Class Eight Math Annual Exam Preparation: Part 1

Class Eight Math Annual Exam Preparation: Part 1

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Subject: Mathematics
Class: Eight
Objective+Essay Type
Time-3 hours; Full Marks- 100
Part-A: Objective Part (Multiple Choice Question and Answer in One Word): Marks-25
Multiple Choice Question
[NB.: Write the correct or best answer in your answerscript (question no. 1-15), each question carries 1 mark]

Marks: 1 x 15=15

1. How many variables are there in the equation 3x + by?
(a) 1
(b) 2
(c) 3
(d) 4
2. What is the volume of a brick if its length, width, and height are 8 cm., 5 cm., and 4 cm., respectively?
(a) 120
(b) 160
(c) 320
(d) 460
3. What is the simple profit of Tk. 1200 in 4 years at the rate of simple profit of 10% per annum?
(a) 120 Tk.
(b) 240 Tk.
(c) 360 Tk.
(d) 480 Tk.
4. What is the new capital that is obtained by adding profit to the capital at the end of a specified period?
(a) Final capital
(b) Initial capital
(c) Compound capital
(d) Simple profit
5. What is the distance of the point R(-4, 0) from origin?
(a) 2
(b) 2√2
(c) 4
(d) 8
6. The vertices of the triangle ABC, A(-2, 1), B(3, t) and C(-1, 5) in anticlockwise order. If the area of ΔABC is 10 square unit, what is the value of t?
(a) 10
(b) 5
(c) 3
(d) 1
7. What is the small arc of a circle called?
(a) Minor arc
(b) Major arc
(c) Semi arc
(d) Minor segment
8. At how many points does the secant intersect a circle?
(a) 0
(b) 1
(c) 2
(d) 3
9. What is the place value of 7 in (1754)10_{10}10?
(a) \[7 \times 10^2\]
(b) \[7 \times 10^3\]
(c) \[7 \times 10^0\]
(d) \[7 \times 10^7\]
10. (11011.001)2_{2}2 − (1011.110)2_{2}2 = (?)2_{2}2
(a) (1011.011)2_{2}2
(b) (1001.001)2_{2}2
(c) (1101.001)2_{2}2
(d) (1111.011)2_{2}2
11. If the range of the data is 26 and the lowest value is 17, what is the highest value?
(a) 42
(b) 26
(c) 16
(d) 9
12. What is indicated by the y-axis line while drawing a histogram?
(a) Range
(b) Frequency
(c) Class Interval
(d) Tally marks
13. In a circle with center O, AB is a chord different from the diameter. If OP ⊥ AB, which of the following relation is correct?
(a) AP = PB
(b) AP > PB
(c) AP < PB
(d) AP = 2PB
14. How is the 9’s complement of a number ‘a’ denoted?
(a) a’
(b) a*
(c) \[a^a\]
(d) \[a^n\]
15. What is the mode of the data 8, 9, 7, 15, 10, 11, 8, 10, 9, 8?
(a) 8
(b) 9
(c) 10
(d) 15

Answer in One Word
[NB: Write the answers of the questions in the provides answerscripts, (question no. 16-25) each question carries mark]

Marks: 1 x 10-10

16. What is the volume of a cube of size x × x × x?
17. What is the profit of 100 taka at a 10% profit rate for 1 year?
18. When the straight line y = mx + c will pass through the origin?
19. ∠B + ∠D of cyclic quadrilateral ABCD = ?
20. What is the largest number that can be expressed in binary with four bits?
21. How many workers are paid an average of 350.5 taka each and the total will be 30493.5 taka?
22. What is the circumference of the circle with radius r units?
23. What is the quotient of \[(110011)_2\]  and  \[(10001)_2\] ? 
24. What is the mode of the data 9, 17, 11, 20, 19, 11, 12, 11, 15?
25. What is the difference between the annual simple profit and the compound profit of Tk. 3800 at the rate of 24% of 1 year?

Part-B: Essay Type Part [Short Answer Questions and Essay Type Questions (Situational)

Marks-75

Short Answer Questions
(There will be 13 questions, all of them must be answered)

2 × 13=26

1. Answer the following questions.
a. Determine the LCM of \[x^2 – 4\], \[x^2 + 3x + 2\], and \[x^3 + 27\].
b. If \[a + b + c = 9\] and \[ab + bc + ca = 31\], then determine the value of \[a^2 + b^2 + c^2\].
c. What is the principal-interest of Tk.100 for 3 years at a 9% simple profit rate?
d. If a bicycle is bought for Tk 10,500 and sold at a profit of 5%, what is the profit?
e. If the length of the side of a square is AB formed by two points A(1, 1) and B(-1, -1), then find the area of the square.
f. If the lines \[5x + 8y – 6 = 0\] and \[bx + 20y + 15 = 0\] are parallel to each other, then find the value of b.
g.

If \[AB = 40\] inch, \[RS = ?\]
h.

Determine the ratio of the circumference of the two circles.
i.
Find 2’s Complement of Let me know if you need more adjustments or further assistance!
j. What is the number of digits in the binary form of the product of the last two prime numbers between 1 and 100?
k. The ages (in years) of some people in an area are given below:
71, 68, 95, 65, 70, 82, 88, 81, 85, 90, 97, 86, 78, 70, 77, 92, 90, 83, 69, 87, 80, 82, 95, 97, 70, 70, 79, 80, 91, 70.

Determine the class number for the given data taking a class interval of 5.

Essay Type Questions (Situational)
(7 questions are to be answered from 10 questions. Each question carries 7 marks.)

l. Determine the median of the data 22, 18, 36, 27, 36, 19, 24, 26, 28, 21.
m. If \[a = 15\], then what is the value of \[8a^3 + 60a^2 + 150a + 130\]?
(7 questions are to be answered from 10 questions)
2. Noor Chowdhury’s fish farming farm has a pond that is 60 meters long, 50 meters wide, and 10 meters deep.
a. What is the formula for the volume of a rectangular solid?
b. What is the volume of water in the pond?
c. To reduce the depth of water by 5 meters, how much must the length of the pond be increased?
3. \[x^2 – 2x + 1\], \[x^2 – 1\], and \[x^2 – 5x + 4\] are three algebraic expressions.
a. If the first expression = 0, prove that \[\left(x – \frac{1}{x}\right)^2 = 0\].
b. If the second expression = 5x, find out the value of \[x^4 + \frac{1}{x^4}\].
c. Determine the L.C.M. of the three expressions.
4. A businessman of rice sold some amount of rice for Tk. 9500 at the loss of 5%. Depositing an equal amount of the sold price at 10% simple profit, for x year the profit becomes \[\frac{3}{5}\] times of the principal.
a. What would be the selling price of that amount of rice for the rice-seller to make a profit of 7%?
b. Determine the value of x.
5. Mr. Riyaz bought a motorcycle for 145000 taka. He sold the motorcycle at a loss of 7% due to poor market conditions. Then he bought five cycles and prepared to sell them with the money he got from selling the motorcycle. His motive is to earn 12% on the principal amount.
a. If Mr. Riyaz’s motive is successful, then at what price should he sell 8 motorcycles?
b. If Mr. Riyaz’s motive is successful, then what is the percentage of money he had to gain in relation to the purchase price of the cycles?
6. E(-2, 6), F(-2, 3), G(4, 3), and H(4, a) are four vertices of a quadrilateral, arranged in an anti-clockwise order.
a. Determine the slope of the line EG.
b. If the area of the triangle FGH is 18 square units, then find the value of a.
c. If a = 6, then determine the characteristic of the quadrilateral EFGH.
7. In a circle with center O, OB = 12 cm.
Diagram included with various triangle sides and angles.
7. In a circle with the center O, OB = 12 cm

a. What kind of triangle do you think \[\triangle OBC\] is?
b. Find the length of arc BC and the area of sector BOC.
c. Determine the perimeter of \[\triangle PQR\].
8. The ages of Afia, Tisha, and their mother are \[(10001)_2\], \[(1110)_2\] and \[(101010)_2\] respectively. The age of Tisha’s brother is \[(10100)_2\]
a. Find the 2’s complement of the product of the ages of Afia and Tisha.
b. How many times is the sum of the ages of the mother and brother of Tisha of the sum of the ages of Afia and Tisha?
9.Scenario-1: The teacher writes the number 92457 on the board.
Scenario-2: \[(1110010101101.111)_2\] and \[(1000001101.101)_2\] are two binary numbers.
a. Determine 10’s complement of the number in scenario-1.
b. Convert the number obtained in ‘a’ into binary.
c. Determine the decimal form of the number in scenario-2.
10. A frequency distribution table of obtaining marks in mathematics of the students of class 10 in K. P. B School is given below:

a. Determine the mid-value of the mode class.
b. Determine the mean by the short-cut method.
c. Determine the difference between the median and mean.
11. The radius of two same-centered circles is 9 cm and 7 cm respectively, and a 30 cm arc of the bigger circle subtended an angle \[\theta\] at the center.
a. If the area of a half-circle is 25.135 sq. cm, then what is the radius of that circle?
b. Determine the difference between the two circles.
c. Determine the length of the arc with respect to the angle \[\theta\] for the smaller circle.

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