SCHOOLS DIVISION OFFICE

CALOOCAN CITY

THIRD PERIODIC TEST

MATHEMATICS 10

Instruction: Read and understand each question. Shade the letter of the correct answer on the answer sheet.

1. It states that if there are 𝑚 ways to do a task, and 𝑛 ways to do another, then there are 𝑚 x 𝑛 ways of
doing both?
A. Table of Outcomes C. Systematic Listing
B. Tree Diagram D. Fundamental Counting Principle

2. Which refers to the product of positive integer n and all the positive integers less than n?
A. powers of n B. multiples of n C. n – factors D. n factorial

3. Which refers to the arrangement of objects in a set into a sequence or linear order?
A. Fundamental Counting Principle C. Probability
B. Permutation D. Combination

4. Which of these situations illustrate permutation?

A. Assembling a jigsaw puzzle
B. Picking 4 balls from a basket of 10 balls
C. Determining the winners of Math Quiz Bee.
D. Forming different triangles, from a pentagon by connecting non – consecutive vertices of it.

5. Which of the following is NOT a permutation of the letters E, F, G, H?

A. EFGH B. FEGH C. EEFG D. HGFE

6. Consider these situations:

I. Opening a digital lock using a 4 – digit code.
II. Entering the PIN (Personal Identification Number) of your ATM card.
III. Selecting 3 posters to hang out of 6 different posters.
IV. Choosing 5 questions to answer out of 10 questions in a test.
Which of the given situations describe a permutation?
A. III only B. III and IV C. I and II D. I, III and IV

7. Which refers to two different arrangements of objects where some of them are identical?
A. distinguishable permutation C. circular permutation
B. unique combination D. circular combination

8. Ms. Santos asked Renz to draw all diagonals of a certain polygon on a blackboard. Renz was able to
draw 27 diagonals which his teacher declared correct. What was the given polygon?
A. pentagon B. hexagon C. nonagon D. decagon

9. What is the value of 5P5 + 5P4?

A. 240 B.125 C. 36 D. 18

10. If P(n, 3) = 720, what is the value of n?

A. 7 B. 9 C. 10 D. 12

11. In how many ways can 8 students be arranged in a circular manner if two of them insist on sitting next
to each other?
A. 720 B. 1 440 C. 2 280 D. 5 040

12. During the Pandemic, the means of transportation is really difficult, so Axcel decided to buy a
motorbike and use it as his service vehicle to go to his place of work. Unluckily, he forgot the
combination of the 4-digit lock code of the chain he uses to secure his motorbike. He only remembers
that the code has the digits 0, 1, 2, and 7, and he is certain that 0 is not in the first digit. How many
possible combinations of codes are there in all?
A. 4 B. 12 C.18 D. 24

13. Given x = P(n, n) and y = P(n, n – 1), what can be concluded about x and y?
A. x=y B. x > y C. x ≠ y D. x < y
 14. Which of these can best define a combination?
A. It is a counting technique where the order of elements matters.
B. It is a counting technique where the order of elements is individually counted.
C. It is a counting technique that considers all possible outcomes where the order of elements is
needed.
D. It is a counting technique that considers all possible outcomes where the order of elements is not
important.

15. Which of these situations does NOT illustrate combination?

A. Enumerating the subset of a set.
B. Selecting 3 songs from 10 choices for an audition.
C. Identifying the lines formed by connecting some given points on a plane.
D. Fixing the schedule of a group of students who must take exactly 8 subjects.

16. There are 11 different food items in buffet. A customer is asked to get a certain number of items. If the
customer has 462 possible ways as a result, which of the following did he possibly do?
A. Choose 4 out of 11 B. Choose 6 out of 11 C. Choose 8 out of 11 D.Choose 7 out of 11

17. To win a 6/42 lotto, a player chooses 6 numbers from 1 to 42. Each number can only be chosen once.
If all 6 numbers match the winning numbers, regardless of the order, the player wins. How many possible
winning numbers are there?
42! 42! 42! 42!
A. B. C. D.
6! 36! 36!6! 42!6!
For numbers 18 – 19,
A math teacher gave the following situations to test the students on differentiating between permutation
and combination:
1. Selecting toppings for a pizza
2. Determining the top three winners in a contest
3. Choosing two household chores to do before the dinner
4. Drawing a set of six numbers in a lottery containing numbers 1 to 45
5. Selecting five basketball players out of ten team members for different positions
18. Which of the given item/s is/are permutation(s)?
A. 2 only B. 5 only C. 2 and 5 D. 2, 4 and 5

19. Which of those item/s is/are combination(s)?

A. 1 only B.1 and 3 C.1 and 4 D.1, 3, and 4

20. Which of the following situations does NOT illustrate a combination?

A. Choose six songs out of twenty to download
B. Five out of 13 students will ride in a car instead of a van
C. Three students in a class of fifteen to sit in a specific seat
D. Four out of ten patients are called to remind them of their appointment

21. What is C(n,n)?

A. n B. r C.1 D. cannot be determined

22. If C(n,r) = 35, which are possible values of n and r?

A. n = 6, r = 4 B. n = 7, r = 3 C. n = 8, r = 3 D. n = 9, r = 2

23. If C(n, 4) = 126, what is n?

A. 11 B. 10 C. 9 D. 7

For items 24 – 25,

Stephen and Michael were asked to solve the problem on the board.
In a 10-item mathematics
problem-solving test, how
The following are their solutions:
many ways can you select
Stephen: Michael:
10! 10! five problems to solve?
5! 5! 5!

24. Who do you think would give the correct answer?

A. Stephen B. Michael C. Both of them D. None of them
25. In how many ways can you choose the five questions if you are required to answer question number
10?
A. 30 240 B. 15 120 C. 252 D. 126
 26. How many committees of 4 persons can be chosen from a group of 10 persons?
A. 200 B. 210 C. 220 D. 250

27. Which is the appropriate definition for the union of two events A and B?
A. The set of all basic outcomes contained within both A and B.
B. The set of all basic outcomes in either A or B, or both.
C. The set of all possible outcomes.
D. Can’t be determined due to lack of data.

28. Which is the appropriate definition for the intersection of two events A and B?
A. The set of all basic outcomes contained within both A and B.
B. The set of all basic outcomes in either A or B, or both.
C. The set of all possible outcomes.
D. Can’t be determined due to lack of data.

For numbers 29-30, suppose you roll a pair of dice. Let A be the event that you observe an even number. Let
B be the event that you observe a number greater than seven.
29. What is the intersection of events A and B?
A. {8, 10, 12}
B. {7, 8, 9, 10, 11, 12}
C. {2, 4, 6, 7, 8, 9, 10, 11, 12}
D. {2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}

30. What is the union of events A and B?

A. {8, 9, 10, 11, 12}
B. {8, 10, 12}
C. {2, 4, 6, 8, 9, 10, 11, 12}
D. {2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}

31. Which of these is a simple event?

A. picking a red and yellow ball C. roll a die and get a 2
B. draw a king and a diamond D. get an average of 90 and rank first in school

32. Which of these can’t be the probability of an event?

1 9
A. B. C. 15 % D. 0.7
3 5

33. What is the probability of a sure event?

A. 0 B. 1 C. 2 D. None of these

34. Which of these is NOT an example of a compound event?

A. tossing three coins and getting at least 2 heads
B. rolling an even number less than 5 on a die
C. drawing a red ace from a deck of cards
D. the team winning a match

35. Which refers to two events that cannot occur at the same time?
A. Dependent Events
B. Independent Events
C. Mutually Exclusive Events
D. Mutually Inclusive Events

36. Which refers to two events that may occur at the same time?
A. Dependent Events
B. Independent Events
C. Mutually Exclusive Events
D. Mutually Inclusive Events

37. Which of the two events are mutually exclusive?

A. Rolling a die and getting an even number or a 6.
B. Tossing two coins and getting two heads or two tails.
C. Drawing a card from a deck and getting a king and a club.
D. Rolling two dice and getting doubles or getting a sum of 8.
38. Which of the two events are NOT mutually exclusive?
A. Rolling a die and getting a 6 or 3.
B. Tossing a coin and getting a head or a tail.
C. Drawing a card from a deck and getting a club or an ace.
D. Tossing a coin and rolling a die and getting a head and an odd number.

39. What is the size of the sample space when three distinct fair coins were tossed simultaneously?
A. 2 B. 4 C. 6 D. 8

40. A coin is tossed 4 times. What is the probability of getting at least one tail?
14 15 15 13
A. B. C. D.
16 17 16 16

41. Based on meteorological records, the probability that it will snow in a certain town on January 1st is
0.315. Find the probability that in a given year it will not snow on January 1st in that town.
A. 0.685 B. 3.175 C. 0.460 D. 1.315

42. What is the probability of randomly selecting a card from a standard 52 – card deck that is a heart or
an ace?
1 4 1 17
A. B. C. D.
13 13 4 52

43. What is the probability of getting a result of three or an even number when you roll a fair die?
2 1 1 1
A. B. C. D.
3 2 3 6

44. Suppose you roll two fair dice simultaneously. What is the probability of getting a double (two of the
same number) or having a sum of ten?
1 1 1 2
A. B. C. D.
12 18 36 9

3 1 4
45. If P(A) = , P(B) = , and P (A ∪ B) = , then Events A and B are mutually exclusive events.
10 2 5
A. True, since P(A) + P(B) = P (A ∪ B).
B. False, since P (A ∪ B) is equal to 0.
C. True, since P (A ∪ B) is not equal to 0.
D. Cannot be determined, since P (A ∩ B) is not provided.

46. Which of the following is a dependent event?

A. flipping a coin
B. rolling a pair of dice
C. picking up a pair of cards
D. picking a card replacing it in the deck and then having someone try to find that card

47. If the events A and B are independent with P(A) = 0.30 and P(B) = 0.40, what is the probability that
both events will occur simultaneously?
A. 0.10 B. 0.12 C. 0.70 D. 0.75

48. What is the probability of getting an odd number or a power of two in rolling a die?
1 1 2 5
A. B. C. D.
3 2 3 6

49. If (𝑨 ∪ 𝑩) = 0.64 and Event A and B are mutually exclusive, which of the following could be possible
probabilities for A and B?
A. 𝑃(𝐴) = 0.8 , 𝑃(𝐵) = 0.8 C. 𝑃(𝐴) = 0.64 , 𝑃(𝐵) = 0.64
B. (𝐴) = 0.42 , 𝑃(𝐵) = 0.22 D. 𝑃(𝐴) = 0.8 , 𝑃(𝐵) = 0.16

50. A family has four children. Suppose that the birth of each child is an independent event and that is
equally likely to be a boy or a girl. Let C denote the event that the family has one boy or one girl. Let D
denote that the family has at most one girl. What can you conclude about events C and D?
A. C and D are independent events.
B. C and D are not independent events.
C. C occurs given that D does not occur.
D. C and D are mutually inclusive events.