## ML Aggarwal Class 7 ICSE Maths Model Question Paper 3

(Based on Chapters 1 to 9)

**Time allowed: 2\(\frac { 1 }{ 2 }\) Hours**

**Maximum Marks: 90**

**General Instructions**

- All questions are compulsory.
- The question paper consists of 29 questions divided into four sections A, B, C and D.
- Section A comprises of 8 questions of 1 mark each.
- Section B comprises of 6 questions of 2 marks each.
- Section C comprises of 10 questions of 4 marks each and
- Section D comprises of 5 questions of 6 marks each.
- Question numbers 1 to 8 in Section A is multiple choice questions where you are to select one correct option out of the given four.

**Section – A**

**Question numbers 1 to 8 are of 1 mark each.**

Question 1.

The number of integers between -16 and 5 is

(a) 19

(b) 20

(c) 21

(d) 22

Solution:

Question 2.

50 m 5 cm is the same as

(a) 50.5 m

(b) 50.05 m

(c) 50.005 m

(d) 5.05 m

Solution:

Question 3.

Solution:

Question 4.

The number 5,540,000,000,000 in the scientific notation can be written as:

(a) 554 × 10^{10}

(b) 55.4 × 10^{11}

(c) 5.54 × 10^{12}

(d) 5.54 × 10^{11}

Solution:

Question 5.

The number of unlike terms in the expression 5x^{2}y – 2xy^{2} – 2yx^{2} + 3y(xy + y^{2}) + 7 is

(a) 3

(b) 4

(c) 5

(d) 6

Solution:

Question 6.

x = -2 is a solution of the equation

(a) 2x + 5 = 9

(b) 3x – 1 = 5

(c) 4x + 3 = 1

(d) 5x + 12 = 2

Solution:

Question 7.

The ratio of the number of girls to the number of boys in a class is 5 : 4. If there are 16 boys in the class, then the number of students in the class is

(a) 20

(b) 32

(c) 36

(d) 45

Solution:

Question 8.

If 12% of a number is 9, then the number is

(a) 36

(b) 48

(c) 60

(d) 75

Solution:

**Section – B**

**Question numbers 9 to 14 are of 2 marks each.**

Question 9.

Using suitable properties, evaluate:

238 × (-44) + (-238) × 56.

Solution:

Question 10.

State whether each of the following statement is true or false for the sets P and Q where P = {letters of TITLE} and Q = {letters of LITTLE}

(i) P ↔ Q

(ii) P = Q

Solution:

Question 11.

Evaluate: -3\(\frac { 3 }{ 8 }\) – (-2\(\frac { 1 }{ 6 }\))

Solution:

Question 12.

Simplify and express in the exponential form: (4^{3} × 3^{6}) ÷ (16 × 9^{2}).

Solution:

Question 13.

If I earn ₹ 75000 per month and spend ₹ 40000 per year for helping poor students then find the ratio of the money spent on helping poor students and the annual income.

Solution:

Question 14.

If ₹ 4000 amounts to ₹ 5000 in 2 years, find the rate of simple interest per annum.

Solution:

**Section – C**

**Question numbers 15 to 24 are of 4 marks each.**

Question 15.

Simplify:

Solution:

Question 16.

Vikram’s monthly salary is ₹ 12750. He spends \(\frac { 1 }{ 5 }\) of his salary on food and out of the remaining, he spends \(\frac { 1 }{ 4 }\) on rent and \(\frac { 1 }{ 6 }\) on the education of children. Find

(i) how much he spends on each item?

(ii) how much money is still left with him?

Solution:

Question 17.

Insert five rational numbers between \(\frac { -2 }{ 5 }\) and \(\frac { -1 }{ 3 }\)

Solution:

Question 18.

Afzal can walks 5\(\frac { 3 }{ 4 }\) km in one hour. How much distance will he cover in 2 hours 40 minutes? What are the health advantages of having a brisk walk?

Solution:

Question 19.

If a vehicle covers a distance of 57.72 km in 3.7 litres of petrol. How much distance will it cover in one litre of petrol?

Solution:

Question 20.

The perimeter of a triangle is 5 – 3x + 7x^{2} and two of its sides are 2x^{2} + 3x – 2 and 3x^{2} – x + 3. Find the third side of the triangle.

Solution:

Question 21.

Solution:

Question 22.

Solve the equation: 3(2x – 1) – 2(2 – 5x) = 1

Solution:

Question 23.

If 74% of the population of a village is illiterate and the number of literate people is 2158, then find the population of the village.

Solution:

Question 24.

Simplify:

Solution:

**Section – D**

**Question numbers 25 to 29 are of 6 marks each.**

Question 25.

If we represent the distance above the ground by a positive rational number and that below the ground by a negative rational number, then answer the following question:

An elevator descends into a mine shaft at the rate of 4\(\frac { 3 }{ 4 }\) metre per minute. If it begins to descend from 7\(\frac { 1 }{ 2 }\) metre above the ground, what will be its position after 18 minutes from the ground?

Solution:

Question 26.

In a competition, the question paper consists of 25 questions. 4 marks are awarded for every correct answer, 2 marks are deducted for every incorrect answer and no marks for not attempting a question. If Vaishali scored 58 marks and got 17 correct answers, how many questions she attempted incorrectly? How many questions she did not attempt?

Solution:

Question 27.

Divide ₹ 216000 into two parts such that one-fourth of one part is equal to one-fifth of the other part. Find the two parts.

Solution:

Question 28.

If a table is sold for ₹ 437 at a loss of 8%, find its cost price. At what price must it be sold to gain 10%?

Solution:

Question 29.

Solve the inequality:

3 – 2x ≥ x – 10, x ∈ N.

Also, represent its solution set on the number line.

Solution: