Class eight (8) math annual exam preparation – model 5

Class eight (8) math annual exam preparation

Section A: Objective (25 Marks)

Multiple Choice Questions: (Write the correct answer in the answer sheet)    1 × 15 = 15

1. The length of the classroom is 2 feet more than its width. If the width is x feet, what is the length?
(a) 2x feet
(b) 2 − x feet
(c) x + 2 feet
(d) x − 2 feet

2. Which of the following is the formula for the volume of a cube?
(a) V = \[ l^3 \]
(b) V = \[ l^2 \]
(c) V = 3l
(d) V = \[ 3l^3 \]

3. At a 12% profit rate, what principal amount will give a profit of 36 Taka in 3 years?
(a) 150 Taka
(b) 100 Taka
(c) 600 Taka
(d) 550 Taka

4. What is the formula to calculate interest when the time period is 1 year?
(a) I = Pnr
(b) I = Pr
(c) \[ \frac{Pn}{r} \]
(d) \[ \frac{Pr}{n} \]

5. What is the index of the compound interest formula (1 + r) at the end of the first year?
(a) 2
(b) 1
(c) 0
(d) n

6. Which of the following points lies on the x-axis?
(a) (0, 1)
(b) (1, 1)
(c) (0, −1)
(d) (2, 0)

7. Who introduced the method of representing the position of a point using coordinates?
(a) Euclid
(b) Newton
(c) Leibniz
(d) René Descartes

8. What is the midpoint of the points (−2, 4) and (4, 6)?
(a) 2
(b) −2
(c) −5
(d) 5

Answer questions 9 and 10 from the following diagram:

9. If AB = CD, what is the distance between AB and CD?
(a) 4 cm
(b) 2 cm
(c) \[ \sqrt{3} \] cm
(d) \[ 2\sqrt{2} \] cm

10. What is the value of OC?
(a) 5 cm
(b) \[ \sqrt{5} \] cm
(c) \[ \sqrt{3} \] cm
(d) None of the above

Class eight (8) math annual exam preparation – part 4

11. What is the binary representation of \[ {(4)}_{10} \]?
(a) \[ {(100)}_{2} \]
(b) \[ {(101)}_{2} \]
(c) \[ {(11)}_{2} \]
(d) \[ {(110)}_{2} \]

12. What is the result of subtracting 10010 from 11101?
(a) 1111
(b) 1010
(c) 1011
(d) 110

13. If the range is 110 and the number of classes is 10, what is the class width?
(a) 10
(b) 11
(c) 12
(d) 13

14. What is the average of the prime numbers from 1 to 19?
(a) 9.625
(b) 10.625
(c) 14.625
(d) 15.625

15. What is the median of the integers from −5 to 5?
(a) −5
(b) −1
(c) 0
(d) 5

One-word answer:1 × 10 = 10

16. What are the dimensions of a cube (length, width, and height)?

17. What is the volume of a square showcase with a length of 2 units?

18. What does “profit” mean?

19. What type of capital is used to start an investment?

20.What is the value of “y” in the fourth quadrant?

21. What is the distance between the points (4, 6) and (−8, 4)?

22. What is the angle measurement of a sector in a circle that is subtended by a chord?

23. How many digits are used in the binary number system?

24. What must we do when drawing conclusions from unordered data?

25. What lies along the horizontal or x-axis in a rectangular shape?

A Section: Short Answer and Descriptive (75 Marks)
1. Answer the following questions: 2 × 13 = 26

(a) Find the cube of xy + z − 3.
(b) Find the LCM (Least Common Multiple) of 5 and 3, and 53 and 33.
(c) Find the compound interest for 3 years on 5000 with an annual interest rate of 10%.
(d) Rayhan deposited 20,000 taka in the bank for 7 years. If the interest rate is 8%, how much interest will he earn?
(e)Sharifa deposited 70,000 taka in the bank at 8% interest. How much interest will she earn after 6 years?
(f)Find the equation of the line passing through the points (0, 0) and (−7, −3).
(g) Find the equation of the line passing through the origin (0, 0) and point P (−4, −2).
(h) Prove that the sum of the opposite angles of any quadrilateral is 180°, or that the quadrilateral’s vertices form a cyclic quadrilateral.
(i)

O is the center of the circle. Find the area of the arc ACB.

(j) Find the 10’s complement of the decimal number 2351.
(k) Multiply (27)₁₀ by (11)₁₀.
(l) The daily market expenses of 20 families are given as:
257, 152, 358, 425, 192, 283, 170, 326, 252, 246, 228, 340, 375, 400, 327, 290, 260, 310, 350, 268
Create a frequency distribution table for the given data, assuming 6 classes and a class width of 50.
(m) A frequency distribution table is given below:

Find the mode of the given data.

Descriptive Questions (7 out of 10 questions must be answered, each worth 7 marks): 7 × 7 = 49

2.
(i) \[ (a^3 + b^3) = (a + b)(a^2 − ab + b^2) \]
(ii) \[ (a − b − c)^3 = a^3 − b^3 − c^3 − 3a^2b + 3ab^2 − 3b^2c − 3bc^2 − 3a^2c + 3ac^2 + 6abc \]

(a)Prove the formula (i) using the identity for the cube of a binomial and trinomial. [2 Marks]
(b) Prove the formula (ii) using the identity for the cube of a binomial and trinomial. [2 Marks]
(c) If a = 8, b = 5, c = 3 , prove formula (ii). [3 Marks]
3. Insa and Wasir have two cubic-shaped boxes, one with a length of 25 cm and the other with a length of 45 cm, in which they place chocolates. The chocolates are also cubic in shape.

(a) What types of chocolates can completely fill both boxes? [2 Marks]
(b)What is the maximum size of chocolate that can completely fill both boxes? [2 Marks]
(c)Find the greatest common divisor (GCD) and least common multiple (LCM) of the lengths of the two boxes. [3 Marks]

4. 75,000 taka was deposited in the bank for 5 years at an 8% interest rate.
(a) What is the simple interest? [2 Marks]
(b)What is the compound interest? [3 Marks]
(c) What is the difference between simple interest and compound interest? [2 Marks]

5. Mr. Kamal bought a car for 700,000 taka and sold it at a 5% loss. Then, he used the money from the car sale to buy 5 motorcycles. He wants to make a 10% profit on the initial amount of money he had by selling the 5 motorcycles.
(a) How much did he sell the car for? [3 Marks]
(b) What price should he sell each motorcycle for in order to make a 10% profit on his initial amount? [4 Marks]

6.Four points are given: A(−3, 1), B(−1, 4), C(3, 2), and D(1, −2).

(a) Find the slope of the line passing through points A and B. [2 Marks]
(b) Find the equation of the line passing through points C and D. [2 Marks]
(c) Determine the nature of the triangle formed by points A, B, and C. [3 Marks]

3. Insa and Wasir have two cubic-shaped boxes, one with a length of 25 cm and the other with a length of 45 cm, in which they place chocolates. The chocolates are also cubic in shape.

(a) What types of chocolates can completely fill both boxes? [2 Marks]
(b)What is the maximum size of chocolate that can completely fill both boxes? [2 Marks]
(c)Find the greatest common divisor (GCD) and least common multiple (LCM) of the lengths of the two boxes. [3 Marks]

4. 75,000 taka was deposited in the bank for 5 years at an 8% interest rate.
(a) What is the simple interest? [2 Marks]
(b)What is the compound interest? [3 Marks]
(c) What is the difference between simple interest and compound interest? [2 Marks]

5. Mr. Kamal bought a car for 700,000 taka and sold it at a 5% loss. Then, he used the money from the car sale to buy 5 motorcycles. He wants to make a 10% profit on the initial amount of money he had by selling the 5 motorcycles.
(a) How much did he sell the car for? [3 Marks]
(b) What price should he sell each motorcycle for in order to make a 10% profit on his initial amount? [4 Marks]

6.Four points are given: A(−3, 1), B(−1, 4), C(3, 2), and D(1, −2).

(a) Find the slope of the line passing through points A and B. [2 Marks]
(b) Find the equation of the line passing through points C and D. [2 Marks]
(c) Determine the nature of the triangle formed by points A, B, and C. [3 Marks]

7.A quadrilateral has four vertices: A(1, 1), B(4, 4), C(4, 8), and D(1, 5).

(a) Plot the points on the xy-plane and draw the quadrilateral on graph paper. [3 Marks]
(b) Determine the nature of the quadrilateral. [4 Marks]

8. In the figure, the circle has center O and a diameter of 27 cm.

(a)Find the length of the perpendicular from O to the chord BC. [3 Marks]
(b) Find the measure of ∠BAC. [4 Marks]

9.The sum of the numbers 69 and 78 is (10010011)₂.

(a) Find the binary sum of the two numbers. [3 Marks]
(b) Subtract 69 from 78 using the complement method. [4 Marks]

10. Consider the following frequency distribution:

The arithmetic mean of the frequency distribution is 54.

(a) Find the value of p using the direct method. [3 Marks]
(b) Verify the value of p using the shortcut method. [4 Marks]
11.The marks obtained in mathematics by 30 students of class 8 are: 80, 75, 85, 95, 90, 80, 85, 70, 95, 90, 90, 80, 60, 70, 75, 65, 70, 80, 75, 90, 95, 75, 80, 72, 86, 92, 78, 68, 72, 70.

(a) Find the mode of the marks. [1 Mark]
(b) Construct the cumulative frequency distribution table for the given data. [3 Marks]
(c) Using the cumulative frequency table from part (b), find the median by drawing the cumulative frequency curve. [3 Marks]