During exam preparation, Std 7 Maths Question Paper Kerala Syllabus Set 3 guide students properly.
Kerala Syllabus 7th Standard Maths Question Paper Set 3
Time : 2 Hrs 15 Min
Instructions:
- 15 minutes is given as cool – off time. Use this time to read and understand the questions and plan answers accordingly.
- Answer all the 6 questions
- Question number 1 and 6 have internal choices (1 A and 1B;6A and 6 B ). Answer to any one of the sub questions A or B under it.
The first question has 2 questions (1A and 1B). You only need to answer one of them.
Question 1.
A. (a) Find the number of factors of 180.
Answer:
Prime factorization: 180 = 22 × 32 × 51
Number, of factors = (2 + 1) (2 + 1) (1 + 1)
= 3 × 3 × 2 = 18
(b) Write each number below either as a power of a single prime or as a product of powers of different primes.
i) 3125
ii) 200
Answer:
i) 3125 = 5 × 5 × 5 × 5 × 5 = 55
ii) 200 = 2 × 2 × 2 × 5 × 5 = 23 × 52
(c) Find the number of factors of each number below:
i) 36
ii) 84
iii) 144
Answer:
i) The factors of 36, expressed as powers of prime numbers, are:
36 = 22 × 32
Therefore, number of factors = (2 + 1)(2 + 1) = 3 × 3 = 9
ii) The factors of 84, expressed as powers of prime numbers, are;
84 = 22 × 31 × 71
Therefore, the number of factors = (2 + 1)(1 + 1)(1 + 1) = 3 × 2 × 2 = 12
iii) The factors of 144, expressed as powers of prime numbers, are:
144 = 24 × 32
Therefore, the number of factors = (4 + 1)(2 + 1) = 5 × 3 = 15
OR
B. (a) Find the common factors of 84 and 126.
Answer:
84 = 22 × 3 × 7
126 = 2 x32 × 7
Common = 21 × 31 × 71 = 42
Common factors are factors of 42 → 1, 2, 3, 6, 7, 14, 21, 42
(b) Which one’has exactly 9 factors?
(a) 23 × 32
(b) 58
(c) 118
(d) 24 × 7
Answer:
(c) 118
Number of factors of 118 = 8 + 1 = 9
(c) (i) What is the largest common factor of two different prime numbers?
(ii) Can the largest common factor of two composite numbers be 1? ‘
(iii) If two numbers are divided by their largest common factor, what would be the largest common factor of the quotients?
Answer:
i) The largest common factor of two different prime numbers is 1, since prime numbers have no common factors other than 1.
ii) Yes, the largest common factor of two composite numbers can be 1 if they are coprime, meaning they have no common factors other than 1.
iii) If two numbers are divided by their largest common factor, the largest common factor of the quotients will be 1. This is because the largest common factor is the greatest number that divides both original numbers, and dividing by it eliminates any common fac¬tors from the quotients.
Question 2.
(a) 60% of a number is 180. What is the number?
(a) 200
(b) 250
(c) 300
(d) 360
Answer:
(c) 300
Let the number = x.
60 % of x = 180
⇒ \(\left(\frac{60}{100}\right)\) × x = 180
⇒ x = \(\frac{180 \times 100}{60}\) = 300
(b) A book is bought for ₹ 240 and sold for ₹ 300. Find the profit percentage.
Answer:
Profit = 300 – 240 = 60
Profit % = (60 ÷ 240) × 100
= 25 % profit
(c) The marked price of a shirt is ₹ 1,000. A shopkeeper offers 20% discount and still makes a profit of ₹ 80. Find the cost price.
Answer:
Selling Price = 1,000 – 20 % of 1,000
= 1,000 – 200 = 800
Profit = 80
⇒ Cost Price = Selling Price – Profit
= 800 – 80 = 720 Rs.
(d) A student scored 36 marks out of 50 in a test.
(i) What fraction of marks did he get?
(ii) What percent of marks did he score?
Answer:
(i) Fraction = \(\frac{36}{50}=\frac{18}{25}\)
(ii) Percent = \(\frac{36}{50}\) × 100 = 72
Question 3.
(a) A square of area 15 square centimetres is drawn on one side of a right triangle. Which of the following are the lengths of the other two sides of this right triangle?
(i) 5 cm, 6 cm
(ii) 6 cm, 7 cm
(iii) 7 cm, 8 cm
(iv) 8 cm, 9 cm
Answer:
(iii) 7 cm, 8 cm
Length of the other two sides = 7 cm, 8 cm
(b) The area of a square vegetable garden is 256 square metres, What is the length of one of its sides?
Answer:
Area of a square vegetable garden = 256 sq.m
Side = \(\sqrt{256}\) = 16m
(c) Draw a square of area of 72 square centimetres.
Answer:
First draw a square with side 6 cm.
Draw another square with diagonal as its side.
Question 4.
(a) A statement and reason is given below:
In a triangle, one exterior angle is 120°. The two interior opposite angles are x and y
Statement (A): x + y = 120°
Reason (R): The .sum of all angles of a triangle is 180°.
Examine the statement and reason, find which is correct.
(a) A is true, but R is false.
(b) A is false, but R is true.
(c) Both A and R are true, and R is the correct explanation of A.
(d) Both A and R are true, but R is not the correct explanation of A.
Answer:
(c) Both A and R are true, and R is the correct explanation of A.
(b) i. The sum of the interior angles of a triangle is always 180°.
ii. An exterior angle of a triangle is equal to the sum of its two interior opposite angles.
iii. A triangle can have more than one obtuse angle.
Which of the above statements are true?
A. i and ii correct
B. ii and iii correct
C. i and iii correct
D. All are correct
Answer:
A. i and ii correct
(c) Zeenath doing a project to find out the measures which can be used to draw a triangle. Which among the following measures can be used to draw a triangle?
(a) 8 cm 4 cm 3 cm
(b) 9 cm 5 cm 12 cm
(c) 5 cm 5 cm 10 cm
(d) 6 cm 7 cm 15 cm
Answer:
(a) 4 + 3 = 7. It is not greater than the third side. So, it is not possible to draw such a triangle.
(b) The sum of the lengths of any two sides is greater than the third side. So, it is possible to draw such a triangle.
(c) 5 + 5 = 10. It is not greater than the third side. So, it is not possible to draw such a triangle.
(d) 6 + 7 = 13. It is not greater than the third side. So, it is not possible to draw such a triangle.
(d) Draw the right triangle whose sides are 4 cm, 12 cm and 10 cm.
Answer:
Question 5.
The figure shows information about the hobbies of students in a class.
(a) Which hobby do children like the most?
Answer:
Drawing
(b) Which hobby is liked by the least children?
Answer:
Dance
(c) If those who select music are \(\frac{1}{8}\) part of the total, what is the part of the total of those who select drawing as a hobby?
Answer:
\(\frac{3}{8}\)
(d) What part of the total is those who select reading and dancing?
Answer:
\(\frac{1}{4}\)
(e) Write another question based on this figure.
What part of the total is those who select reading, dancing and music?
Answer:
What part of the total is those who select reading, drawing and music?
The sixth question has 2 questions (6 A and 6 B). You only need to answer one of them.
Question 6.
A. (a) A triangle has a base of 12 cm and an altitude of 8 cm. Its area is:
(i) 48 cm2
(ii) 96 cm2
(iii) 32 cm2
(iv) 64 cm2
Answer:
(i) 48 cm2
Area = \(\frac{1}{2}\) × 12 × 8 = 48 cm2
(b) Two triangles have the same base of 12 cm . One has a height of 7 cm and the other has its vertex on a parallel line. Find the area of both triangles.
Answer:
Area = \(\frac{1}{2}\) × 12 × 7 = 42cm
Both triangles = 12 cm2 each
(c) A triangular plot of land has base 100 m and altitude 60 m. A farmer wants to divide it into 2 equal-area plots by drawing a line parallel to the base. At what height from the base should the line be drawn?
Answer:
Total area = \(\frac{1}{2}\) × 100 × 60 = 3000 m2
Half area = 1500 m2
Let required height = h
\(\frac{1}{2}\) × 100 × h = 1500
Therefore h = 30 m
B. (a) A triangle has an area of 60 cm2 and a base of 15 cm . The height is:
(i) 6 cm
(ii) 8 cm
(iii) 10 cm
(iv) 12 cm
Answer:
Area = \(\frac{1}{2}\) × base × height
60 = \(\frac{1}{2}\) × 15 × h
h = 8 cm
(b) A field is in the shape of a triangle with base 50 m and altitude 24 m . If the cost of fencing the field is ₹ 10 per square meter, find the total cost.
Answer:
Area = \(\frac{1}{2}\) × 50 × 24 = 600 m2
Cost = 600 × 10 = ₹ 6000
(c) What is the area of the triangle shown below?
i) Draw a right triangle of the samfe area
ii) Draw a triangle of the same area with one angle greater than a right angle
Answer:
Area = \(\frac{1}{2}\) × Base × Height
= \(\frac{1}{2}\) × 9 × 4
= 18 sq cm
