Annual exam last preparation class 9 math
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Mathematics
Time: 3 hours Class 9 Full Marks: 100
Section A: Objective (25 Marks)
Multiple Choice Questions: (Write the correct answer in your answer script) 1 × 15 = 15
1. What is the algebraic form of a sequence called?
(a) Arithmetic Sequence
(b) Geometric Sequence
(c) Both (a) and (b)
(d) None of these
2. The sequence \frac{1}{3},\frac{1}{6},....... \frac{1}{999} is ————-
i. Finite
ii. Infinite
iii. Geometric
Which of the following is correct?
(a) i and ii
(b) i and iii
(c) ii and iii
(d) i, ii, and iii
3. What is the common difference in the sequence 3 + 6 + 9 + 12 + …. ?
(a) 2
(b) 3
(c) 4
(d) 6
4. In 2^3 = 8 , what is the base of the exponent?
(a) 4
(b) 2
(c) 3
(d) 8
5. If 0 < b < 1 and 0 < x < 1 , which of the following is correct?
(a) \log_b x > 0
(b) \log_b x > -1
(c) \log_b x > -2
(d) \log_b x > -3
6. What is the unit for measuring the intensity of sound?
(a) Decibel
(b) mm
(c) km
(d) Watt
Refer to the following passage for Questions 7 and 8:
The difference between two numbers, x and y, divided by 2 is 7. If five times the smaller number is added to the larger number, the sum is 50, where x > y.
7. What is the first condition?
(a) \frac{x - y}{2}
(b) x – y = 7
(c) x – y = 14
(d) \frac{x + y}{2} = 7
8. Which of the following is the value of (x, y)?
(a) (10, 8)
(b) (20, 6)
(c) (8, 12)
(d) (6, 20)
9. In right triangle PMO, PM is the opposite side, OM is the adjacent side, and OP is the hypotenuse. Then:
i. sin θ = \frac{Opposite side} {hypotenus} = \frac{ PM} {OP}
ii. cos θ = \frac{adjacent side} {hypotenus} = \frac{ OM} {OP}
iii. cos θ = \frac{Opposite side} {adjacent side} = \frac{ PM} {OM}
Which of the following is correct?
(a) i and ii
(b) i and iii
(c) ii and iii
(d) i, ii, and iii
10. If sin θ = \frac{1} {2} and cos θ = \frac{\sqrt3} {2} , what is tan θ?
(a) {\sqrt3}
(b) {\sqrt2}
(c) 1
(d) \frac{1}{\sqrt2}
11. What is any line located on the Earth’s surface called?
(a) Geodetic Line
(b) Vertical Line
(c) Straight Line
(d) Curved Line
12. What is the maximum value discussed for an angle in geometry?
(a) – 180°
(b) 180°
(c) 930°
(d) 360°
13. In the standard position, in which quadrant does the terminal side of a 210° angle lie?
(a) 1st
(b) 2nd
(c) 3rd
(d) 4th
14. What is the class interval of the (35 – 39) class?
(a) 5
(b) 46
(c) 9
(d) 6
15. If L = 36, Fc = 24, n = 50, h = 5, and fm = 25, what is the median?
(a) 30.2
(b) 32.4
(c) 31.2
(d) 36.2
One-word Answer: 1 × 10 = 10
16. What is the algebraic form of a sequence?
17. Write the formula for the general term of an arithmetic sequence.
18. What will be the logarithmic form of the exponential equation 2^3 = 8 ?
19. If b > 0 and b 1 , what is n generally like?
20. What do you call an equation when the variable is of the first degree?
21. What does the word “Trigon” mean?
22. What is the distance between the starting and ending positions of a ray called?
23. How many types of angles are there in terms of angular distance?
24. If the spread of data is high, what are the values like?
25. Which two values of data are used to calculate the range?
Section B: Short and Descriptive (75 Marks)
1. Answer the following questions: 2 × 13 = 26
(a) If 7x + 2, 5x + 12, 2x – 1 form an arithmetic sequence, find the value of x.
(b) What is the sum of the first 30 terms of the sequence 7 + 12 + 17 + …?
(c) Find the general term of the sequence 3, 6, 9, ….
(d) Find the simplified value of \frac{7^3 × 7^{-3}}{3×3^{-4}}
(e) If the coronavirus spreads from 1 person to 3 people per day, in how many days will 10 million people be infected?
(f) Check the solvability of the equations 2x + 3y = 32 and 11y – 9x = 3.
(g) Solve the equations 3x – 5y = -9 and 5x – 3y = 1 by the elimination method.
(h) If 12 cot θ = 7, find the value of csc θ.
(i) In the right triangle ABC, where angle C = 60°, angle B = 90°, and the length of side AB = 16 cm, find the length of side BC.
(j) Express the angle 1.3177 radians in degrees.
(k) Find the reference angle of 300°.
(l) When does the value of the discriminant become zero?
(m) Find the arithmetic mean of the dataset 8, 15, 53, 49, 19, 62, 7, 15, 95, 77.
Descriptive Questions (Scenario-based): (Answer any 7 out of 10 questions. Each question is worth 7 points) 7 × 7 = 49
2. 3, 6, 12, 24, 48, ……….. is a sequence.
(a) What is the name of this sequence, and why? 2
(b) Find the 25th term of the sequence. 2
(c) Write the series of this sequence and find the sum of the first 20 terms. 3
3.
Several triangular-shaped pieces of paper were cut and attached to a wall as shown in the picture.
(a) Determine the number of pieces that will be in the 5th row of the wall. 3
(b) How many more pieces will the 7th row have compared to the 5th row? 2
(c) Find the total number of pieces attached up to the 6th row of the wall. 2
4. \frac{\log_ky}{p^2+pq+q^2} = \frac{\log_ky}{q^2+qr+p^2} = \frac{\log_kz}{r^2+rp+p^2} and Q = m^{4b}.n^{8+2b}-m^{7b}.n^{5-b}
(a) If m = n = 1 and b = 0 , find the value of Q . 1
(b) Show that x^{p-q}.y^{q-r}.z^{r-p}=1 . 3
(c) If Q = 0 , prove that b\log_k\left(\frac{m}{n}\right) = \log_k n . 3
5. 
(a) Determine the sound level of the sound device. 3
(b) If the sound level of the device increases by 20 decibels, check whether the intensity of the modified sound will be 100 times the previous level. 4
6. The equations 3x – 5y = 7 and 6x + 10y = 14 form a system of equations.
(a) Explain whether the system of equations is consistent/inconsistent, dependent/independent, and determine the number of solutions. 3
(b) Solve the system using the cross-multiplication method. 4
7. Mr. Rafiq bought some geometry boxes from a wholesale shop for 60,000 Taka. At another shop, he found each geometry box for 3 Taka less and bought the same amount in Taka but received 35 more geometry boxes.
(a) How many geometry boxes did Mr. Rafiq initially buy? 3
(b) What was the price of each geometry box? 2
(c) At what price per box should he sell them to make a profit of 15,000 Taka in total? 2
8. A bamboo pole broke in such a way that the unbroken part formed a 45° angle with the standing portion and touched the ground 10 meters away from the base.
(a) What is the total length of the bamboo? 3
(b) If the broken part makes a 60° angle with the ground, at what height did the bamboo break? 4
9. A mountain has a height of 8.848 kilometers. The peak of the mountain forms an angle of 2.25° from a distant location. Ratan was trying to view the mountain from that location at 10:35 a.m.
(a) Determine the distance from the mountain to that location. 3
(b) Express the angle between the hour and minute hands of the clock at that time in radians. 4
10. A table of frequency distribution of marks obtained by 125 ninth-grade students in mathematics is provided.
| Obtained number | 10 – 20 | 20 – 30 | 30 – 40 | 40 – 50 | 50 – 60 | 60 – 70 |
| Students number | 10 | 17 | 30 | 40 | 20 | 8 |
(a) What is the average mark of the ninth-grade students in mathematics? 3
(b) Determine the mean deviation of the data using the assumed mean method or the short-cut method. 4
11. Moti and Sumon spend 40 Taka and 60 Taka per day, respectively, on tiffin.
(a) Calculate the mean deviation of Moti’s and Sumon’s expenditures. 3
(b) Show that the mean deviation of the two values is half of the range. 4
