CLASS 8 MATHEMATICS - SELF ASSESSMENT TERM 2 MODEL PAPER - 2024 - 2025- SA2/CBA3
Section A: Multiple Choice Questions
1. The length and breadth of a rectangle are represented by the expressions (3x + 2) and (x - 5), respectively. Which of the following represents the area of the rectangle?
A) 3x² - 10
B) 3x² + 2x - 10
C) 3x² - 13x - 10
D) 3x² + 17x + 10
Answer: C) 3x² - 13x - 10
2. What type of quadrilateral has all sides equal and two adjacent angles measuring 150° and 30°?
A) Kite
B) Rhombus
C) Square
D) Parallelogram
Answer: B) Rhombus
3. Which of the following sets of numbers forms a Pythagorean triplet?
A) 8, 15, 18
B) 7, 24, 25
C) 10, 20, 22
D) 6, 9, 12
Answer: B) 7, 24, 25
4. The volume of a cube is three times the volume of a cuboid. The cube has a side length of 9 cm, while the cuboid has a height of 6 cm and a width of 3 cm. What is the length of the cuboid?
A) 13.5 cm
B) 25 cm
C) 40.5 cm
D) 121.5 cm
Answer: A) 13.5 cm
5. Which of the following equations demonstrates the multiplicative identity property of integers?
A) 5 × 5 = 25
B) 5 × 1 = 5
C) 5 × 0 = 0
D) 5 × -1 = -5
Answer: B) 5 × 1 = 5
6. Lalitha rolls a fair six-sided die. What is the probability that she gets a number less than 5?
A) 1/3
B) 1/2
C) 2/3
D) 5/6
Answer: C) 2/3
7. Mr. Harigopal has 20,500 kg of rice. How much is this in grams, expressed in scientific notation?
A) 2.05 x 10⁶
B) 2.05 x 10⁷
C) 20.5 x 10⁶
D) 20.5 x 10⁷
Answer: B) 2.05 x 10⁷
8. A rectangular metal sheet 22 cm long is rolled into a cylinder along its length without any overlap. If the cylinder's lateral surface area is 154 cm², what is its height?
A) 3.5 cm
B) 7 cm
C) 9.1 cm
D) 22 cm
Answer: B) 7 cm
9. If the area of a circle is given by the expression πx² + 6πx + 9π, then the radius of the circle is:
A) (x + 3) units
B) (x + 6) units
C) (x + 9) units
D) (x + 15) units
Answer: A) (x + 3) units
10. The cost of a movie ticket is Rs 250. Charan got a 20% discount on buying a ticket through online booking. How much rupees did Charan pay for this ticket?
A) Rs 50
B) Rs 200
C) Rs 220
D) Rs 230
Answer: B) Rs 200
11. A teacher writes the equation 3t = 5t - 8/5 on the board. Three students rewrote the equation independently to solve it.
Anil: 15t = 25t - 8
Charmi: 5t - 3t = 8/5
Balaji: 3t = 25t - 8
Which of the following statements is true?
A) Only Anil and Charmi rewrote the equation correctly.
B) Only Charmi and Balaji rewrote the equation correctly.
C) Only Anil and Balaji rewrote the equation correctly.
D) All three students rewrote the equation correctly.
Answer: A) Only Anil and Charmi rewrote the equation correctly.
12. A village is shown on two different maps. Map A has a scale of 1:10000, and Map B has a scale of 1:20000. If a road in the village is 5 cm long on Map A, how long will it be on Map-B?
A) 2.5 cm
B) 5 cm
C) 10 cm
D) 40 cm
Answer: A) 2.5 cm
13. How many natural numbers lie between 2025² and 2026²?
A) 2025
B) 2026
C) 4050
D) 4052
Answer: C) 4050
14. In a parallelogram ABCD if ∠B : ∠C = 3:2 then find the measure of 2∠A?
A) 36°
B) 72°
C) 108°
D) 144°
Answer: D) 144°
15. Which type of graph is best suited for displaying data that changes continuously over time?
A) bar graph
B) line graph
C) pictograph
D) none of these
Answer: B) line graph
16. Which of the following statements is FALSE?
A) The cube of any odd number is an odd number.
B) The cube of a number can end with any digit.
C) The cube of a single-digit number may be a single-digit number.
D) The cube of an even number may be an odd number.
Answer: D) The cube of an even number may be an odd number.
17. Rahul walks to his tuition class at an average speed of 5 km/h and takes 30 minutes to reach. If he wants to reach in 20 minutes, what should be his average speed?
A) 1.6 km/h
B) 3.3 km/h
C) 7.5 km/h
D) 8.3 km/h
Answer: C) 7.5 km/h
18. A teacher draws a quadrilateral having two pairs of adjacent sides of equal length and opposite angles are not equal. James says that the quadrilateral could be a rhombus. Aditya says that the quadrilateral could be a kite. Which statement is correct?
A) Only James' statement is correct.
B) Only Aditya's statement is correct.
C) Both James' and Aditya's statements are correct.
D) Neither James nor Aditya's statement is correct.
Answer: B) Only Aditya's statement is correct.
19. A cuboid tank has a base with dimensions of 18 meters by 10 meters and a height of 5 meters. The tank needs to be painted on all sides except the base. If 1 litre of paint covers 10 square meters, how many litres of paint are needed?
A) 90 litres
B) 64 litres
C) 46 litres
D) 28 litres
Answer: C) 46 litres
Solving for x
Solve for x: 2x+1 + 2x+1 = 128
The problem is: 2x+1 + 2x+1 = 128
Step 1: Combine like terms
Since we have two of the same term, we can write it as: 2 * 2x+1 = 128
Step 2: Simplify using exponent rules
2 is the same as 21, so we have: 21 * 2x+1 = 21 + (x+1) = 2x+2
The equation is now: 2x+2 = 128
Step 3: Express 128 as a power of 2
128 can be written as 27. So, we have: 2x+2 = 27
Step 4: Equate the exponents
Since the bases are the same, the exponents must be equal: x + 2 = 7
Step 5: Solve for x
Subtract 2 from both sides: x = 7 - 2 = 5
The value of x is 5.
Section B
Question 21 - Solve for Smallest Integer
Question 21 - Finding the Smallest Positive Integer
Question:
Find the smallest positive integer that should be added to
1500 to make it a perfect square.
Answer:
Step 1: Calculate the approximate square root of
1500.
√1500 ≈ 38.73.
Step 2: Identify the two nearest perfect squares:
38² = 1444 (less than 1500)
39² = 1521 (greater than 1500).
Step 3: To make 1500 a perfect square, calculate the difference between
39² and 1500:
1521 - 1500 = 21.
The smallest positive integer to add is: 21.
22. A child builds a big cube using 27 smaller cubes, each measuring 3 cm on each side. He wants to paint the entire surface of the big cube, and it costs Rs 5 to paint every square centimeter. How much will it cost the child to paint the whole structure? Show your steps.
Answer: Rs 2430
Question 22 - Cube Painting Cost
Question 22 - Cube Painting Cost
Question:
A child builds a big cube using 27 smaller cubes, each measuring
3 cm on each side. He wants to paint the entire surface of the big cube, and it costs
₹5 to paint every square centimeter. How much will it cost the child to paint the whole structure? Show your steps.
Answer:
Step 1: Determine the dimensions of the big cube.
- Since the child uses 27 smaller cubes arranged in a 3 × 3 × 3 configuration,
- Each smaller cube has a side length of 3 cm.
- Thus, the side length of the big cube is:
3 × 3 cm = 9 cm.
Step 2: Calculate the total surface area of the big cube.
- A cube has 6 faces.
- The area of one face is:
9 × 9 = 81 cm².
- Total surface area is:
6 × 81 = 486 cm².
Step 3: Compute the total painting cost.
- Cost per square centimeter is ₹5.
- Total cost is:
486 × ₹5 = ₹2,430.
The total cost to paint the big cube is: ₹2,430.
Age Problem Solution
Age Problem
23. Bindu's father is 29 years older than Bindu. Bindu's grandfather is 55 years older than Bindu. The sum of the ages of all three is 135 years. What is the age of Bindu and her father?
Solution:
Let Bindu's age be "x".
Then, Bindu's father's age is "x + 29" and Bindu's grandfather's age is "x + 55".
The sum of their ages is 135, so: x + (x + 29) + (x + 55) = 135
Simplifying the equation: 3x + 84 = 135
Solving for x: 3x = 51 => x = 17
Therefore:
- Bindu's age = 17 years
- Bindu's father's age = 17 + 29 = 46 years
Answer: Bindu's age = 17 years: Bindu's father's age = 17 + 29 = 46 years
Rhombus Area Problem
Rhombus Area Problem
24. Area of a rhombus with perimeter 68 cm and one diagonal 16 cm?
Solution:
Let the rhombus be ABCD, and let the diagonals AC and BD intersect at point O.
Perimeter of rhombus = 4 × side
Given perimeter = 68 cm, so 4 × side = 68 cm
Side = 68 cm / 4 = 17 cm
Given one diagonal (say AC) = 16 cm, so AO = OC = 16 cm / 2 = 8 cm
In right triangle AOB, by the Pythagorean theorem: AB² = AO² + BO²
17² = 8² + BO²
289 = 64 + BO²
BO² = 289 - 64 = 225
BO = √225 = 15 cm
Therefore, the other diagonal BD = 2 × BO = 2 × 15 cm = 30 cm
Area of rhombus = (1/2) × diagonal1 × diagonal2
Area = (1/2) × 16 cm × 30 cm = 240 cm²
Answer: The area of the rhombus is 240 cm².
Answer: The area of the rhombus is 240 cm²
