Math for AI Class 9 Questions and Answers

These Class 10 AI Important Questions Chapter 5 Math for AI Class 9 Important Questions and Answers NCERT Solutions Pdf help in building a strong foundation in artificial intelligence.

Math for AI Class 9 Important Questions

Class 9 Math for AI Important Questions

Important Questions of Math for AI Class 9 – Class 9 Math for AI Important Questions

Multiple Choice Questions

Question 1.
If you are to throw an arrow to this pie chart, in which color is the arrow more likely to fall?

(a) Red
(b) Blue
(c) Yellow
(d) Green
Answer:
(b) Blue

Question 2.
If you select a balloon witthout looking, how likely is it that you will pick a blue one?

(a) Probable
(b) Certain
(c) Unlikely
(d) Impossible
Answer:
(d) Impossible

Question 3.
With one throw of a 6 -sided die, what’s the probability of getting an even number?
(a) 1 / 5
(b) 2 / 5
(c) 5 / 6
(d) 1 / 2
Answer:
(d) 1 / 2

Question 4.
Which of the following is an equation?
(a) 2x + 5
(b) x + 2 = 4x
(c) x² + 2x
(d) 5 + 5x + 5x²
Answer:
(b) x + 2 = 4x

Question 5.
What is the value of x ? 10x – 8 = 6x
(a) 8
(b) 4
(c) 2
(d) 6
Answer:
(c) 2

Question 6.
Which two are examples of descriptive statistics?
(a) Median and correlation.
(b) Mean and standard deviation.
(c) Mode and regression analysis.
(d) Variance and Hypothesis testing.
Answer:
(b) Mean and standard deviation.

Question 7.
What is the probability of getting head when you toss a coin once?
(a) 0.75
(b) 1
(c) 0
(d) 0.5
Answer:
(d) 0.5

Question 8.
Getting seven in die throwing is a possible event. (True/False).
Answer:
False

Question 9.
The median of the data: 155,160,145,149,150, 147,152,144,148 is
(a) 149
(b) 150
(c) 147
(d) 144
Answer:
(a) 149

Match the column

Question 1.
Match the following:

A	B
i. Probability	a) exploring data
ii. Calculus	b) finding out unknown or missing values
iii. Statistics	c) predicting different events
iv. Linear Algebra	d) training and improving AI model.

Answer:

A	B
i. Probability	c) predicting different events
ii. Calculus	d) training and improving AI model.
iii. Statistics	a) exploring data
iv. Linear Algebra	b) finding out unknown or missing values

Math for AI Class 9 Subjective Type Questions

Question 1.
Explain the relationship between Mathematics and Artificial Intelligence, providing justification for their interconnection.
Answer:
Mathematics serves as the backbone of Artificial Intelligence (AI), providing the theoretical framework and tools necessary for understanding and developing AI algorithms. Concepts from various branches of mathematics such as calculus, linear algebra, probability theory, and statistics are used extensively in AI for modeling, optimization, decision-making, and machine learning.

Question 2.
Aman is confused, how probability theory is utilized in artificial intelligence, help Aman by providing two examples to illustrate its importance.
Answer:
Probability theory plays a crucial role in AI by providing a mathematical framework for dealing with uncertainty. For example, in machine learning, probabilistic models like Bayesian networks are used to represent and reason about uncertainty in data. Another example is in natural language processing, where probabilistic models such as Hidden Markov Models are used for tasks like speech recognition and part-of-speech tagging.

Question 3.
Define Certain events and likely events with examples.
Answer:
Certain events are those that are guaranteed to happen, with probability 1 . For example, when you flip a fair coin, the event “getting either heads or tails” is certain. Likely events are those with a high probability of occurring, but not guaranteed. For instance, in rolling a fair six-sided die, the event “rolling a 3 or a 4 ” is likely.

Question 4.
Write any two examples of Impossible and equal probability events.
Answer:
Impossible events are those with zero probability of occurring. For example, rolling for a seven with a fair six-sided die is an impossible event. Equal probability events are those with the same likelihood of occurring. For instance, when you roll a fair six-sided die, each face has an equal probability of 1 / 6 of appearing.

Question 5.
Radhika collected the data of the age distribution of cases admitted during a day in a hospital.

Find the average number of cases admitted in hospital. Also, draw a line graph to represent the data graphically.
Answer:
To find the average number of cases admitted in the hospital, we can use the formula :
Average = (Sum of all cases admitted) /( Number of data points)
Let’s calculate the sum of all cases admitted:
Sum = 5 + 7 + 9 + 22 + 11 = 54

Now, there are 5 data points, so the average is:
Average =54 / 5=10.8
So, the average number of cases admitted in the hospital is 10.8 per day.

Now, let’s create a line graph to represent the data:

Question 6.
Identify the likely, unlikely, impossible and equal probability events from the following
(a) Tossing a coin
(b) Rolling an 8 on a standard die
(c) Throwing ten 5’s in a row
(d) Drawing a card of any suite
Answer:
(a) Tossing a coin This is an equal probability event. There are two possible outcomes (heads or tails), and each outcome has an equal chance of happening.

(b) Rolling an 8 on a standard die This is an unlikely event. A standard die has six sides, and only one side has an 8 . So, the probability of rolling an 8 is 1 out of 6 , which is a low chance.

(c) Throwing ten 5’s in a row This is an impossible event. While unlikely things can happen, throwing ten 5 s in a row is extremely improbable. There are 6 possible outcomes when rolling a die (1-6), and getting a 5 ten times in a row is statistically very unlikely.

(d) Drawing a card of any suite This is a likely event. There are four suits in a standard deck (hearts, diamonds, clubs, spades), and you only need to draw a card from any of those suits. There are 52 cards total, and 4 of them satisfy the condition (one from each suit), so the chance of drawing a card of any suit is quite high.

Question 7.
Why is math necessary for designing an Al project?
Answer:
Math is the language of AI for a few reasons:
Foundations of AI algorithms Many AI algorithms rely on complex mathematical formulas to analyze data, recognize patterns, and make predictions. This could involve anything from linear algebra for image recognition to calculus for optimizing machine learning models.

Data representation and manipulation Real-world data is often messy and needs to be processed and transformed before feeding it into an AI system. Math provides the tools to represent this data in a way that computers can understand and manipulate.

Evaluation and performance You need to be able to measure how well your AI system is performing. Math provides the framework to define metrics and assess the effectiveness of your design.

Math for AI Class 9 Very Short Answer Type Questions

Question 1.
What branch of math helps Al understand data patterns?
Answer:
Statistics

Question 2.
Which mathematical technique is used to optimize AI model parameters?
Answer:
Gradient descent

Question 3.
How does probability benefit Al systems?
Answer:
It helps AI make decisions under uncertainty.

Question 4.
What is the role of linear algebra in Al ?
Answer:
It helps represent and manipulate data.

Question 5.
Why is calculus important for training AI models?
Answer:
It optimizes the model’s performance by minimizing errors.

Question 6.
What foundational concepts empower machines to make intelligent decisions?
Answer:
Statistics and probapility, particularly in analyzing data and handling uncertainty.

Question 7.
How does mathematics contribute to Al algorithms?
Answer:
Mathematics, including linear algebra, calculus, and probability theory, forms the basis for AI models and predictions.

Question 8.
Why is statistics crucial for AI?
Answer:
Statistics enables understanding and analyzing data, identifying patterns, and making informed predictions in AI systems.

Question 9.
How does calculus improve AI models?
Answer:
Calculus optimizes AI models by adjusting parameters through techniques like gradient descent for enhanced performance.

Question 10.
Why is linear algebra important in Al?
Answer:
Linear algebra helps represent and manipulate data for AI models, essential for understanding and processing information efficiently.

Question 11.
What role does probability play in Al systems?
Answer:
Probability helps AI systems make decisions under uncertainty and model data variability for accurate predictions.

Question 12.
What are the primary measures of central tendency?
Answer:
Mean, median, and mode are the main measures of central tendency in statistics.

Question 13.
Define variance and its importance in statistics.
Answer:
Variance measures data variability from the mean, crucial for understanding the spread of data points in a dataset.

Question 14.
How does mathematics support various fields beyond Al?
Answer:
Mathematics, particularly statistics, is applied in diverse fields such as sports analytics, disaster management, finance, and education.

Math for AI Class 9 Short Answer Type Questions

Question 1.
How does mathematics contribute to the foundation of Al ?
Answer:
Mathematics serves as the language of AI , enabling machines to process information through numbers and equations, essential for creating algorithms and machine learning models that recognize patterns and make predictions.

Question 2.
What role does statistics play in preparing data for Al learning?
Answer:
Statistics aids in cleaning data, identifying outliers, and selecting relevant features for training AI models. This ensures more accurate and efficient learning by quantifying uncertainty and building robust models.

Question 3.
Can you explain the significance of measures of central tendency in statistics?
Answer:
Measures like mean, median, and mode provide . insights into the central position within a dataset. They help in understanding data distribution, essential for analyzing trends and making informed decisions in AI.

Question 4.
How do variance and standard deviation measure data spread?
Answer:
Variance quantifies the average squared deviation from the mean, indicating data variability. Standard deviation, the square root of variance, expresses data spread in the same units as the original data, aiding in assessing data consistency.

Question 5.
In what ways does probability theory benefit AI systems?
Answer:
Probability theory enables AI systems to make decisions under uncertainty by modeling probabilistic outcomes.
This is crucial in machine learning for handling data uncertainty and making informed predictions, enhancing the reliability of AI algorithms.

Math for AI Class 9 Long Answer Type Questions

Question 1.
How does statistics contribute to the robustness of Al models?
Answer:
Statistics plays a crucial role in ensuring the robustness of AI models by addressing the uncertainties and imperféctions in data.

It helps in identifying outliers, cleaning data, and selecting relevant features for training models. By quantifying uncertainty, statistics enables the creation of models that are resilient to errors and variations in data, enhancing their accuracy and efficiency in making predictions.

Additionally, statistical techniques such as hypothesis testing and confidence intervals allow for the validation and generalization of AI models, ensuring they perform reliably on new, unseen data. This comprehensive approach helps in building robust AI systems that can withstand the challenges of real-world applications.

Question 2.
Explain the significance of calculus in optimizing AI models.
Answer:
Calculus provides the mathematical framework for optimizing the performance of AI models. Techniques like gradient descent utilize calculus to adjust the parameters of models iteratively, minimizing errors and improving performance over time.

By enabling precise adjustments based on the rate of change of variables, calculus ensures that AI models converge towards optimal solutions, enhancing their effectiveness in tasks such as pattern recognition and decision-making.

Moreover, advanced calculus methods such as partial derivatives and multivariable functions allow for the optimization of complex models with numerous parameters, facilitating the fine-tuning necessary for achieving high accuracy and efficiency in diverse AI applications.

Question 3.
How does probability theory aid AI systems in handling uncertainty?
Answer:
Probability theory is essential for AI systems to make decisions under uncertainty. By modeling uncertainty in data, probability theory enables AI systems to quantify the likelihood of different outcomes and make informed decisions. This is crucial in various applications, such as natural language processing and autonomous vehicles, where AI systems must navigate complex and uncertain environments.

Probability theory provides a solid foundation for reasoning about uncertainty, allowing AI systems to make optimal choices and adapt to changing circumstances effectively.

Additionally, techniques such as Bayesian inference and probabilistic graphical models offer powerful tools for updating beliefs based on new information, further enhancing the decision-making capabilities of AI systems in dynamic settings.

Math for AI Class 9 Activities

Activity 1

Purpose Observing and analyzing the numbers and Find the pattern.

Problem 1 : Missing Number Series
In each of the series, the missing number can be found by looking at the difference between consecutive terms. Here’s how to find the missing number in each case:
Series 1: 2,4,6,8,10,12, ? The difference between consecutive terms is always 2(4-2=2,6-4=2, and so on). Therefore, the missing number is the last term (12) plus the difference (2): 12+2=14.

Series 2: 4,10,16,22,28, ? The difference between consecutive terms is always 6(10-4=6,16-10=6, and so on). The missing number is the last term (28) plus the difference (6): 28+6=34.

Series 3: 34,31,28,25,22, ? The difference between consecutive terms is always 3(31-34=-3,28-31=-3, and so on). Here, we have a subtraction instead of addition. So, the missing number is the last term (22) minus the difference (3): 22-3=19.

Problem 2 : Predicting Profit
Following the pattern of increasing profits by INR 500 each year, the predicted profit for year 5 would be:

Last year’s profit (Year 4) + Increase in profit per year
2500(INR)+500(INR)=3000(INR)

Therefore, the predicted profit for year 5 is INR 3000.

Activity 2

Purpose To find connections between sets of images and using that to solve problems, think smartly, and grasp tricky ideas. Complete the sequence in the left column by identifying the correct missing piece in the right column out of A or B.

Activity 3

Purpose To implement the concept of data collection, analysis, and interpretation.

Activity Introduction

• In this activity, students will engage in data collection and tabulation.
• Data collection plays a key role in Artificial Intelligence as it forms the basis of statistics and interpretation by AI.
• This activity will also require students to answer a set of questions based on the recorded data.

Data Collection

1. Preparation

• Before starting the video, prepare a table with the following columns: Colour of Car, Tally, and Total Count.
• The colours to include are: Red, Blue, Black, White, Silver, and Other.

2. Watch the Video

• Visit the following link: Car Spotting Video
• As you watch the video, use tally marks to record each car you see based on its colour.

Example Table

Data Analysis

1. How many cars are spotted in total?
2. Which colour has been spotted the maximum amount of times?

Data Interpretation

1. What is the most common colour choice for the residents of this area?
(Hint The colour observed the maximum number of times.)

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