During exam preparation, 6th Standard Maths Question Paper with Answers Kerala Syllabus Set 1 guide students properly.
Kerala Syllabus 6th Standard Maths Question Paper Set 1
Time: 2 Hrs 15 min.
Instructions:
- First 15 minutes is allotted as cool-off time. Red the questions carefully and plan the answers during this time
- Answer all six questions. Answer all the sub questions.
- Two questions are there in Question 3 and 4. Attempt any one of them (3 A or 3 B and 4 A or 4 B)
Question 1.
The graph below shows the rainfall of a place in different months:
(a) What is the highest amount of rainfall received in this place? (1)
Answer:
35 cm
(b) In which month is the rainfall the lowest? (1)
Answer:
January, March and December
(c) Between which months does the largest difference in rainfall occur? (1)
Answer:
May, June
(d) On the basis of the graph, prepare two questions? (2)
Answer:
(i) What is the rainfall received in the month of December?
(ii) During which months did the place receive rainfall between 25 cm and 35 cm?
Question 2.
To buy a pen from a shop, one has to pay Rs. 10 for the first pen. Each pen brought after the first one costs Rs.9.
(a) Complete the table given below. (2)
| Number of Pens | Price |
| 1 | 10 |
| 2 | – |
| 3 | – |
| 4 | – |
Answer:
| Number of Pens | Price |
| 1 | 10 |
| 2 | 19 |
| 3 | 28 |
| 4 | 37 |
(b) What is the relation between the number of pens and the cost? (1)
Answer:
The total cost is obtained by multiplying the number of pens by 9 and adding 1.
(c) If the number of pens is marked by n and the total cost by p, write the relation between them? (2)
Answer:
Number of pens = n
Total cost = p
p = 9n + 1
Question 3.
(A) (a) In this table below, the fist column contains some numbers and the second column shows the remainders obtained when these numbers are divided by 9. (1)
| 1 | 2 |
| (a) 3245 | (1) 0 |
| (b) 5876 | (2) 2 |
| (c) 3494 | (3) 8 |
| (d) 5004 | (4) 5 |
Choose the correct matches from the following:
(A) a – 2, b – 4, c – 3, d – 1
(B) a – 4, b – 3, c – 2, d – 1
(C) a – 4, b – 3, c – 1, d – 2
(D) a – 4, b – 2, c – 1, d – 3
Answer:
(B) a – 4, b – 3, c – 2, d – 1
(b) Write 575 as a multiple of 9 and also the sum of its digits. (1)
Answer:
Sum of the digits = 5 + 7 + 5 = 17
575 = 558 + 17
= (62 × 9) + 17
(c) If all four-digit numbers using the digits 3, 4, 7, 8 and 9 are written, how many of them are multiples of 3? Give reason? (2)
Answer:
Sum of the digits = 3 + 4 + 7 + 8 + 9 = 31
Since 31 is not divisible by 3, any four digit number formed using all these digits will not be divisible by 3.
Therefore no four digit numbers formed are multiples of 3.
(d) Write a four digit number that is divisible by 2, 3, 5 and 9 without leaving any remainder. (1)
Answer:
The number in the ones place should be 0. And the sum of the digits should be multiple of 9.
5310 (or 1980, 1080, 1170 1260, 1620 etc.) is a number.
OR
(B) Look at the figure given below:
In the figure angle a and c are equal, and angle b is a right angle. (1)
(a) What is the measure of angle d?
Answer:
Given that, ∠a = ∠c and ∠b = 90° Angles a, b and c are on a straight line.
Therefore a + b + c = 180°
a + 90° + a = 180°
2 a = 90° a = 45°
∠a = 45° = ∠c
∠d = ∠a = 45° (opposite angles)
(b) Check the statements given below for angle e. (1)
(i) It is a right angle.
(ii) It is 45°
(iii) Its measure is equal to the sum of the measures of angle a and c.
(iv) Its measure is equal to the sum of the measures of angle b and c.
Chose the correct option from the following
(A) (i) and (ii)
(B) (iii) and (iv)
(C) (i) and (iii)
(D) (i) and (iv)
Answer:
(C) (i) and (iii)
(c) Draw the figure with same measurements and mark the point. Draw a line through the marked point and parallel to the horizontal line. (3)
Answer:
Question 4.
(A) (a) Write 196 as the product of prime factors. (2)
Answer:
196 = 2 × 2 × 7 × 7
(b) Find all the factors of 105? (2)
Answer:
105 = 3 × 5 × 7
Factors of 105 are: 1, 3, 5, 7, 15, 21, 35, 105.
(c) Choose the correct statement from the following? (1)
(A) Sum of the two prime numbers is always a prime number.
(B) The multiples of two prime numbers are also a prime numbers.
(C) The common factors of two prime numbers is 1.
(D) In case of prime numbers, there are no even numbers.
Answer:
(C) The common factors of two prime numbers is 1.
OR
(B)
(a) Is it true that when two numbers are divided by 5 and both give a remainder of 2, the difference of the numbers is a multiple of 5? Why? (2)
Answer:
Yes, the statement is true. When both numbers give the same remainder on division by 5, subtracting one number from the other cancels the remainder. Therefore the difference is exactly divisible by 5, which means the difference of the two numbers is a multiple of 5.
(b) Prove that, when two numbers are divided by 3 and both gives a remainder of 1, then the difference of the numbers is a multiple of 3. (2)
Answer:
Let 4 and 10 be the numbers
When 4 and 10 are both divided by 3 we get a remainder 1.
The difference of two numbers is,
10 – 4 = 6 (multiple of 3)
(c) From the numbers given below, identify of the following are divisible by 3, 9 and 5 with no remainder. (1)
(a) 4327
(b) 3520
(c) 4950
(d) 1490
Answer:
(c) 4950
Question 5.
(a) Suja brought 1 \(\frac{3}{4}\) litres of milk in the morning and 2\(\frac{1}{2}\) litres of milk in the evening. If she used 3\(\frac{1}{4}\) litres of milk, how much milk remains? (2)
Answer:
Milk brought in total = 1\(\frac{3}{4}\) + 2\(\frac{1}{2}\) = 4\(\frac{1}{4}\) litre
Milk used = 3\(\frac{1}{4}\) litre
Remaining milk = 4 \(\frac{1}{4}\) – 3 \(\frac{1}{4}\) = 1 litre
(b) If \(\frac{5}{6}\) metre long rope and \(\frac{3}{4}\) metre long rope are joined end to end find there total length in metre? (2)
Answer:
Length of the first rope = \(\frac{5}{6}\)
Length of the second rope = \(\frac{3}{4}\)
Two ropes are joined end to end = \(\frac{5}{6}+\frac{3}{4}=\frac{10}{12}+\frac{9}{12}\) = 1\(\frac{7}{12}\) metres
Total length = 1 \(\frac{7}{12}\) metres
(c) Find an equivalent fraction of with a denominator 40 from the following. (1)
(a) \(\frac{37}{40}\)
(b) \(\frac{20}{40}\)
(c) \(\frac{25}{40}\)
(d) \(\frac{30}{40}\)
Answer:
(c) \(\frac{25}{40}\)
Question 6.
(a) What part of the circle is shaded in the figure? (1)
Answer:
\(\frac{1}{3}\) part of the circle is shaded.
(b) Draw the given triangle.
Answer:
(c) Look at the picture given below
Choose the correct statement about this picture from the following?
(A) In the figure, one angle is 90°
(B) In the figure, all angles are less than 90°.
(C) In the figure, one angle is greater than 90°.
(D) In the figure all angles are greater than 90°.
Answer:
(C) In the figure, one angle is greater than 90°.