Samacheer Kalvi Class 6 Maths Solutions Term 1 Chapter 2 Introduction to Algebra Exercise 2.1

Tamilnadu Samacheer Kalvi 6th Maths Solutions Term 1 Chapter 2 Introduction to Algebra Ex 2.1

Question 1. Fill in the blanks:
(i) The letters a, b, c, .., x, y, z are used to represent ______.
(ii) A quantity that takes ______ values is called a variable.
(iii) If there are 5 students on a bench, then the number of students in 'n' benches is '5 × n'. Here ______ is a variable.

Answer:
(i) Variables
(ii) Different
(iii) n
In simple words: Letters in math stand for numbers we don't know yet, called variables. Variables can change their value, unlike fixed numbers. In '5 × n', 'n' is the variable because its value can change depending on how many benches there are.

🎯 Exam Tip: Remember that variables are letters used to represent unknown values, while constants are fixed numbers. This distinction is key in algebra.

Question 2. Say True or False.
(i) The length of part B in the pencil shown is 'a – 6'.
(ii) If the cost of an apple is 'x' and the cost of a banana is Rs.5, then the total cost of fruits is 'x + 5'.
(iii) If there are 11 players in a team, then there will be '11 + q' players in 'q' teams.

Answer:
(i) False
(ii) True
(iii) False
In simple words: For (i), if the total length is 'a' and one part is 6, the other part is 'a-6'. For (ii), to find the total cost of two different items, you add their individual costs. For (iii), if there are 11 players in *one* team, then in 'q' teams, there would be 11 multiplied by 'q' (11q), not 11 plus 'q'.

🎯 Exam Tip: Read word problems carefully to identify whether you need to add, subtract, multiply, or divide. Pay attention to terms like "total," "difference," "in 'n' groups," etc.

Question 3. Draw the next two patterns and complete the table

Answer: The patterns for squares and circles increase by one in each step. So, for the 4th pattern, there will be 4 squares and 4 circles. For the 5th pattern, there will be 5 squares and 5 circles. The pattern for triangles increases by two in each step (2, 4, 6...). So, for the 4th pattern, there will be 8 triangles. For the 5th pattern, there will be 10 triangles. Identifying the rule for change helps predict future items in a sequence.
In simple words: The number of squares and circles goes up by one each time. The number of triangles goes up by two each time. We just follow these rules to fill in the missing parts of the table.

🎯 Exam Tip: When completing pattern tables, first identify the rule for how each row's numbers change from one pattern to the next. Look for simple addition, subtraction, or multiplication patterns.

Question 4. Use a variable to write the rule, which gives the number of ice candy sticks required to make the following patterns.
a) a pattern of letter as C
b) a pattern of letter M as M

Answer:
(a) A letter 'C' is made using 3 ice candy sticks. If there are 'n' such 'C' patterns, the total sticks needed would be \( 3 \times n = 3n \).
(b) A letter 'M' is made using 4 ice candy sticks. If there are 'n' such 'M' patterns, the total sticks needed would be \( 4 \times n = 4n \). Algebra uses letters to show these general rules easily.
In simple words: Count how many sticks make one letter. Then, multiply that number by 'n' to find how many sticks are needed for 'n' letters.

🎯 Exam Tip: For simple repeating patterns, the rule is often (number of items per unit) \( \times \) (number of units). Clearly define your variable (e.g., 'n' for the number of patterns).

Question 5. The teacher forms groups of five students in a class. How many students will be there in 'p' groups?

Answer: If there are 5 students in one group, and the teacher forms 'p' groups, the total number of students will be \( 5 \times p = 5p \). This is a simple multiplication problem to find the total.
In simple words: Multiply the number of students in one group by the number of groups to find the total students.

🎯 Exam Tip: When a quantity is repeated a certain number of times, multiplication is the correct operation to find the total. Look for keywords like "in 'p' groups" or "each".

Question 6. Arivazhagan is 30 years younger than his father. Write Arivazhagan's age in terms of his father's age.

Answer: Let Arivazhagan's father's age be represented by 'x' years. Since Arivazhagan is 30 years younger, his age will be his father's age minus 30, which is \( (x - 30) \) years. Variables help us write down these relationships clearly.
In simple words: We use 'x' for the father's age. Since Arivazhagan is 30 years younger, his age is 'x' minus 30.

🎯 Exam Tip: When expressing one quantity in terms of another, clearly define the variable for the unknown quantity and then use addition or subtraction based on the comparison (younger/older, less/more).

Question 7. If 'u' is an even number, how would you represent
(i) the next even number?
(ii) the previous even number?

Answer:
(i) Even numbers always differ by 2. So, if 'u' is an even number, the next even number will be \( u + 2 \). For example, if u=4, the next even number is 4+2=6.
(ii) Similarly, to find the previous even number, we subtract 2 from the current even number. So, the previous even number will be \( u - 2 \). For example, if u=4, the previous even number is 4-2=2.
In simple words: Even numbers are always two apart. So, to get the next one, add 2. To get the one before, subtract 2.

🎯 Exam Tip: Remember that consecutive even (or odd) numbers always have a difference of 2. This is a fundamental property of number sequences.

Objective Type Questions

Question 8. Variable means that it
(a) can take only a few values
(b) has a fixed value
(c) can take different values
(d) can take only 8 values
Answer: (c) can take different values
In simple words: A variable is like a placeholder that can be replaced by many different numbers, not just one fixed number or a few specific ones.

🎯 Exam Tip: The core definition of a variable is its ability to represent *any* possible value within a given context, not a limited set.

Question 9. '6y' means
(a) 6 + y
(b) 6 - y
(c) 6 x y
(d) \( \frac{6}{7} \)
Answer: (c) 6 x y
In simple words: When a number and a letter are written next to each other without any sign, it always means multiplication. So, '6y' is the same as '6 multiplied by y'.

🎯 Exam Tip: In algebra, an implied operation between a number and a variable (or two variables) is always multiplication. This is a crucial notation to understand.

Question 10. Radha is 'x' years of age now. 4 years ago, her age was
(a) x - 4
(b) 4 - x
(c) 4 + x
(d) 4x
Answer: (a) x - 4
In simple words: To find someone's age in the past, you subtract the number of years from their current age. So, if Radha is 'x' now, 4 years ago she was 'x' minus 4.

🎯 Exam Tip: Be careful with subtraction order. "4 years ago" means subtracting from the current age, not subtracting the current age from 4.

Question 11. The number of days in 'w' weeks is
(a) 30 + w
(b) 30w
(c) 7 + w
(d) 7w
Answer: (d) 7w
In simple words: Since there are 7 days in one week, to find the total days in 'w' weeks, you multiply the number of weeks by 7.

🎯 Exam Tip: Remember standard conversions like days in a week. When converting a larger unit to a smaller unit, you typically multiply.

Question 12. The value of 'x' in the circle is
(a) 6
(b) 8
(c) 21
(d) 22
Answer: (d) 22
In simple words: Look at the numbers in a clockwise order starting from 2. The pattern is that each number is found by adding an increasing number (+2, +3, +4, +5, +6) to the previous one. Starting with 2, the next is \( 2+2=4 \), then \( 4+3=7 \), then \( 7+4=11 \), then \( 11+5=16 \). Following this, \( 16+6=22 \), so 'x' is 22.

🎯 Exam Tip: For number puzzles in circles, look for patterns in consecutive numbers, opposite numbers, or sums/products along diagonals or specific segments. Often, there's a simple arithmetic progression or a series of operations.