O measures 32°
A. 6.36 cm B. 7.5 cm
C. 9.23 cm
D. 10.18 cm
8.What is the length of g if l = 8m and ∠ O= 40°?
A. 5.14 m
B. 5.65 m
C. 6.12 m
D. 6.71 m
9.What is the angle of elevation formed if l = 16 and g = 14?
A. 28.96º
B. 32.16º
C. 41.19º
D. 61.04º
10. What is the measurement of l if o = 20 and g = 10?
A. 19.02
B. 21.32
C. 22.01
D. 22.36
11. From the top of a mountain, 135 meters high, a ship is seen below in the sea.
It is observed that the angle of depression of the ship is 210. How far is the
ship from the top of the mountain?
A. 376.71 𝑚
B. 376 𝑚
C. 376.72 𝑚 D. 376.73 𝑚
12. On the rooftop of a school building, an observer saw a broken chair on the
school ground 4 meters away from the base of the building. What is the angle
of depression of the observer to the broken chair if the building is 18 meters
high?
A. 77 o 38′
B. 77 o 18′
C. 77 o28′
D. 77o
13. A pilot on a plane saw a nearby island in front of him. If he is 2975 m above
the ground and the horizontal distance of the island to the pilot 2345 m away.
What is the angle of depression of the pilot to the island?
A. 51o45′
B. 51 o40′
C. 51 o 43′
D. 51o
14. A boy is seen standing on the highest part of a mango tree. On top of the tree,
he saw an observer looking at him 5 meters away. If the angle of depression
of the boy to the observer is 34o26’, what is the height of the tree?
A. 3.44 𝑚
B. 3.4 𝑚
C. 3.42 𝑚
D. 3.43 𝑚
15. A man is seen on top of a coconut tree. 3 meters away from him is another
coconut tree. On the bottom of the other tree, there is a fallen coconut. If the
angle of depression of the man to the fallen coconut is 68 o17’, how high is the
coconut tree that he is located?
A. 7.55 𝑚
B. 8 𝑚
C. 7.53 𝑚
D. 7.5 �
Direction: Determine whether the following statements represent an Angle of
Elevation or Angle of Depression.
____________ 16. Two points on the same side of a tree are 19.8 m apart. Their angles
to the top of the tree are 21011’ from one point and 16 0 17’ from the other point.
____________ 17. The angle of a boy standing from a point on a lighthouse 30.5 m
above from the surface of the water makes an angle of 3 0 17’with the sea.
____________1 8. A bird sits on top of a 5-meter lamppost. The angle from the bird to
the feet of an observer standing away from the lamppost is 35 o22’.
____________19. A stargazer saw the planet Jupiter at midnight and assumed that
his angle to the planet in the sky is 43 o 17’.
____________20. From an airplane at an altitude of 1,200 meters, its angle in
connection with a rock from the ground is 28 0 18’.
SUMMATIVE TEST 3
MATH 9/4TH QUARTER
NAME:______________
SCORE:_____
1. Which of the following combinations can be solved using Law of Sines?
A. AAA
C. SSA
B. SAS
D. SSS
2. How many distinct triangles can be formed if 𝑎 = 23, 𝑏 = 19 and ∠A = 500?
A. 0
C. 2
B. 1
D. more than two
3. For which value of 𝑎 is it not possible to have ∆𝐴𝐵𝐶 if ∠A = 300 and 𝑏 = 10?
A. 4
C. 8
B. 5
D. 12
4. In ∆𝐴𝐵𝐶, 𝑎 = 22, 𝑏 = 12 and ∠A = 420, what is the measure of ∠𝐵 to nearest
hundredth?
A. 21.41
C. 116.59
B. 29.40
D. 150.60
5. A triangular lot has sides 14 meters and 11 meters. If the third side makes
an angle of 600 with the longer side, what is the length of the third side to
the nearest meter?
A. 15 meters
C. 17 meters
B. 16 meters
D. 18 meter
6. With respect to the given angle, what is the ratio of the opposite side to the
hypotenuse?
A. sine
B. cosine
C. tangent
D. cosecant
7. With respect to the given angle, what is the ratio of the adjacent side to the
hypotenuse?
A. sine
B. cosine
C. tangent
D. cosecant
8. Refer to the figure at the right.
Which of the following statement is correct?
𝑦
A. x = 8
C. sin 60° = 4
60
x
1
4
o
o
B. sin 30 = 𝑥
D. cos 60 = 𝑦
4
y
9. The expression 2(sin 30°) – tan 45° is equal to
A. -1
B. 0
C. 1
D. 2
10. ΔXYZ is an oblique triangle. If XY measures 20 cm, XZ measures 15 cm and ∠Z
measures 35° then what is the measure of ∠Y?
A. 25.84°
B. 24.85°
C. 25.48
D. 24.58°
Use calculator to find the value of the following:
11. sine 100o = _______________
cosine 100o = ________________
12. sine 700 = _______________
cosine 70o = _______________
Find the measure of the unknown parts of the following oblique triangles:
13. ∠𝑱 = _______
14. o = _______
15. y = _______
16. Two angles of a triangle are 55o and 590. If the smallest side is 200 cm, find the
measure of the longest side.
A. 200 cm
C. 223 cm
B. 209 cm
D. 240 cm
17. ΔTOP is an oblique triangle with two sides o=7m, t=10m and one angle ∠𝑷 =300
. What is the measures of the side p?
A. 5.27m
C. 9.5 m
B. 6.31m
D. 11 m
18. Given ΔBES where b=6 ft. , ∠𝑬 = 45o, ∠𝑺=105o. Which is the longest side?
A. b
C. s
B. e
D. b and s
19. This Law states that given a defined triangle with sides a,b and c and angles
opposite them ∠𝐴, ∠𝐵 and ∠𝐶 respectively, the ratio of the sine of angle to its
opposite side is equal in all three.
A. Sine Law
C. both A and C
B. Cosine Law
D. none of them
20. This Law states that, the square of a side is equal to the sum of the square of the
other two sides, the product of twice the negative of the other two sides and the
cosine of the angle opposite the unknown side.
A. Sine Law
C. both A and C
B. Cosine Law
D. none of the
Identification. Write LS (Law of sines) and LC (Law of cosines) which is
appropriate in the given statement. Write your answers on your answer sheets.
_______ 21. Two angles and the included side (ASA Case)
_______ 22. Two angles and the side opposite one of the angles (SAA Case)
_______ 23. Two sides and an angle opposite one of them (SSA Case)
_______ 24. Two sides and the included angle is given (SAS Case)
_______25. Three sides are given (SSS Case)
SUMMATIVE TEST 4
MATH 9/4TH QUARTER
NAME:______________
SCORE:_____
Encircle the letter of the correct answer.
1. Which of the following formulas can be used to solve for side 𝑎 in ∆𝐴𝐵𝐶 given the angles 𝐴, 𝐵, and
𝐶 and sides 𝑏 and 𝑐?
I. 𝑎 2 = 𝑏 2 + 𝑐 2 + 2𝑏𝑐 𝑐𝑜𝑠 𝐴
II. 𝑎 2 = 𝑏 2 − 𝑐 2 + 2𝑏𝑐 𝑐𝑜𝑠 𝐴
III. 𝑎 2 = 𝑏 2 + 𝑐 2 − 2𝑏𝑐 𝑐𝑜𝑠 𝐴
A. Only I
C. Only III
B. Only II
D. I, II, and III
2. Given ∆𝐴𝐵𝐶 where ∠𝐴 = 102o , 𝑏 = 5, and 𝑐 = 3, how long is 𝑎?
A. 2.00
C. 6.09
B. 4.36
D. 6.34
3. In ∆𝐴𝐵𝐶, 𝑎 = 7, 𝑏 = 16 and ∠𝐶 = 95o . Using the law of cosines, what is the
measure of ∠𝐵?
A. 22.78o
C. 59.16o
o
B. 25.84
D. 62.22o
4. What is the measure of the smallest angle in ∆𝐴𝐵𝐶 with sides 𝑎 = 7, 𝑏 = 16
and 𝑐 = 10?
A. 16.39o
C. 32.25o
o
B. 25.36
D. 57.75o
5. A rhombus has side lengths of 25 inches. The diagonal opposite the obtuse
angles is 45 inches. What is the measure of its obtuse angle to the nearest degree?
A. 108 o
C. 128o
o
B. 118
D. 138o
6. Which of the following formulas can be used to solve for the measure of ∠𝐴
in ∆𝐴𝐵𝐶?
I. 𝑐𝑜𝑠 𝐴 = 𝑏 2+𝑐 2+𝑎 2 / 2𝑏𝑐
II. 𝑐𝑜𝑠 𝐴 = 𝑏 2+𝑐 2−𝑎 2 / 2𝑏𝑐
III. 𝑐𝑜𝑠 𝐴 = 𝑏 2−𝑐 2−𝑎 2 / 2𝑏𝑐
A. Only I
B. Only II
C. Only III
D. I, II, and III
7. Which of the following describes the Law of Cosines?
A. The third side of a triangle equals the sum of the squares of the other two
sides minus the product of the two sides and an included angle.
B. The square third side of a triangle equals the sum of the squares of the other
two sides minus the product of the two sides and an included angle.
C. The square third side of a triangle equals the sum of the squares of the
other two sides minus twice the product of the two sides and an included angle
D. None of the above
8. What is the measure of the largest angle in a triangle with sides 6, 9, and 13?
A. 98.78o
B. 118.78o
C. 128.78o
D. 138.78o
9. What is the measure of ∠𝐴 in ∆𝐴𝐵𝐶 with sides 𝑎 = 8, 𝑏 = 10 and ∠𝐶 = 85o?
A. 40.59o
B. 54.41o
C. 57.75o
D. 61.21o
10. The diagonals of a rectangle are 48 centimeters long and intersect at an angle of 32o .
What is the length of the longer side of the rectangle?
A. 13.23 centimeters
C. 40.50 centimeters
B. 25.76 centimeters
D. 46.14 centimeters
11. Which of these triangles is NOT an oblique triangle?
A. Equilateral triangle
C. Right triangle
B. Obtuse triangle
D. Scalene triangle
12. What is the formula used in the law of cosine?
A. a2 = b2 + c2
C. c2 = a2 + b2 – 2ab cos C
sin 𝐴 sin 𝐵 sin 𝐶
B. b2 = a2 + c2
D. 𝑎 = 𝑏 = 𝑐
13. What information do we need to find the measure of the side of a triangle
using the law of cosines?
A. The measurements of all three sides
B. The measurements of all the three angles
C. The measurements of the two sides and the angle opposite the side
you want to find
D. The measurements of the two angles that are not opposite the side
you want to find and the side to the left of the side you want to find
14. What Information do we need to find the measure of an angle in a triangle using the
law of sines?
A. The measurements of all three sides
B. The measurements of all three angles
C. The measurements of the two sides next to the angle
D. The measurements of the side opposite the angle and the
other two angle
15. What is the sum of the angles of a triangle?
A. 45o
B. 90o
C. 135 o
D. 180o
NAME:______________
PERFORMANCE TASK 1
MATH 9 /4TH QUARTER
SCORE:___________
A. Answer the given problems. WRITE YOUR ANSWER ON THE OTHER SIDE OF
THIS PAPER.
3
1. Find the remaining trigonometric functions 𝛽 𝑖𝑓 cos 𝛽 = 5 and 𝛽 is an
angle in a right triangle.
2. Evaluate the following trigonometric functions.
a) sin 300 + cos 300
d) sin 450 + cos 450
0
0
0
b) 3 sin 60 – sin 30 + sin 60
e) tan 600 – 2 cos 450
0
0
0
c) 2 cos 45 – tan 45 + cos 60
B. Perform the activity below.
Activity 1: Using Calculator to Find Trigonometric Ratios
a) Finding a ratio given the angle
Example: To find the value of sin 380 ensure that your calculator is
operating in degrees.
Solution: Press → sin → 38 → =
Example: sin 𝜃 = 0.725 , find 𝜃 to → 0.615661475
Hence, sin 380 = 0.616, correct to three decimal places
b) Finding an angle given the ratio
the nearest minute
Solution: Press → 2ndF → sin → 0.725 → = → 46.46884783
To convert this to degrees/minutes/seconds mode,
Press → 2ndF →D 0M’S
The calculator gives you 46028’ (nearest minute)
c) Degrees and minutes
Example: Write 54.460 in degrees and minutes, giving an answer correct
to the nearest minute
Solution: Press → 54.460 → 2ndF → D 0M’S The calculator gives 54 027’36”, or 54028’
(nearest minute)
Try This
1) Use your calculator to find the value of the following, correct to two
decimal places.
i) cos 850
ii) tan 350
2) Write each of the following in degrees and minutes, give answers to the
nearest minute.
i) 17.80
ii) 63.70
3) Find the size of the angle 𝜃 (to the nearest degree) where 𝜃 is acute.
i) sin 𝜃 = 0.529
ii) tan 𝜃 = 0.7
NAME:______________
PERFORMANCE TASK 2
MATH 9 /4TH QUARTER
SCORE:___________
Draw a real-life situation which angle of elevation and angle of depression involves. Draw your answer on
this page.
NAME:______________
PERFORMANCE TASK 3
MATH 9 /4TH QUARTER
SCORE:___________
Choose from sine law or cosine law to solve the problem below. Write your works on your answer sheets.
Jose Angara St. and Osmeña St. intersect at 1000 . Anna’s gate in Jose Angara St. is 8 meters from the
intersection. Elsa’s gate is on Osmeña St. and is 12 meters away from the intersection. How far is Elsa’s gate from
that of Anna’s?
Sketch/ Draw the problem here:
Write your solutions here:
NAME:______________
PERFORMANCE TASK 4
MATH 9 /4TH QUARTER
SCORE:___________
Directions. Solve each of the given situational problems. Please write the answer on the other side of this paper.
1. Sketch the required triangle to solve the problem
2. Use the Law of Cosines to solve it
a. My son, Zane, has three sticks measuring 19 cm, 23 cm, and 27 cm.
He lays them down to form a
triangle. Find the measure of the angle formed by the 19-cm and the 23-cm sides to the nearest degree.
b. An aircraft tracking station determines the distance from common point O to each aircraft and the angle
between the aircrafts. If between the two aircrafts is 490 and the distance from point O to the two aircrafts are 50 km
and 72 km, find the distance between the two aircrafts. (Round off the answer to the nearest tenth)
c. A triangular parcel of land has sides 50 m., 40 m., and 35 m. What are the measures of the angles between
the sides? Express answers to the nearest degree
NAME:______________
SUMMATIVE TEST 2
MATH 8 /4TH QUARTER
SCORE:_____
Encircle the letter of the correct answer.
1. What do you call a line that intersects two or more other coplanar lines at
two or more distinct points.?
A. horizontal B. intersecting C. transversal D. vertical
For item numbers 2-3, use Figure 1.
2. If m is parallel to n and l is a transversal, which of the following relationship
is true?
l
A. ∠5 and ∠7 are complementary
1 2
m
B. ∠3 and ∠5 are supplementary
3 4
C. ∠1 = ∠3
5
6
D. ∠7 = ∠8
7 8
n
Fig. 1
3. If m || n and l is a transversal. Which of the following are corresponding angles?
A. ∠3 and ∠6, ∠4 and ∠5
C. ∠1 and ∠8, ∠2 and ∠7
B. ∠1 and ∠5, ∠2 and ∠6
D. ∠3 and ∠5, ∠4 and ∠6
4. Lines j and k are parallel cut by transversal t, which is perpendicular to j and k.
Which statement is NOT correct based on the figure?
J
k
A. ∠1 and ∠4 are congruent
B. ∠2 and ∠5 are supplementary
C. ∠3 and ∠6 are congruent
1
2 t
D. ∠1 and ∠6 form a linear pair
3 4
5 6
Fig. 2
For item numbers 5 -7, use Figure 3.
Given: a || b and t is a transversal
5. Which statement proves that a ||b?
t
A. ∠2 = ∠3
B. ∠1 = ∠5
1 2
C. ∠7 = ∠8
4
3
D. ∠2 = ∠5
5 6
6. Which angles are congruent to ∠7?
8
A. ∠1, ∠2 and ∠4
C. ∠1, ∠3 and ∠5
B. ∠1, ∠2 and ∠6
D. ∠1, ∠4 and ∠8
7. If m∠1 = 80, what is the measure of ∠7?
A. 10
B. 80
C. 100
D. 185
a
b
7
Fig. 3
For item numbers 8 – 11, use Figure 4.
P
1 2
3 5x +250
5 6
55 8
r
s
0
Fig. 4
8. What type of angle pair is ∠1 and ∠5?
A. alternate interior angles
C. supplementary angles
B. corresponding angles
D. vertical angles
9. What is the value of x?
A. 20
B. 25
C. 40
D. 45
10. What is the measure of ∠8?
A. 145°
B. 130°
C. 125°
D. 105°
11. What is the measure of ∠2?
A. 30°
B. 35°
C. 40°
D. 55°
12. Which could be used to prove that a || b in this figure?
A. alternate exterior angles
a
B. alternate interior angles
t
C. corresponding angles
D. consecutive angles
13. In figure 5, find the value of b that makes x || y. t
A. 25
C. 45
B. 35
D. 55
2b + 5
p
b
55
y
For item nos. 14-15, use the choices below to give the missing reason in the proof
below.
A. Alternate exterior angle
C. Corresponding Angle Postulate
B. Complementary angle
D. Vertical angles are congruent.
t
Given: p || q
3
p
Prove: ∠1  ∠2
2
1
q
SUMMATIVE TEST 3
MATH 8 /4TH QUARTER
NAME:______________
SCORE:_____
Directions: Choose the letter of the correct answer. Write your answer on a separate sheet of paper.
1. What is the set of all possible outcomes of an experiment?
A. Sample Space
B. Outcome
C. Intersection
D. Event
2. Which of the following is the subset of the sample space?
A. Complement
B. Event
C. Outcome
D. Sample Space
3. What is the process that has a number of possible outcomes in which the result
cannot be predicted?
A. Union
B. Set
C. Experiment
D. Element
4. If the event E1 is to spin a spinner wheel with 3 equal parts, what is n(E1)?
A. 2
B. 3
C.5
D. 6
5. If the event E2 is to roll a pair of dice, what is n(E2)?
A. 2
B. 6
C. 12 D. 36
6. If a coin is tossed and a die is rolled, list all the event in which coin comes up
tail and the die is an even number?
A. {(2,4,6)}
C. {(T,1), (T,3),(T,5)}
B. {(T,2), (T,4), (T,6)}
D. {(H,2),(H,4),(H,6)}
7. A pair of dice is tossed (a white die and a red die), list the element of the
event that the number less than 3 shown on each of the dice.
A. {(1,1), (2,2),(3,3)}
C. {(1,1), (1,2),(2,1),(2,2)}
B. {(3,1), (3,2),(3,3)}
D. {(3,1), (2,1),(2,2),(1,1)}
8. If four coins are tossed, which is the correct outcome of getting three heads
and one tail?
A. {(HHHT)}
C. {(HTTT), (THTT), (THTT),(TTTH)}
B. {(HHT), (HHT),(HTH),(THH)} D. {(HHHT),(HHTH),(HTHH),(THHH)}
9. What is the possible outcome in picking 2 marbles one at a time from a bag
that contains many black and white marbles?
A. {(B,B),(B,W),(W,B), (W,W)}
C. {(B,B), (W,W)}
B. {(B,2), (2,B),(W,2),(2,W)}
D. {(B,W)}
10.If you toss one coin and spin a 4section spinner numbered 1, 2, 3 and 4, what
is the correct sample space for this event?
A. {(H, T)}
B. {(H, T,1, 2, 3, 4, 5, 6)}
C. {(H,1), (H,2), (H,3), (H,4), (T,1), (T,2), (T,3), (T,4)}
D. {(H,1), (H,2), (T,3), (T,4)}
11.Find the sample space for the gender of children if a family has 3 children?
A. {(BBB), (BBG), (BGG), (GGG)}
B. {(BBB), (BGB), (BGG), (GBB), (GBG), (GGG)}
C. {(BBA), (BBB), (BBC), (BBD), (BBE), (BBF), (BBG), (BBH)}
D. {(BBB), (BBG), (BGB), (BGG), (GBB), (GBG), (GGB), (GGG)}
12.Which of the following give the sample space in which a classmate is born on
31st of the month?
A. {February, April, June, August, November, December}
B. {January, March, May, July, August, October, December}
C. {January, March, May, July, September, November}
D. {September, October, November, December}
For item numbers 13-15.
Let S = {5,10,15,20,25,30} be the sample space of an experiment and
T ={5,10}, V= {5,20,30} and W= {10,15,25} will be the event of the
experiment
13.Find T ∪ V
A. {5,10}
B. {5,20,30}
C. {10,15,25,30}
D. {5,10,20,30}
14.Find T ∩ W
A. {10}
B. {5,10}
C. {5,20,30}
D. {10,15,25}
15.Find W ’
A. {5,30}
B. {5, 20,30}
C. {10,15,25}
D. {5,10,15,30}
16. Jenny rolled a die and tossed a coin. How many times will the head possibly occur in the experiment?
A.1
B.2
C.4
D.6
17. What are the possible outcomes if you toss a coin twice?
A. {HH, HT, TH, TT}
B. {HH, TT}
C. {TH, HT}
D. {H, T, H, T}
18.Which experiment has the highest number of possible outcomes?
A.rolling a die and tossing a coin
B.choosing a combo-meal from 2 kinds of rice and 3 kinds of dish
C.picking a card from a deck of cards and rolling a die
D.choosing what to wear from 5 colours of t-shirt and 2 pairs of jeans
19 .In the table, how many possible milk tea options are there?
Flavors/Toppings Pearls
Jellies
Pudding
Chocolate
Chocolate - Pearls Chocolate - Jellies Chocolate - Pudding
Coffee
Caramel
A. 3
Coffee - Pearls
Caramel - Pearls
B. 6
Coffee - Jellies
Caramel - Jellies
C. 9
Coffee - Pudding
Caramel - Pudding
D. 15
20. There are 5 different flavored juice drinks and 3 different flavored sodas in the cooler. How many possible
outcomes will there be if you choose a juice drink and a soda?
A.5
B.8
C.15
D.20
21.Two children are playing jack-en-poy. How many possible outcomes can occur?
A.6
B.12
C.18
D.24
For item numbers 22-25, refer to the table below of the menu in a school cafeteria:
Main Dish
Adobo
Rice
Fried rice
Pakbet
Garlic rice
Menudo
Plain rice
Dessert
Ice Cream
Halo-halo
22.How many possible ways can you choose a meal consisting of 1 main dish, 1 rice, and 1 dessert?
A.3
B.6
C.8
D.18
23.How many possible outcomes can you choose by having a meal with Pakbet as main dish?
A.1
B.6
C.9
D.18
24. How many possible outcomes can you have to a meal with ice cream as dessert?
A.2
B.4
C.9
D.12
25. How many possible outcomes can you have to a meal with menudo and garlic rice as main dish and rice?
A.2
B.3
C.4
D.6
26. Angel Ice Cream Parlor offers 10 flavors of ice cream and 6 toppings which can be served on a waffle, sugar or
plain cone. How many different single scoop ice-cream cones can be possibly bought at the store?
A. 60
B. 90
C. 150
D. 180
27. James picked 1 candy and 1 bubble gum in his pocket. If there were 16 possible combinations, how many candies
were in his pocket?
A.3
B.4
C.8
D.12
28.Which of the following is true?
A. Rolling a die has 3 possible outcomes.
B. Flipping a coin twice has one possible outcome.
C. Answering 4-multiple choice test has 4 possible outcomes.
D. A standard deck of card has 13 cards only.
29. How many possible ways of choosing 1 color each from the Philippine flag, and the traffic light?
A.6
B.12
C.18
D.24
30. There are 3 choices for the kind of crust for a pizza. If there are 24 possible outcomes of pizza available, how
many toppings choices are there?
A. 6
B. 8
C. 10
D. 21
NAME:______________
SUMMATIVE TEST 4
MATH 8 /4TH QUARTER
SCORE:_____
Read each item carefully, choose the letter of the correct answer among the
given choices.
1. Which of the following terms shows the result of a single trial of an experiment?
A. Outcome
B. Probability Experiment
C. Sample Point
D. Sample Space
2. How do we call the set of all the possible outcomes or sample points?
A. Outcome
B. Probability Experiment
C. Sample Point
D. Sample Space
3. How many possible outcomes are possible in rolling a fair die?
A. 2
B. 4
C. 6
D. 8
4. An eight-spinner was spun by a man, what is the probability of getting a 9?
A. 0
B. 1
C. 2
D. 3
For item numbers 5 to 7,
use letters of the word “ALPHABET” as the sample space.
5. Find the number of elements in the sample space for the letters of “ALPHABET”.
A. 8
B. 10
C. 11
D. 12
6. Find the favorable outcomes for the chance of getting Letter A.
A. 2
B. 3
C. 4
D. 5
7. What is the probability of drawing a consonant letter?
A. 1/4
B. 1/2
C. 5/8
D. 1
8. What is the probability of having at least one tail in tossing a coin twice?
A. ¼
B. ½
C. ¾
D. 1
9. Which of the following statements has a 100% chance to happen?
A. Mt. Arayat will experience a snowstorm.
B. Not wearing a face mask will save you from COVID-19.
C. The capital city of Bulacan will be San Jose del Monte.
D. The sun will rise at the East tomorrow.
10. A number cube is rolled. What is the probability of rolling a number that is NOT 4?
A. 0
B. 1/6
C. 5/6
D. 1
11. Mark gave four one-peso coins to his son and accidentally dropped it on the floor. What is the probability that
four tails will appear?
A. 1/32
B. 1/16
C. 1/8
D. 1/4
12. The spinner numbered 1 to 20, what is the probability of getting an odd number divisible by 5?
A. 1/10
B. 2/15
C. 1/5
D. 1
13. Aling Josie sells 3 Globe sim cards, 4 Smart sim cards, and 3 Sun sim cards. What is the chance that a customer
will purchase a Smart sim cards to be used in his online class?
A. 1/5
B. 2/5
C. 3/5
D. 4/5
14. The local weather station forecasted that there is a 70% chance that it will not rain on Monday. What is the
probability that it will rain on Monday?
A. 0.3
B. 0.4
C. 0.5
D. 1
15. Mark is part of an organization and they planned to have a raffle for a cause. They printed 500 tickets. If Maria
bought 60 tickets, what is the probability that she will win
one of the prizes?
A. 3/25
B. 4/25
C. 0.6
D. 1
16. A fair die is rolled. What is the probability that a seven comes up?
A. -1
B. 0
C. 1
D. 2
17. A cafeteria offers 3 super meals, 2 budget meals and 4 barkada meals. What is the probability that a group of
customers would order a non-budget meal?
A. 5/9
B. 2/3
C. 7/9
D. 1
18. Suppose that the probability that aftershocks will be experienced 5 minutes after an earthquake is 0.678. What is
the probability that it will not occur?
A. -0.678
B. -0.322
C. 0.322
D. 0.678
19. Which of the following can be used to express probability of an event to happen?
I. decimal
II. fraction
III. percentage
A. I or II
B. II or III
C. I or III
D. I, II, or III
20. A two-letter code is to be formed using A,B or C. If repetition of the letters is allowed, find the probability that the
letters are the same?
A. 1/3
B. 2/3
C. ½
D. 1
21. How many outcomes are there in the sample space of an experiment that involves spinning a wheel numbered 1
to 8 and tossing a fair coin simultaneously?
A. 2
B. 8
C. 10
D. 16
22. A jar contains 10 candies, 4 of which are mint. If one candy is taken at random, determine the probability that the
candy is non-mint.
A. 0
B. 2/5
C. 3/5
D. 1
23. A pair of die is rolled once. Which of the following is not true about the outcomes?
A. The sample space has 12 outcomes.
B. The probability that numbers are the same is 1/6.
C. The probability that the digits are different is 83.33%
D. The chance that a 1,2,3,4,5 or 6 will appear are equally likely.
For item numbers 24-27, refer to the given situation.
Two baskets contain fruits. The first has 2 lemons and 3 atis while the
second has 2 lemons and an atis. A boy takes one fruit from each basket
blindfolded.
24. What is the total number of possibilities?
A. 10
B. 15
C. 20
D. 25
25. What is the probability of getting the same fruit?
A. 7/10
B. 7/15
C. 9/20
D. 9/25
26. What is the probability of getting exactly one lemon?
A. 8/25
B. 7/25
C. 8/15
D. 4/5
27. Which of the following indicates the chance for getting different fruits?
A. 4/5
B. 8/15
C. 7/25
D. 8/25
For item numbers 27-30, refer to the given experiment.
Trial
1
2
3
4
5
6
7
Result
T
H
T
H
T
T
T
28. What is the probability that a head comes up?
A. 2/7
B. 3/7
C. 5/7
D. 1
29. What is the probability that a tail comes up?
A. 2/7
B. 3/7
C. 5/7
D. 1
30. The activity of tossing a coin seven times with the results provided above is an example of what probability?
A. dependent
B. experimental
C. independent
D. theoretical
NAME:______________
PERFORMANCE TASK 1
MATH 8 /4TH QUARTER
SCORE:___________
FIND THE MEASURE
Directions: Below is the Muzon Crossing map in San Jose Del Monte Bulacan, use a protractor to measure the
following angles of the establishment’s location. Refer to the given measurement as a guide
1.
2.
3.
4.
5.
Convenience Store
110°
Pawnshop
__________
Save More
__________
Jewelry Shop __________
Public Market __________
6.Pizza Parlor __________
7.Hospital
__________
8. Bank __________
9.Machine Shop __________
10. Drug Store __________
Questions:
1.Based on the map, what is the pair of angles formed between:
a. Convenience Store and Pizza Parlor?
b. Pawn Shop and Hospital?
c. Save More and Bank?
d. Jewelry Shop and Machine Shop? What can you say about their measurements?
2.What is the pair of angles formed between
a.Save More and Hospital?
b.Jewelry Shop and Pizza Parlor? What can you say about their measurements?
3.What is the pair of angles formed between
a.Save More and Pizza Parlor?
b.Jewelry Shop and Hospital? What can you say about their measurements?
4.Based on the measurement of the pairs of angles formed, does this guarantee that Benito Nieto St. is parallel with
San Jose Heights St.? Graceville St. with St. Vivian St.?
NAME:______________
PERFORMANCE TASK 2
MATH 8 /4TH QUARTER
SCORE:___________
Choose Me!
Directions: Read and understand the problem. Write your answer on a separate sheet of paper.
The mathematics teacher will choose two students from a set of 6 equally qualified students, four boys and two girls,
to represent the class in the math competition.
Let A, B, C, and D represent the four boys and E,F represent the two girls.
a.What is the sample space of the class in the next competition?
b.What is the subset of the sample space defining the event of choosing “a boy and a girl”?
c.How many possible outcomes defining the event of choosing 2 boys and a girl?
d.How many possible outcomes in the event choosing 1 boy and 2 girls?
PERFORMANCE TASK 3
MATH 8 /4TH QUARTER
SCORE:___________
NAME:______________
CREATE YOUR OWN
Direction: Create a real-life situation using the given items below and enumerate all the possible outcomes
from them using different counting methods. Write your answer on a separate piece of paper.
Masks
Alcohol
Surgical Mask
Ethyl
Cloth Mask
Isopropyl
N95
KN95
Your output is rated using the scoring rubric below:
5
Originality
Shows
uniqueness
and creativity of
ideas
Presentation
Presents
complete,
organized and
clear
3
Shows some
uniqueness and
creativity with little
evidence of another’s
ideas
Presents complete
and organized
1
Shows total ‘copy
right’ of another’s
ideas
Presents
incomplete
and disorganized
Concepts
and
Application
Illustration is
correct
and accurate
Illustration is correct
with minor errors
Has no illustration
PERFORMANCE TASK 4
MATH 8 /4TH QUARTER
SCORE:___________
NAME:______________
Analyze the given figure below and answer the questions that follow.
1. A die was rolled 100 times. The result is shown in the table below
Event
1
Frequency 16
2
18
3
15
4
16
5
18
6
17
a. How many times the die was rolled?
b. How many times does the “1” appear?
c. How many times does the “5” appear?
2. A coin tossed 40 times. The result of 40 trials is shown in the following table.
Event
Head
Tail
Tally Marks
IIII – IIII – IIII - III
IIII – IIII – IIII – IIII - II
a) How many tosses were done?
b) How many times the head appeared?
c) How many times the tail appeared?
d) Estimate the probability of getting a head.
e) Estimate the probability of getting a tail
Frequency
18
22