NEW
Font size
WorksheetsReview Test in Mathematics
Total questions: 50
Worksheet time: 25mins
A bakery offers 3 types of bread (B1, B2, B3) and 4 types of fillings (F1, F2, F3, F4). A customer chooses one bread and one filling for a sandwich. How many different sandwiches can the customer make? Which is the solution for the problem?
A. 3! 4!
B. (3)(4)
C. 3! + 4!
D. 3 + 4
A clothing store offers 4 different shirt styles (S1, S2, S3, S4) and 3 different pants styles (P1, P2, P3). A customer wants to buy one shirt and one pair of pants. How many different outfits can the customer choose?
From the problem above, Liam answered there are 12 different outfits the customer can choose. Is he correct?
A. Yes, because the solution is 4 - 3.
B. Yes, because the solution is (4)(3).
C. No, because the solution should be 4! 3!.
D. No, because the solution should be 4 + 3.
A box contains 2 apples (A1, A2) and 3 bananas (B1, B2, B3). You randomly select one fruit and then another without replacement. Use a tree diagram to visualize the possible outcomes. Which of the following is the correct illustration of the problem?
A classroom has 5 students: Alice, Bob, Clara, David, and Emily. They want to line up for a photo. What type of permutation is used to calculate the number of arrangements when all 5 students are distinct?
A. Distinct permutation
B. Circular permutation
C. Repeated permutation
D. Indistinguishable permutation
Which situation illustrates repeated permutation?
A. Arranging the letters in the word "BALLOON"
B. Selecting a captain and co-captain from 8 players
C. Forming a license plate with 3 letters and 3 digits and repetition is allowed
D. Creating a password for your email
A basketball coach needs to select 3 players from a group of 8 to form a lineup. How many distinct arrangements of 3 players can the coach make? Miguel's solution is 8•7•6 and has an answer of 336 arrangement while Gabriel's solution is 8! and has an answer of 40,320 arrangement. Who is correct and why?
A. Miguel is correct because he is using the formula for permutations of selecting 3 players from 8 which is appropriate when the order of selection matters.
B. Gabriel is correct because 8! gives the total number of ways to arrange 8 players, and since the coach only selects 3 players, the full factorial is the correct approach.
C. Miguel is correct because he is calculating the number of possible ways to arrange 3 players in a specific lineup, which is what the coach needs.
D. Neither is correct because both Miguel's and Gabriel's methods are incorrect for this problem.
A company manufactures necklaces with 6 beads: 2 red, 2 blue, and 2 yellow beads. How many unique arrangements can the beads be arranged in a straight line?
A. 90
B. 120
C. 180
D. 720
Four friends are sitting around a circular table: Anna, Ben, Carla, and Dan. How many distinct seating arrangements are possible?
A. 6
B. 12
C. 24
D. 120
A password consists of 4 characters. Each character can be a letter from the English alphabet (A-Z), and repetition of characters is allowed. How many distinct possible passwords can be created? Daniel's solution is (26)(4) and has an answer of 104 while Gideon's solution is 264 and has an answer of 456,976. Who is correct and why?
A. Daniel is correct because the total number of possible characters is 26, and there are 4 positions for the characters in the password.
B. Gideon is correct because for each of the 4 positions, there are 26 possible choices, so the total number of possible passwords is 264.
C. Both Daniel and Gideon are correct because their methods give the same result.
D. Daniel nor Gideon is correct because repetition is not allowed.
A teacher chooses 4 out of 10 questions for a quiz and wants to determine the order in which they will appear. How many distinct arrangements are possible?
A. 210
B. 5,040
C. 15,120
D. 302,400
How many distinct 4-digit numbers can be formed using the digits 1, 2, 3, 4, and 5, if repetition of digits is not allowed?
A. 120
B. 60
C. 24
D. 5
A bookstore has 8 different books, and the owner wants to arrange 5 of them on a shelf. How many distinct ways can the bookstore owner arrange the 5 books? The following are the steps on how to solve the problem. Arrange their order.
I. There are 6,720 ways to arrange the books.
II. The given are n=8 and r=5.
III. Use the formula: P=n!/(n-r)!
IV. Substitute the values of n and r in the formula then simplify.
A. I, II, III, IV
B. II, III, IV, I
C. IV,III, II, I
D. III, II, IV, I
Amari will travel in Switzerland to see The Matterhorn. She realized that the word “Matterhorn” has letters that repeat.
What equation can be used to find the number of distinguishable permutations that can be formed in the word 'MATTERHORN'?
A. P=10!/2!
B. P=10!/2!2!
C. P=10!/4!
D. P=10!/4!2!
Amari will travel in Switzerland to see The Matterhorn. She realized that the word “Matterhorn” has letters that repeat.
How many distinguishable permutations can be formed in the word 'MATTERHORN'?
A. 1, 814, 400
B. 907,200
C. 151,200
D. 75,600
In how many ways can 6 people be seated around a circular table if two of them insist on sitting beside each other?
A. 24
B. 36
C. 48
D. 52
Which problem does NOT illustrate combination?
A. From alphabets D, E, F, find possible different selections taking 2 alphabets at a time.
B. From number 3478, find possible different combinations taking 3 numbers at a time.
C. From the word COMBINE, find possible different combinations taking 3 letters at a time.
D. A team of 8 basketball players needs to choose a captain and co-captain.
Suppose that Rosa’s favorite is sausage and onion, but her mom cannot remember that, and she is going to randomly choose 2 different toppings. If Rosa’s mom will use combination, what are the values of n and r?
A. n=2, r=2
B. n=6, r=2
C. n=8, r=2
D. n=8, r=8
Which equation shows the number of ways Rosa can choose 2 toppings?
How many choices of 2 different toppings can Rosa's mom choose for the pizza?
A. 1
B. 28
C. 840
D. 20,160
If a committee of 8 members is to be formed from 8 students of Grade 10 and 5 students of Grade 7 such that there must be 5 students of Grade 10 in the committee, which of the following is/are true?
I. The 8 committee members can be selected in 1 287 ways.
II. The 5 grade 10 can be selected in 56 ways.
III. The 3 grade 7 can be selected in 10 ways.
A. I only
B. I and II
C. II and III
D. I, II, and III
How many matches will be played in the final round?
A. 10 games
B. 20 games
C. 30 games
D. 40 games
In how many possible ways can the top five players in the semi-finals come up?
A. 20 ways
B. 21 ways
C. 35 ways
D. ways
How many matches will be played altogether?
A. 73 matches
B. 42 matches
C. 21 matches
D. 10 matches
What type of permutation is illustrated in the situation below?
"The number of arrangements of the letters in the word ISOSCELES is 120."
A. Distinct Permutation
B. Circular Permutation
C. Repeated Permutation
D. Indistinguishable Permutation
In how many ways can you form a 5-sided polygon by choosing any of 5 of 11 points located on a circle to be the vertices?
A. 132
B. 720
C. 462
D. 360
There are 5 men and 4 women officers in the school PTA. A committee of 5 members is being selected at random to study the feasibility of the PTA project in the school. What is the probability that the committee will have 3 men?
A. 10/21
B. 5/21
C. 15/21
D. 18/21
The ABC band has 15 songs to perform in a concert. At the upcoming Battle of the Bands, they will play 2 songs. In how many different orders can they perform two of their songs?
A. 30
B. 150
C. 90
D. 210
Consider a standard deck of 52 cards. Which combination notation will represent the problem if you are asked to determine the different four-card hands that can be formed with at most two queens?
There are 15 chips numbered from 1 to 15 in a bag. A chip is drawn at random from the bag. Let A be the event that the number is multiple of 3 and let B be the event that the number is odd. What is A ∩ B?
A. {3, 9, 15}
B. {3, 6, 9}
C. {3, 6, 12}
D. {3, 7, 11}
A card is drawn at random from a standard deck of 52 playing cards. Which of the statements below would lead to the probability that a card is an Ace (A) or a King (K)?
A. P(A U K) = P(A) + P(K)
B. P(A U K) = P(A) ● P(K)
C. P(A U K) = P(A) + P(K) - P(A U K)
D. P(A U K) = P(A) + P(K) - P(A) ● P(K)
In a six-sided die experiment:
A. represents the event that the number is even.
B. represents the event that the number is a multiple of 3.
C. represents the event that the number is a multiple of 5.
Below is the representation using the Venn diagram with the sample space, S = {1, 2, 3, 4, 5, 6}.
What are the elements that are not in event A?
A. Elements 1, 3, and 5
B. Elements 2, 4, and 6
C. Elements 3, 4, and 5
D. Elements 4, 5, and 6
The two events A and B have a common element which is 6. It is the intersection of events A and B, written as A B = {6}. Using the same Venn diagram, what is the union of two events A or B?
A. A U B = {2, 3, 5, 6}
B. A U B = {2, 3, 4, 6}
C. A U B = {2, 3, 4, 5}
D. A U B = {2, 4, 6}
Your cousin wanted to buy a lottery ticket worth one thousand pesos because he wants to try his luck and according to his horoscope he is so lucky that day. But for you, it is very expensive. Will you support your cousin in buying a lottery ticket?
A. No, because I do not like it.
B. Yes, because that is what he wants.
C. Yes, because according to his horoscope he is so lucky that day.
D. No, because the chance of winning is very low, and he will be wasting his money and time.
What is the probability of getting at least 2 heads in tossing a coin three times?
A. 1/8
B. ¼
C. ½
D. 5/8
The Venn Diagram below shows the probabilities of Grade 10 students who joined either Mathematics Club (M) or Science Club (S).
The Venn diagram illustrates the relationship of these sets of data. What is the sum of all the values in the diagram?
A. 0.12
B. 0.38
B. 0.43
D. 1
Which is the correct solution in finding the probability of selecting a student who joined Mathematics Club or Science Club?
A. P(M ∪ S) = 0.12
B. P(M ∪ S) = 0.43 + 0.12
C. P(M ∪ S) = 0.43 + 0.12 + 0.38
D. P(M ∪ S) = 0.43 + 0.12 + 0.38 + 0.07
What is the probability of selecting a student who joined Mathematics Club or Science Club?
A. 0.12
B. 0.55
C. 0.93
D. 1
What do you call the events that do not have something in common?
A. Dependent events
B. Independent events
C. Mutually exclusive events
D. Not mutually exclusive events
In this 'new normal situation', nobody can go out without wearing a face mask. Mark has 15 disposable face masks: 4 are red, 6 are blue and 5 are green. The probability that Mark will wear a red or a blue face mask will be determined. What does the given problem illustrate?
A. two events that are mutually exclusive
B. two events that are not mutually exclusive
C. three events that are mutually exclusive
D. three events that are not mutually exclusive
In this ‘new normal situation’, nobody can go out without wearing a face mask. Mark has 15 disposable face masks: 4 are red, 6 are blue and 5 are green. The probability that Mark will wear a red or a blue face mask will be determined.
What is the probability that Mark will wear a red or blue face mask?
A. 2/5
B. 5/15
C. 10/15
D. 2/3
A card is drawn at random from a standard deck of 52 cards. What does the given describe if the probability of drawing an ace, a 10 or a king is being determined?
A. two events that are mutually exclusive
B. two events that are not mutually exclusive
C. three events that are mutually exclusive
D. three events that are not mutually exclusive
Refer to the Venn Diagram below. When rolling a die, find the probability of rolling a number less than five (𝐿) or an even number (𝐸)?
A. 2/6
B. 3/6
C. 4/6
D. 5/6
There is a 25% chance of getting a yellow ball (𝑌) from a box with 4 differently colored balls. There is also a 25% chance of picking a red (𝑅) ball from the same box. If you are to pick a ball from the box, what is the probability that it is yellow or red?
A. 25%
B. 50%
C. 75%
D. 100%
Janna asks her classmates on the social media platforms they frequently use during their free time. The result shows that out of 28 students of Grade 10 Taurus, 19 use Facebook, 11 use Instagram, and 5 use both Facebook and Instagram.
What is the probability that student selected Facebook or Instagram?
A. 11/28
B. 14/28
C. 19/28
D. 25/28
Janna asks her classmates on the social media platforms they frequently use during their free time. The result shows that out of 28 students of Grade 10 Taurus, 19 use Facebook, 11 use Instagram, and 5 use both Facebook and Instagram.
What is the probability that students selected neither of the two social media platforms?
A. 3/28
B. 1/7
C. 5/28
D. 3/14
In order to prevent Covid-19 Pandemic to spread rapidly, Jean volunteered to give box contains face masks. Consider the box contains 14 red masks, 12 blue masks, and 9 yellow masks. Suppose that the two masks are drawn one after the other without putting back the first mask.
In the given situation, what is the probability of drawing the two masks in the box if the first mask is yellow and second mask is red?
A. 9/17
B. 7/17
C. 9/85
D. 63/85
In order to prevent Covid-19 Pandemic to spread rapidly, Jean volunteered to give box contains face masks. Consider the box contains 14 red masks, 12 blue masks, and 9 yellow masks. Suppose that the two masks are drawn one after the other without putting back the first mask.
What is the probability of choosing one blue mask and one red mask?
A. 12/85
B. 24/175
C. 42/169
D. 26/35
If Jean added 5 more yellow masks, what is the probability of getting both yellow masks?
A. 91/800
B. 7/60
C. 13/85
D. 26/175
Andrea is thinking about her lessons in Math 10 about dependent and independents events. She comes up with different situations and write it in her notes.
I. Not paying your water bill on time and having your water cut off.
II. Eating too much and getting fatter.
III. Entering the bus first and finding a good seat.
IV. Owning a cat and growing your own vegetable garden.
Which among her list are examples of dependent events?
I
III
I & II
II & IV
A class contains 16 males and 12 females. Half of the male and half the female like Korean Dramas. What is the probability that a student chosen at random is a female or likes Korean Dramas?
A. 21%
B. 43%
C. 50%
D. 71%
