Class Eight Math Annual Exam Preparation: Part 2

Class Eight Math Annual Exam Preparation: Part 2

Time: 3 hours

Section A: Objective (25 Marks)

Multiple Choice Questions: (Write the correct answer in the answer sheet)

1. Which of the following is a metric object?

(a) Cube
(b) Area
(c) Cuboid
(d) Sphere
2. How many panes are there in the classroom window?

(a) One
(b) Two
(c) Three
(d) None
3. What is the interest on 100 taka for three years at a 7% interest rate?

(a) 7 taka
(b) 14 taka
(c) 21 taka
(d) 25 taka
4. What could be the minimum type of interest?

(a) 2
(b) 3
(c) 4
(d) 5
5. Which symbol represents compound interest?

(a) A
(b) C
(c) P
(d) I
6. Which symbol represents compound interest?

(a) A
(b) C
(c) P
(d) I
7.What is the first component of a coordinate of a point called?

(a) Abscissa
(b) Hypotenuse
(c) Base
(d) Both (a) and (c)
8. What is the distance between the origin and the point (4, 0)?

(a) 2 units
(b) 4 units
(c) 3 units
(d) None of these
9.Into how many parts can the xy-plane be divided by the axes?

(a) 4
(b) 2
(c) 6
(d) 3
10. How many diameters can be drawn through the center of a circle?

(a) One
(b) Two
(c) Both (a) and (b)
(d) Infinite
11. For a circle standing on the same pressure, the inscribed angle is ———– of the central angle.
(a) Three times
(b) Half
(c) Four times
(d) Triple
12. Who first introduced the binary number system?
(a) Gottfried Leibniz
(b) George Boole
(c) Newton
(d) Carl Friedrich Gauss
13. Which of the following number systems is used?
(a) Binary
(b) Decimal
(c) Octal
(d) Hexadecimal
14. How many quantities are there in the central tendency?
(a) 3
(b) 2
(c) 3
(d) 4
15. What is required to process the frequency distribution?
(a) Class number
(b) Class interval
(c) Environment
(d) Frequency

Section B: Short and Descriptive (75 Marks)

Answer the following questions:

(a) Factorize \[ x^6 – 729 \].

(b) If \[ a = 6 \] and \[ b = 2 \], show that \[ a^3 + b^3 = (a + b)(a^2 – ab + b^2) \].

(c) Calculate the simple interest for 3 years on an amount of \[ 5000 \] taka at an annual interest rate of \[ 10% \].

(d) What should be the principal amount for the compound interest to reach \[ 20000 \] taka in 5 years at a \[ 13% \] rate?

(e) Find the equation of a straight line with a slope of \[ -2 \] that passes through the point \[ (4, -5) \].

(f) Determine the slope of the line joining the origin and the point \[ (4, 0) \].

(g) Show that the points \[ A(3, 9) \], \[ B(-2, -16) \], and \[ C\left(\frac{1}{5}, -5\right) \] are collinear.

(e) A circular arc of a circle with a radius of 5 cm creates a 30° angle at the center. Calculate the area of the circular segment formed by this arc.

(f) \[ AB \] and \[ CD \] are two parallel chords, and \[ AB = CD = 10 \] cm. The chords \[ AB \] and \[ CD \] are 4 cm apart. What is the diameter of the circle?

(g) Convert the binary number \[ 110011 \] into a decimal number.

(h) Convert the decimal number 56 into binary.

(i) A data table:

Calculate the arithmetic mean of the data using the direct method.

(j) The ages of 25 people in a village are given below:
44, 50, 22, 17, 15, 54, 48, 26, 24, 21, 38, 46, 32, 37, 38, 20, 40, 34, 10, 19, 13, 24, 33, 57, 36
Here is the translation:

Create a frequency distribution table based on the given data.

Descriptive Questions (Context-Based): (Answer any 7 out of 10 questions. Each question carries 7 marks)

1. In a compound interest scheme, if a principal earns 19500 taka as one year’s compound interest and 20280 taka as two years’ compound interest:

(a) Determine the principal amount.
(b) Calculate the difference between simple interest and compound interest after 3 years at the same rate.
2. Given \[ A(-2, 0), B(5, 0) \], and \[ C(1, 4) \] as the vertices of \[ \triangle ABC \]:

(a) Determine the lengths of \[ AB, BC, CA \] and the perimeter of \[ \triangle ABC \].
(b) Find the area of the triangle.
3. Given the Cartesian coordinates of four points \[ A(0, -1), B(-2, 3), C(6, 7) \], and \[ D(8, 3) \]:

(a) Determine the nature of the quadrilateral.
(b) Calculate the area of the quadrilateral.

4. The math teacher wrote the numbers 112.2 and 45 on the board.

(a) Convert 15 and 7 to binary.
(b) Determine the product of the two binary numbers obtained in part (a).
(c) Convert the two decimal numbers given in the problem to binary and multiply them.
5. The heights (in centimeters) of 40 students in 8th grade are: 90, 140, 97, 125, 97, 134, 97, 97, 110, 125, 110, 134, 110, 125, 110, 140, 125, 134, 125, 134, 110, 125, 97, 125, 110, 125, 97, 134, 125, 110, 134, 125, 134, 90, 140, 148, 148, 110, 125

(a) Arrange the data in ascending order.
(b) Arrange the data in descending order.
(c) Calculate the average height of the students.
6.The frequency distribution table of the weights of 70 students:

(a) Create a cumulative frequency table.
(b) Determine the median.
(c) Calculate the mode.

7. \[ 45x^3, 60x^2y, 15x^2y^2 \] are three algebraic expressions.

(a) Determine the LCM of the three expressions.
(b) Determine the GCD of the three expressions.
(c) Subtract the GCD from the LCM, divide the result by \[ 15x^2 \], and cube the quotient.
8. Shipra Barua deposited \[ 3000 \] taka in a bank, and after 2 years, she received \[ 3600 \] taka including interest.

(a) Calculate the rate of simple interest.
(b) If she deposits \[ 3000 \] taka at the same rate with compound interest, what will be the compound amount after 2 years?
9. A decimal and a binary number are given as 229.6875 and 11010101, respectively.

(a) Convert the binary number to a decimal number.
(b) Convert the decimal number to a binary number.