REGIONAL UNIFIED QUARTERLY ASSESSMENT

(RUQA) SY 2024-2025

Third Quarter – Grade 10 (Mathematics)

GENERAL INSTRUCTIONS. Do not write anything on this test paper. After carefully
reading all the questions, reflect all your answers on the separate ANSWER
SHEET. Shade the circle that corresponds to your chosen answer.

1. Which of the following statements best describes the difference

between permutation and combination?
a) Permutation involves arranging objects in a specific order, while combination does
not consider the order.
b) Permutation involves selecting objects without replacement, while combination
involves selecting objects with replacement.
c) Permutation and combination are the same concept and can be used interchangeably.
d) Permutation involves selecting objects with replacement, while combination
involves selecting objects without replacement.

2. Which of the following scenarios best represents an example of a

permutation?
a) Choosing three books to read from a shelf.
b) Selecting a committee of three members from a group of ten.
c) Arranging five different colored balls in a row.
d) Picking two candies from a jar without replacement.

3. A teacher has a collection of 10 books, out of which 4 books are to be

arranged on a shelf. In how many different orders can the teacher arrange the
books?
a) 120
b) 240
c) 5,040
d) 10,000

4. A group of 4 students is going to perform in a talent show. In how many

different orders can they arrange themselves on stage?
a) 4
b) 16
c) 24
d) 28

5. Given the letters FIRST. In how many ways can we arranged all these letters?
a) 1
b) 10
c) 20
d) 120

6. A restaurant offers a menu with 8 appetizers, 12 main courses, and 6

desserts. If a customer selects one appetizer, one main course, and one
dessert, how many different meal combinations are possible?
a) 192 b) 576 c) 5,760 d) 1,152
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7. How many ways can a 4 – digit number be formed from the digits 0, 1, 2, 3,
4, 5, 6, 7, 8, 9 if repetition of digits is not allowed?
a) 90
b) 720
c) 4,320
d) 5,040

8. In how many ways can a 4 – digit number be formed from the digits 0, 1, 2,
3, 4, 5,
6, 7, 8, 9 if repetition of digits is allowed?
a) 720
b) 5,040
c) 9,000
d) 10,000

9. A jar contains 10 different types of candies. If you want to select 4 candies

to fill a gift bag, how many different combinations of candies can you choose?
a) 120
b) 210
c) 360
d) 5,040

10. How many ways can you select a committee of 3 officers out of 5 officers?
a) 6
b) 10
c) 15
d) 60

11. In a group of 10 students, how many different ways can a president, vice
president, and treasurer be selected if each student can hold only one
position?
a) 30
b) 120
c) 720
d) 990

12. Mr. Ruan is a math teacher. He made 10 questions for his students to
answer. If the students are allowed to answer only 5 questions, in how many
ways can the student choose the questions?
a) 50
b) 150
c) 225
d) 252

13. How many triangles can be drawn on a plane using 4 non-collinear points?
a) 3
b) 4
c) 12
d) 24

14. A pizza parlor offers 4 types of crust, 3 types of sauce, and 5 toppings. If a
customer can choose one crust, one sauce, and one topping, how many
different pizza combinations are possible?
a) 20
b) 30
c) 40
d) 60
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15. A combination lock has 4 digits, each ranging from 1 to 9. If repetition of

digits is not allowed, how many different combinations are possible?
a) 36
b) 504
c) 3,024
d) 3,528

16. How many ways can 7 people sit around a circular table?
a) 14
b) 120
c) 360
d) 720

17. How many ways can 20 students be paired off for a performance task in
math?
a) 40
b) 190
c) 380
d) 6,840

18. A bag contains 6 blue marbles and 4 red marbles. What is the probability
of getting a red mable?
a) 2/5
b) 3/5
c) 3/10
d) 5/3

19. A bakery offers a variety of cakes, including chocolate, vanilla, and

strawberry flavors. If a customer can choose one cake flavor, one frosting
type, and one decoration style, how many different combinations of cake can
the customer create if there are 3 cake flavors, 4 frosting types, and 5
decoration styles available?
a) 12
b) 20
c) 60
d) 180

20. A clothing store sells shirts in 4 different colors (red, blue, green, and
yellow), pants in 3 different colors (black, khaki, and denim), and shoes in 2
different styles (sneakers and boots). If a customer wants to buy one shirt,
one pair of pants, and one pair of shoes, how many different outfit
combinations are possible?
a) 12
b) 24
c) 48
d) 72

21. Consider rolling a fair six-sided die once. Event A is defined as rolling an
even number, and Event B is defined as rolling a number greater than 3. What
is the intersection of Event A and Event B?
a) {2, 4}
b) {4, 5, 6}
c) {2, 3, 4, 5, 6}
d) {3, 6}
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22. In a deck of 52 playing cards, Event C is defined as drawing a heart, and

Event D is defined as drawing a face card (Jack, Queen, or King). What is the
union of Event C and Event D?
a) {Jack of Hearts, Queen of Hearts, King of Hearts}
b) {All heart cards, All face cards}
c) {All cards}
d) {All face cards}

23. In a survey of 100 people, 60 reported owning a smartphone (Event A),

and 40 reported owning a tablet (Event B). Of those surveyed, 30 reported
owning both a smartphone and a tablet. What is the probability that a
randomly selected person from the survey owns either a smartphone or a
tablet?
a) 0.30
b) 0.50
c) 0.60
d) 0.70

24. A numbered balls from 1 to 10 is placed in the jar, find the probability of
getting an odd number.
a) 0.50
b) 0.60
c) 0.70
d) 0.80

25. In tossing a die, what is the probability of getting 2 or 6?

a) 1/6
b) 1/3
c) 2/3
d) 3/4

26. In a group of 50 students, 30 students are members of the math club

(Event M) and 25 students are members of the science club (Event S). If 15
students are members of both clubs, what is the probability that a randomly
selected student is either a member of the math club or the science club?
a) 0.4
b) 0.6
c) 0.8
d) 0.9

27. A die is rolled once. What is the probability of getting an even number or a
5?
a) 1/6
b) 1/3
c) 2/3
d) 3/4

28. A coin is tossed two times. Find the probability in getting all tails?
a) 20%
b) 25%
c) 50%
d) 75%

29. Out of 100 employees in a company, 60 employees have received a

promotion (Event P) and 40 employees have received a salary raise (Event R).
If 25 employees have received both a promotion and a salary raise, what is
the probability that a randomly selected employee has either received a
promotion or a salary raise?
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a) 0.35
b) 0.5
c) 0.75
d) 0.9

30. In a bag containing 5 blue balls, 3 white balls, and 8 red balls, one ball is
drawn. What is the probability that the ball is either white or red?
a) 5/16
b) 8/16
c) 11/16
d) 13/16

31. A weather company forecasted that there will be a 25% chance of rain
shower in the morning. What is the probability that it will not rain?
a) 25%
b) 50%
c) 75%
d) None of the above

32. A coin is tossed three times. Find the probability of getting either all
heads or getting all tails?
a) 1/4
b) 1/3
c) 1/2
d) 3/4

33. From the problem 32, what is the probability of getting either all heads or
getting heads exactly once?
a) 1/4
b) 1/3
c) 1/2
d) 3/4

34. A die is rolled once. Find the probability of getting an even number or
getting a number greater than 2?
a) 1/6
b) 1/3
c) 3/4
d) 5/6

35. A card is drawn from a standard deck of 52 cards. What is the probability
of getting a Queen or a King?
a) 2/13
b) 4/13
c) 6/13
d) 8/13

36. In a deck of cards, Event A represents drawing a red card, and Event B
represents drawing a black card. Are events A and B mutually exclusive?
a) Yes
b) No
c) Sometimes
d) Cannot be determined
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37. Consider rolling a six-sided die. Event C represents rolling an odd

number, and Event D represents rolling an even number. Are events C and D
mutually exclusive?
a) Yes
b) No
c) Sometimes
d) Cannot be determined

38. In a group of 50 students, Event E represents students who play soccer,

and Event F represents students who play basketball. If 30 students play
soccer and 25 students play basketball, including 10 students who play both
sports, are events E and F mutually exclusive?
a) Yes
b) No
c) Sometimes
d) Cannot be determined

39. In a company with 80 employees, Event G represents employees who have

a college degree, and Event H represents employees who have a certification.
If 50 employees have a college degree and 35 employees have a certification,
including 15 employees who have both, are events G and H mutually
exclusive?
a) Yes
b) No
c) Sometimes
d) Cannot be determined

40. A survey was conducted among 200 individuals to determine their

preferred mode of transportation. Event I represents individuals who prefer
cars, and Event J represents individuals who prefer bicycles. Out of the
surveyed individuals, 120 preferred cars, 80 preferred bicycles, and 40
preferred both cars and bicycles. Are events I and J mutually exclusive?
a) Yes
b) No
c) Sometimes
d) Cannot be determined

41. In a school with 300 students, Event K represents students who play
soccer, and Event L represents students who play basketball. If 150 students
play soccer, 120 students play basketball, and 50 students play both soccer
and basketball, are events K and L mutually exclusive?
a) Yes
b) No
c) Sometimes
d) Cannot be determined

42. A survey is conducted to determine the preferences of people for ice

cream flavors. Participants can choose either chocolate, vanilla, or strawberry.
Which of the following pairs of events are mutually exclusive?
a) Selecting chocolate and vanilla flavors
b) Selecting vanilla and strawberry flavors
c) Selecting chocolate and strawberry flavors
d) Selecting chocolate flavor only
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43. A card is drawn from a standard deck of 52 cards. What is the probability
of getting an Ace or a Red?
a) 2/13
b) 5/13
c) 6/13
d) 7/13

44. A fair six-sided die is rolled twice. What is the probability of getting a sum
of 7 on the two rolls?
a) 1/6
b) 1/3
c) 1/4
d) 1/12

45. A box contains 7 white marbles and 7 red marbles. What is the
probability of drawing 2 white marbles and 1 red marble in the succession
without replacement?
a) 1/3
b) 2/7
c) 3/52
d) 7/52

46. What is the probability of getting a heart or a face card when drawing a
single card at random from a regular deck of cards?
a) 1/13
b) 11/26
c) 1/2
d) 3/52

47. What are the chances of not rolling a six on a six – sided die?
a) 1/6
b) 1/3
c) 1/2
d) 5/6

48. A box contains 4 white marbles and 5 blue marbles. What is the
probability of drawing 2 blue marbles and a white marble in succession
without replacement?
a) 10/63
b) 13/63
c) 5/72
d) 13/72

49. A card is drawn from a standard deck of 52 cards. What is the probability
that it is a face card (jack, queen, or king)?
a) 3/13
b) 1/4
c) 1/3
d) 1/2

50. How many different ways can the letters of the word FOLLOW be arranged?
a) 120
b) 180
c) 360
d) 720

Congratulations!
You completed the test!