Algebra Worksheet

Subjective Type Questions

1. Amy likes to make patterns using matchsticks. One day she was practicing making the letter P with matchsticks. If she has made 5 ‘P’s, then find the total number of match sticks used by Amy.
   
   
2. Zari bought 5 boxes of sweets, and she wishes to distribute them amongst her friends and classmates. Now, Zari does not know about the total number of sweets in one box. If she assumes that there are ‘s’ sweets in one box, then help Zari to come up with a way to calculate the total number of sweets, given that each box has same number of sweets.
   
   
   
3. Observe the following matchstick pattern and find the rule that gives the number of matchsticks.
   
    
4. Jay’s mother has made some Jalebis at home. Jay loves jalebis so much, that he keeps eating them throughout the day whenever his mother is not around. Now, at the end of the day, Jay’s mother found that there are only 10 jalebis left. If Jay has eaten “j” number of jalebis, then find the total number of jalebis made by this mother that day.
   
   
   
5. Luka likes to make patterns using matchsticks. He has created the following patterns.
   
   Now find the number of matchsticks that he will require to construct the next pattern.
   
   
6. A large water tank in a residential complex supplies water to 4 identical small water tanks. Now there is an automatic system in place that ensures that the 4 identical small water tanks do no overflow once their full capacity is reached. One day all the 4 tanks was filled to its full capacity and yet 50 liters of water was left in the large water tank. Find the total amount of water that was stored in the large water tank, if the capacity of each small tanks is “w” liters.
   
   
7. Anu likes to draw Rangoli outside her house. She made 8 rows with equal number of dots in each row. Now if each row has ‘d’ number of dots then find the total number of dots made by Anu.
   
   
   
8. In a test Anju scored 5 marks more than Anuj, if Anju scored ‘m’ marks, then calculate the marks of Anuj.
   
   
   
9. Raju and his friend Sham likes to collect marbles. One day they decide to count the number of marbles that each of them has. They found out that both of them together has 500 marbles. Now if the number of marbles that Sham has is given by ‘s’, then find the number of marbles that Raju has.
   
   
   
10. Dileep’s school had organized a crafts completion and the students were asked to make an increasing pattern using matchsticks that would follow a rule. Dileep created the following pattern using matchsticks.
    Now on the day of competition, Dileep’s teacher examined his pattern and pointed out that he has made a mistake. What was the mistake in Dileep’s pattern?
    
    
    Multiple Choice Questions
    
    
11. The number matchsticks required to form ‘n’ number of letter “A” is given by
    (a) 6n
    (b) 5n
    (c) 4n
    (d) 3n
    
    
12. Juan is Jose’s older brother. Jose is 4 years younger than Juan. If Jose’s age is “x” years then Juan’s age will be given by
    (a) 4x
    (b) 4 + x
    (c) x - 4
    (d) 4 - x
    
    
13. Narendra’s school organizes a group prayer every morning. All the students are asked to stand in rows. Now, represent the total number of students in the prayer, if 10 students are present in each row. (use ‘4’ for number of rows)
    (a) 10 - x
    (b) 10 + x
    (c) 10 ¸ x
    (d) 10 ´ x
    
    
14. Rajeev had 30 lollipops with him, and he had decided to distribute all 30 lollipops amongst his friends. Now the number of lollipops received by each friend is given by…(use ‘f’ for number of friends)
    
    (a) 30 - f
    (b) 30 + f
    (c) 30 ¸ f
    (d) 30 ´ f
    
    
15. Amar uses matchsticks to represent the number 8888. How many match sticks would he require to form this number?
    (a) 28
    (b) 24
    (c) 20
    (d) 32
    
    
16. If a train covers a distance of 1 km in a minute, then the total distance covered by the train in ‘t’ hours is given by…
    
    (a) t hrs.
    (b) 30t hrs.
    (c) 60t hrs.
    (d) 1200t hrs.
    
    
17. If there are 10 apples in a box then how many apples are there in ‘(x+2)’ boxes.
    
    (a) x+20
    (b) 20x+10
    (c) 10x+20
    (d) 10x + 10
    
    
18. The number of matchsticks in the following pattern can be given by the expression…
    
    (a) n+1
    (b) 2n
    (c) 2n+1
    (d) 3n
    
    
19. Amey’s class had twice the number of boys as it had girls. If the number of boys were denoted by ‘b’, then find the number of girls in the class.
    (a) b ¸ 2
    (b) b - 2
    (c) b + 2
    (d) b ¸ 2
    
    
20. Find the number of matchsticks required to form the 7th pattern in the given series
    
    (a) 15
    (b) 18
    (c) 21
    (d) 24

Subjective Type Questions

1. Amy likes to make patterns using matchsticks. One day she was practicing making the letter P with matchsticks. If she has made 5 ‘P’s, then find the total number of match sticks used by Amy.
   Solution:
   For making one P, Amy would need 5 matchsticks
   
   Hence to make ‘n’ number of Ps, Amy would require 5n matchsticks.
   Thus, to make 5 Ps, Amy would need 5×5 = 25 matchsticks.
   
   
2. Zari bought 5 boxes of sweets, and she wishes to distribute them amongst her friends and classmates. Now, Zari does not know about the total number of sweets in one box. If she assumes that there are ‘s’ sweets in one box, then help Zari to come up with a way to calculate the total number of sweets, given that each box has same number of sweets.
   
   Solution:
   Total boxes of sweets Zari bought = 5
   Number of sweets in one box = s
   ∴ Total number of sweets = Total boxes of sweets × No. of sweets in one box
   = 5 × s
   = 5s
   Hence, there will be ‘5s’ sweets in total.
   
   
3. Observe the following matchstick pattern and find the rule that gives the number of matchsticks.
   
   Solution:
   
   We have number pattern 2, 4, 6, 8, …
   Which can be represented as 2 × 1, 2 × 2, 2 × 3, 2× 4, …
   Hence, we can use 2n to represent the number of matchsticks in the given pattern.
    
4. Jay’s mother has made some Jalebis at home. Jay loves jalebis so much, that he keeps eating them throughout the day whenever his mother is not around. Now, at the end of the day, Jay’s mother found that there are only 10 jalebis left. If Jay has eaten “j” number of jalebis, then find the total number of jalebis made by this mother that day.
   
   Solution:
   Number of jalebis left = 10
   Number of jalebis eaten by jay = j
   Total number of jalebis made by his mother = No. of jalebis left + No. of jalebis eaten
   = 10 + jHence, Jay’s mother made ‘10 + j’ jalebis.
   
   
5. Luka likes to make patterns using matchsticks. He has created the following patterns.
   
   Now find the number of matchsticks that he will require to construct the next pattern.
   Solution:
   
   The number of matchsticks of the above patterns are 4, 8, 12, 16,...
   Hence, we can write these number patterns as
   4 × 1, 4 × 2, 4 × 3, 4 × 4,…
   Hence, we can use 4n to represent the number of matchsticks in the given pattern.
   Therefore, the next number in the pattern will be 4×5 = 20.
   Hence, he will require 20 matchsticks to construct the next pattern.
   
   
6. A large water tank in a residential complex supplies water to 4 identical small water tanks. Now there is an automatic system in place that ensures that the 4 identical small water tanks do no overflow once their full capacity is reached. One day all the 4 tanks was filled to its full capacity and yet 50 liters of water was left in the large water tank. Find the total amount of water that was stored in the large water tank, if the capacity of each small tanks is “w” liters.
   Solution:
   Water left in the large water tank = 50 liters
   Full capacity of one small tank = w
   Full capacity of 4 small tanks = 4w
   ∴ Total amount of water = 50 + 4 w
   Hence, the total amount of water that was stored in the large water tank is 50 + 4w
   
   
7. Anu likes to draw Rangoli outside her house. She made 8 rows with equal number of dots in each row. Now if each row has ‘d’ number of dots then find the total number of dots made by Anu.
   
   Solution:
   No. of rows of Rangoli = 8
   No. of dots in each row of Rangoli = d
   Total no. of dots = 8×d
   Hence, there are ‘8d’ dots in the Rangoli made by Anu.
   
   
8. In a test Anju scored 5 marks more than Anuj, if Anju scored ‘m’ marks, then calculate the marks of Anuj.
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   Solution:
   Anju’s marks = m
   By given data
   Anju’s mark = Anuj’s marks + 5
   ∴ m = Anuj’s marks + 5
   ∴ Anuj’s marks = m – 5
   Hence, Anuj’s marks will be m - 5
   
   
9. Raju and his friend Sham likes to collect marbles. One day they decide to count the number of marbles that each of them has. They found out that both of them together has 500 marbles. Now if the number of marbles that Sham has is given by ‘s’, then find the number of marbles that Raju has.
   
   Solution:
   Total number of marbles with Raju and Sham = 500
   No. of marbles with Sham = s
   Now,
   No. of marbles with Raju and Sham = No. of marbles with Sham + No. of marbles with Raju
   ∴ No. of marbles with Raju = No. of marbles with Raju and Sham - No. of marbles with Sham
   ∴ No. of marbles with Raju = 500 – s
   ∴ Hence Raju has ‘500 – s’ marbles with him.
   
   
10. Dileep’s school had organized a crafts completion and the students were asked to make an increasing pattern using matchsticks that would follow a rule. Dileep created the following pattern using matchsticks.
    Now on the day of competition, Dileep’s teacher examined his pattern and pointed out that he has made a mistake. What was the mistake in Dileep’s pattern?
    
    Solution:
    If we consider the number of matchsticks for first three pattern.
    We get numbers 2, 4 and 6, which can be represented as
    2 × 1, 2 × 2, 2 × 3, …
    Hence, we can use 2n to represent the number of matchsticks in the first 3 patterns.
    Therefore, the next number in the pattern will be 2×4 = 8.
    But here in the 4th pattern, Dileep has used 10 matchsticks instead of 8.
    Hence, Dileep’s 4th pattern is wrong.
    
    
    Multiple Choice Questions
    
    
11. The number matchsticks required to form ‘n’ number of letter “A” is given by
    (a) 6n
    (b) 5n
    (c) 4n
    (d) 3n
    Correct option: (a) 6n
    For making one A, we would need 6 matchsticks
    
    Hence to make ‘n’ number of ‘A’s, we would need 6n matchsticks.
    
    
12. Juan is Jose’s older brother. Jose is 4 years younger than Juan. If Jose’s age is “x” years then Juan’s age will be given by
    (a) 4x
    (b) 4 + x
    (c) x - 4
    (d) 4 - x
    Correct option: (b) 4 + x
    Jose’s age = x years
    Jose is 4 years younger than Juan = Juan is 4 years older than Jose
    ∴ Juan’s age = x + 4
    
    
13. Narendra’s school organizes a group prayer every morning. All the students are asked to stand in rows. Now, represent the total number of students in the prayer, if 10 students are present in each row. (use ‘4’ for number of rows)
    (a) 10 - x
    (b) 10 + x
    (c) 10 ¸ x
    (d) 10 ´ x
    Correct option: (d) 10 × x
    Number of students in one row = 10
    Number of rows = r
    Total number of students = No. of students in one row  No. of rows
    = 10 × x
    Hence, there are ‘10 × x’ students in the prayer gathering.
    
    
14. Rajeev had 30 lollipops with him, and he had decided to distribute all 30 lollipops amongst his friends. Now the number of lollipops received by each friend is given by…(use ‘f’ for number of friends)
    
    (a) 30 - f
    (b) 30 + f
    (c) 30 ¸ f
    (d) 30 ´ f
    Correct option: (c) 30 ÷ f
    Number of lollipops = 30
    Number of friends = f
    Lollipops received by each friend = Number of lollipops ÷ No. of friends
    = 30 ÷ f
    Hence, ‘30 ÷ f’ lollipops are received by each friend.
    
    
15. Amar uses matchsticks to represent the number 8888. How many match sticks would he require to form this number?
    (a) 28
    (b) 24
    (c) 20
    (d) 32
    Correct option: (a) 28
    For making a digit 8, 7 matchsticks will be required.
    
    Hence to make ‘n’ number of ‘8’s, we would need 7n matchsticks.
    Thus for four ‘8’s we will need = 7 × 4 = 28 matchsticks.
    
    
    
16. If a train covers a distance of 1 km in a minute, then the total distance covered by the train in ‘t’ hours is given by…
    
    (a) t hrs.
    (b) 30t hrs.
    (c) 60t hrs.
    (d) 1200t hrs.
    Correct option: (c) 60t hrs.
    Distance covered by the train in 1 minute = 1 km
    Now,
    1 hour = 60 min
    ∴ Distance covered by train in 1 hrs. = 60 × 1 km = 60 km
    Now,
    Distance covered by train in ‘t’ hrs = Distance covered by train in 1 hrs. × t
    = 60t km
    Hence, the train covers 60t km in ‘t’ hours.
    
    
17. If there are 10 apples in a box then how many apples are there in ‘(x+2)’ boxes.
    
    (a) x+20
    (b) 20x+10
    (c) 10x+20
    (d) 10x + 10
    Correct option: (c) 10x + 20
    Apples in one box = 10
    Apples in (x + 2) boxes = apples in x boxes + apples in 2 boxes
    =10x + 20
    Hence, the total number of apples in ‘x + 2’ boxes is 10x + 20
    
    
18. The number of matchsticks in the following pattern can be given by the expression…
    
    (a) n+1
    (b) 2n
    (c) 2n+1
    (d) 3n
    Correct option: (c) 2n + 1
    The number of matchsticks of the above patterns are 3, 5, 7, 9,…
    Hence, we can write these number patterns as
    2 × 1 + 1, 2 × 2 + 1, 2 × 3 + 1, 2 × 4 + 1,…
    Hence, we can use 2n + 1 to represent the number of matchsticks in the given pattern.
    
    
19. Amey’s class had twice the number of boys as it had girls. If the number of boys were denoted by ‘b’, then find the number of girls in the class.
    (a) b ¸ 2
    (b) b - 2
    (c) b + 2
    (d) b ¸ 2
    Correct option: (a) b ¸ 2
    Number of boys in Amey’s class = b
    Also,
    Number of boys in Amey’s class = 2 × Number of girls in Amey’s class
    ∴ b = 2 × Number of girls in Amey’s class
    ∴ Number of girls in Amey’s class = b × 2
     
20. Find the number of matchsticks required to form the 7th pattern in the given series
    (a) 15
    (b) 18
    (c) 21
    (d) 24
    Correct option: (c) 21
    The number of matchsticks of the above patterns are 3, 6, 9, 12, 15,...
    Hence, we can write these number patterns as
    3 × 1, 3 × 2, 3 × 3, 3 × 4,…
    Hence, we can use 3n to represent the number of matchsticks in the given pattern.
    Therefore, the next number in the pattern will be 3 × 7 = 21.
    Hence, he will require 21 matchsticks to construct the 7th pattern.