CBSE Class 6 Mathematics Algebra Worksheet Set 01

Question. Tapan thinks of a number, triples it and subtracts 60 to the answer. He gets the answer 120. What was Tapan's original number?
(a) 290
(b) 70
(c) 60
(d) 20

Answer : C

Question. The patterns below are made with circles. How many circles will be On the base of NINETEENTH figure if the patterns are continued?

(a) 10
(b) 17
(c) 19
(d) 70

Answer : C

Question. If a number is divided by 30 and then multiplied by 5, the resulting number will be
(a) 25 more than the original number
(b) 6 times the original number
(c) 25 less than the original number
(d) 1/6 of the original number

Answer : D

Question. Amir's book is lying open. The sum of the page numbers of these two pages is 97. What is the digit in the ONES place of the page number on the left?

(a) 9
(b) 8
(c) 4
(d) 3

Answer : B

Question. An electronic display is used in a bank to show token numbers. As you can see 5 segments (parts) are lit when the display shows 17. How many segments will be lit when the display shows the number 53?

(a) 5
(b) 10
(c) 11
(d) 14

Answer : B

Question. Ritu added 177 to 33  and she again added 711. What final number did  Ritu get?
(a) 888
(b) 1021
(c) 921
(d) 1158

Answer : C

Question. Suppose a number is multiplied by the product of ALL the numbers from 1 to 29. What will be the last digit of the product?
(a) 0
(b) 4
(c) 9
(d) we can't say for sure.

Answer : A

Question. Rounded off to the nearest THOUSAND, Rajiv's bank account has Rs. 34,000/-. Similarly, rounded to the nearest thousand, Sunita's bank account has Rs 36,000/- . What COULD BE the actual MAXIMUM difference between the amounts in their accounts?
(a) Almost Rs. 1000
(b) Almost Rs. 2000
(c) Almost Rs. 3000
(d) Almost Rs. 10,000

Answer : C

Question. If 7846, 7896 and 8802 are rounded to the nearest hundred and then added to a number to get the answer 25000, the numberadded will be
(a) 400
(b) 500
(c) 544
(d) 550

Answer : B

Question. What will be the remainder when (250 + 1) + (265 + 1) + (270 + 1) + (285 + 1) + (290 + 1) is divided by 5?
(a) 0
(b) 1
(c) 2
(d) 4

Answer : A

Question. 800x - 80 = 1700 Which of the following is equal to x? 
(a) 170 ÷ 8
(b) 178 ÷ 8
(c) 178 ÷ 80
(d) 1780 ÷ 80 

Answer : C

Question. ▲is a number such that ▲ x ▲ = 36. Then ▲ + ▲ + ▲ will be equal to
(a) 9
(b) 12
(c) 18
(d) 216

Answer : C

Question. Children at a party are seated at 3 different tables. On table 1, four children share three chocolate bars equally. On table 2, three children share two chocolate bars equally. On table 3, six children share three chocolate bars equally. If all the chocolate bars are of equal size, who gets the maximum amount of chocolate?
(a) A child on table 1
(b) A child on table 2
(c) A child on table 3
(d) All the children get the same amount

Answer : A

Question. Look at this room tariff card of Palace Hotel Mr. and Mrs. Ratnam checked into this hotel at 7:00 PM on 12th April with their two daughters aged 4 years and 12 years. They booked a Deluxe AC double room with an extra bed. What will be the bill for their stay (before taxes) if they check out on the morning of 14 April?

(a) Rs. 2200
(b) Rs. 2390
(c) Rs. 2590
(d) Rs. 3885

Answer : C

Question. Renu bought the following material to make some cards for the school exhibition. Renu used this material to make 25 cards. If she managed to sell all except 4 of them at the exhibition for Rs. 10 each, how much profit did she make?

(a) Rs. 210
(b) Rs. 87
(c) Rs. 62
(d) Rs. 47

Answer : D

I) Fill in the blanks :

1. Letters used to represent numbers are called _________________

2. The literals whose value vary from problem to problem are called _____________

3. Numerals whose value is fixed are called _____________________

4. The statement of equality which involves literals is called an ___________

5. The value of the variable which satisfies the equation is called the _to the equation.

Answer :

1. Variables

2. Variables

3. Constants

4. Equation

5. Solution

II) Write the expression :

1. m increased by 8.

2. b decreased by 31.

3. Five items x increased by 5 gives 55.

4. Half of p subtracted from the sum of a and b.

5. Product of 7 and x divided by the difference of 7 and x.

6. Sum of p, q and r divided by the product of a and 5.

7. One fourth of the difference of x and y.

8. 4 subtracted from n, gives 36.

9. z minus twice x.

10. m taken away from 50, gives 15.

Answer :

1. m+8

2. b31

3.5x+5=55

4.(a+b) - (1/2) p

5. 7x/7-x

6. p+q+r/5a

7. 1/4(x-y)

8. n4=36

9. z2x

10. 50m=15

III) Identify the solution and show that other values do not satisfy

1. X+8 = 24 (x = 3, x = 15, x = 16, x = 0)

2. 4a = 32 (a = 8, a = 4, a = 6, a = 7)

3. y9 = 29(y = 20, y = 38, y = 37, y = 39)

4. P/5 = 16 (p = 75, p = 85, p = 90, p = 80)

Answer :

1. x=16

2.a=8

3.y=38

4.p=80

IV) Solve :

1.X+11 = 30

2. 6a = 24

3. m-5 = 2

4. x/4 = 2

5. x/7 = 5

6. a/9 = 4

7. 10n = 70

8. 16 = y+10

9. t - 14 = 0

10. 4x = 32

11. 17 - p = 15

12. 23 - y = 0

Answer :

1. x = 19

2.a = 4

3.m = 7

4.x = 8

5.x = 35

6.a = 36

7.n = 7

8.y = 6

9.t = 14

10.x = 8

11.p = 2

12.y = 23

Question 1. i) Write equation for the given picture
Answer: Looking at the balance scale, there are 4 weights on the left pan (represented by circles with X inside) and a weight of 12 on the right pan. Assuming each weight represents an unknown variable \(x\), the equation is \(4x = 12\).
In simple words: Total weight on the left equals the weight on the right, which gives \(4x = 12\).

Exam Tip: Always equate the total value on the left side of the balance pan to the value on the right side.

Question 1. ii) _______ No. of matchsticks are use in a pattern of letter F
Answer: 4
In simple words: The letter F requires 4 straight matchsticks to draw (1 vertical and 3 horizontal).

Exam Tip: Count each straight segment of the geometric letter to find the number of matchsticks.

Question 1. iii) 5 is added to P, the expression is _____________ .
Answer: \(P + 5\)
In simple words: Adding 5 to the variable P means writing it as \(P + 5\).

Exam Tip: The word "added to" translates directly to the plus sign (\(+\)).

Question 2. Match following with their expressions.
i) x is added to 8                  4x-2
ii) x is multiplied by 9            x+8
iii) 4 times x and 2 is subtracted     9x
Answer:
i) x is added to 8 matches with \(x + 8\)
ii) x is multiplied by 9 matches with \(9x\)
iii) 4 times x and 2 is subtracted matches with \(4x - 2\)
In simple words: Match each verbal phrase with its correct algebraic representation.

Exam Tip: Read each phrase carefully word by word to identify operations and terms.

Question 3. What will be perimeter of square have side 9 cm.
Answer:
Formula for the perimeter of a square = \(4 \times \text{side}\)
Side = 9 cm
Perimeter = \(4 \times 9 = 36\text{ cm}\)
In simple words: To find the perimeter of a square, multiply the length of one side by 4.

Question 4. If Maya's present age is x years then what will be her age two years ago.
Answer:
Present age of Maya = \(x\) years
Age two years ago = \(x - 2\) years
In simple words: "Ago" means in the past, so we subtract 2 from her present age.

Exam Tip: Words like "ago" or "less than" indicate subtraction, while "hence" or "more than" indicate addition.

Question 5. There are some expression given below. Which of these are equations.
i) x - 5 > 9          ii) 8+5 = 9          iii) 9x<5          iv) 2x + 1 = 15
Answer:
An equation is a condition on a variable with an equals sign (=).
i) \(x - 5 > 9\) is an inequality (contains >).
ii) \(8 + 5 = 9\) is a numerical statement with an equals sign (considered an equation of numbers).
iii) \(9x < 5\) is an inequality (contains <).
iv) \(2x + 1 = 15\) is an algebraic equation (contains a variable and an equals sign).
Therefore, the equations are (ii) and (iv).
In simple words: An equation must always contain an equals sign (=).

Exam Tip: Look strictly for the '=' symbol to distinguish equations from inequalities (> or <).

Question 6. Give expressions for the following :
i) k is multiplied by 10. ___________
ii) x is multiplied by 2 and 9 is subtracted ___________
iii) z is divided by 9 ___________
Answer:
i) \(10k\)
ii) \(2x - 9\)
iii) \(\frac{z}{9}\)
In simple words: Translate each mathematical operation directly into algebraic symbols.

Exam Tip: Multiplication of a number and a variable is written together without a sign, like \(10k\).

Question 7. Pick out the solution of equation from values given in the bracket next to equation.
P + 5 = 9      (3, 0, 4, -4)
Answer:
Testing each value from the given bracket in the equation \(P + 5 = 9\):
For \(P = 3\): \(3 + 5 = 8 \neq 9\) (Not a solution)
For \(P = 0\): \(0 + 5 = 5 \neq 9\) (Not a solution)
For \(P = 4\): \(4 + 5 = 9\) (Solution found)
For \(P = -4\): \(-4 + 5 = 1 \neq 9\) (Not a solution)
Therefore, the solution of the equation is \(4\).
In simple words: Substitute each number into the equation until the left side equals the right side.

Exam Tip: Show substitution for each value clearly to justify your final selected solution.

Choose the correct option in Q. 1, 2, 3 and 4

Q.1 The co-efficient of z in -25xy²z is _______
(a) 25y²x
(b) -25y²x
(c) -25xyz
(d) 25xyz

Q.2 Which of the following is an algebraic expression?
(a) 3 × 8 – 7
(b) 8 ÷2 + 6
(c) 2x + 8
(d) none

Q.3 If p = 1, q = 2, r = 3 then the value of p²+q²+r² is
(a) 8
(b) 26
(c) 14
(d) none

Q.4 The like terms in the expression 2x² + y2-3x² – 7z²x are
(a) 2x², -3x²
(b) 2x², 7x
(c) -3x², 7x
(d) y², z²

Q.5 Write down the terms of these algebraic expression
(i) 4a-6b
(ii) 3xy – 4zx +7yz
(iii) -6p – 4ab + 7pq – abc
(iv) ax + 4by + 9cz

Q.6 Combine the following terms to form an algebraic expressions.
(i) 7xy, -4yz, 8xyz
(ii) -4ac, -abc, 3ab
(iii) –pqx, pq, -8r
(iv) -11x, 14xy

Q.7 Identify the monomials, binomials and trinomials.
(i) pr – rst + 4sp
(ii) 4abc
(iii) 7xy + 4 xz
(iv) 7by – 4ax + 3z

Q.8 Write down the coefficient of
(i) x in -3axy
(ii) yz in 4axbyz
(iii) abc in -5abcx²
(iv) ab in 13abc

Q.9 Write the numerical coefficient in each of the following terms
(i) 5abc (ii) –st
(iii) -7xyza
(iv) pqr

Q.10 Find the value of the following if x = -1, y = 1 and z = -2
(i) 3x² – 7y
(ii) 4x + y – 7z
(ii) 4xy + 3yz – 7zx
(iv) x³ – y³ + z³

Q11 Which of the following are equations with variables
(i) 7 ×4 +15 = 43
(ii) 4t < 38
(iii) 5y – 2 = 13
(iv) 10y = 60
(v) t – 3 > - 35

Q.12 Pick out the solution from the value given in the brackets against each equation.
(i) 5n = 60 (5, 15, 12)
(ii) q/3 = 7 ( 7, 21, 12)
(iii) a + 12 = 18 (10, 6, 4)
(iv) l – 8 = 7 ( 21, 10, 15)

Q.13 Write the following statements in the form of equation
(i) 5 times y from which 3 is subtracted
(ii) 4 times of x taken away from one third of y
(iii) 6 subtracted from -6 times –y
(iv) Quotient of x by 8 is multiplied by y

Q.14 Solve each of the following equations
(i) a + 9 = 14
(ii) l – 6 = 8
(iii) y + 10 = 25
(iv) = 9
(v) 6x = 24
(vi) 3 – x = 5

Q.15 The difference of two numbers is 6. If you write x for the smaller number, how do you write the larger?

Q1. Tick the correct answer.

1. Which of the following expression does not involve a variable?
a. 2x+3
b. 5x+4
c. 5-7x
d. 7x20-5

2. 3 added with the product of x and y is
a. 3+xy
b. 3+x+y
c. 3+x-y
d. xy -3

3. Sarita’s present age is x years then her age after 10 years will be
a. (x-5) yrs
b. (5x+5)yrs
c. (x+10)yrs
d. (x-10)yrs

Q2.Match the following:

Q1. Solve the following riddles

WHO AM I?

a. I am a special number

Take away from me a six

A Whole cricket team

You will still be able to fix

b. Tell me who I am

I shall give a pretty clue!

You will get me back

If you take me out of twenty two