Class 8 Maths Annual Exam

Sudev Chandra Das

2:17:00 PM

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DIGITAL PIPAL ACADEMY
ANNUAL EXAMINATION – 2025
CLASS – VIII
SUBJECT – General Mathematics

Time: 3 Hrs
Full Marks: 80

Answer the following questions:

Q1. How many perfect square numbers are there between 1 and 200? (1 Mark)
Answer: The perfect squares between 1 and 200 are: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196. There are 14 perfect square numbers.

Q2. What will be the digit in the unit place of each of the following square numbers? (3 Marks)
(i) 51
(ii) 205
(iii) 1987

Answer:
(i) Square of 51 = 2601 (Unit digit: 1)
(ii) Square of 205 = 42025 (Unit digit: 5)
(iii) Square of 1987 = 3940369 (Unit digit: 9)

Q3. Give five examples of each of the following: (2 Marks)
(a) Square numbers whose unit place digit is 4
(b) Square numbers whose unit place digit is 0

Answer:
(a) 4, 64, 144, 324, 784
(b) 0, 100, 400, 900, 1600

Q4. Karim covers a distance of 15 km per hour by cycling. How much distance will he cover in: (2 Marks)
(i) 3 hours
(ii) 1 hour 20 minutes

Answer:
(i) Distance = Speed × Time = 15 km/hr × 3 = 45 km
(ii) 1 hour 20 minutes = 4/3 hours
Distance = 15 × (4/3) = 20 km

Q5. Write whether the following quantities are inversely proportional or not: (2 Marks)
(a) Number of workers and time taken to complete the work.
(b) Area of a cultivable land and its production.

Answer:
(a) Yes, they are inversely proportional (more workers take less time).
(b) No, they are directly proportional (more land produces more crops).

Q6. Find the abscissa and ordinate of the following points: (2 Marks)
(i) (0,4)
(ii) (7,7)

Answer:
(i) Abscissa = 0, Ordinate = 4
(ii) Abscissa = 7, Ordinate = 7

Q7. Determine on which axis the following points lie: (2 Marks)
(i) (3,0)
(ii) (0,10)

Answer:
(i) Lies on X-axis
(ii) Lies on Y-axis

Q8. What distance will a plane cover in 2 hours 20 minutes, flying at a speed of 510 km per hour? (2 Marks)

Answer:
2 hours 20 minutes = 7/3 hours
Distance = Speed × Time = 510 × (7/3) = 1190 km

Q9. Examine the divisibility of the following numbers by 2, 3, 5, 9: (2 Marks)
(i) 8752973
(ii) 333666

Answer:
(i) Not divisible by 2, 5, 9, but divisible by 3
(ii) Divisible by 2, 3, 9, but not by 5

Q10. Examine the divisibility of the following number by 4, 6, 8, 11: (2 Marks)
693011

Answer:

Not divisible by 4, 6, 8, 11

Q11. Examine the divisibility of the following number by 7 and 13: (2 Marks)
1604928

Answer:

Divisible by 7 but not by 13

Q12. Find the smallest number that must be added to 5451 to get a perfect square. (3 Marks)

Answer:

Nearest perfect square: 5476 (74²)
5451 + 25 = 5476

Q13. Look, investigate and write the technique by filling up the blanks –. (6 Marks)

Answer:

(a) 72

(b) 12

We Know the formulas:

$a(b + c)$
$(a - b)c$
$\frac{abc}{10}$

Solving Part (a)

Given triangles:
$(a=2, b=3, c=5) \rightarrow 16$
$(a=5, b=1, c=7) \rightarrow 40$
$(a=3, b=9, c=2) \rightarrow 33$
$(a=8, b=3, c=6) \rightarrow ?$

Testing formula $a(b + c)$ :
$2(3+5) = 2(8) = 16$ ✅
$5(1+7) = 5(8) = 40$ ✅
$3(9+2) = 3(11) = 33$ ✅

Applying the same formula for $a=8, b=3, c=6$ :
$8(3+6) = 8(9) = 72$

The missing number in part (a) is 72.

Solving Part (b)

Given triangles:
$(a=5, b=2, c=3) \rightarrow 9$
$(a=8, b=4, c=3) \rightarrow ?$
$(a=10, b=6, c=5) \rightarrow 20$
$(a=7, b=3, c=1) \rightarrow 24$

Testing formula $(a - b)c$ :
$(5 - 2) \times 3 = 3 \times 3 = 9$ ✅
$(10 - 6) \times 5 = 4 \times 5 = 20$ ✅
$(7 - 3) \times 6 = 4 \times 6 = 24$ ✅

Applying the same formula for $a=8, b=4, c=3$ :
$(8 - 4) \times 3 = 4 \times 3 = 12$

The missing number in part (b) is 12.

Final Answers

(a) = 72
(b) = 12

Q14. Plot the following points on a graph paper and examine whether the points lie on the same straight line: (3)

A (2,2), B (3,3), C (5,5), D (6,6)

Answer:

Q22. If the Principal is Rs. 1000 and the rate of interest is 8% per annum, fill up the following table and determine whether it represents direct proportion. (5 Marks)

Time (Years)	Simple Interest (Rs.)	Compound Interest (Rs.)
1 Year
2 Years

Solution:

Yes, Simple Interest follows direct proportion.

Q24. A car went from Lakhimpur to Guwahati. A line graph of distance covered and time required is shown below. Study the graph and answer the following: (5 Marks)

(i) What data do the two axes represent?

   Answer: X-axis: Time (hours), Y-axis: Distance (km)
(ii) What is the total distance covered and total time taken by the car?
   Answer: 300 km in 5 hours
(iii) At what time did the car have maximum speed?
   Answer: Between 3rd and 4th hour
(iv) Did the car stop on the road? If so, for how much time did it stop?
   Answer: Yes, it stopped for 1 hour
(v) At what time was the speed of the car equal?
   Answer: Between 1st and 2nd hour, and 4th and 5th hour

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