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Class 9 Math Preparation Strategies
Mathematics
Time: 3 hours Full Marks: 100
Section A: Objective (25 Marks)
Multiple Choice Questions: Write the correct answer in your answer sheet
1 × 15 = 15
1. Fibonacci was —-
(a) Mathematician
(b) Statistician
(c) Physicist
(d) Chemist
2. What is the sum of n natural numbers?
(a) S_n=\frac{n(n+1)}2
(b) S_n=\frac{(n+1)(n+2)}2
(c) S_n=\frac{n^2(n+2)}3
(d) S_n=\frac{n(n+3)}2
3. If the general term of a sequence is \frac{1}{3^n} , what is the second term?
(a) \frac{1}{6}
(b) \frac{1}{3}
(c) \frac{4}{9}
(d) \frac{1}{9}
4. The base of an exponent and the base of log are —–
i The same
ii Equal
iii Different
Which of the following is correct?
(a) i and ii
(b) ii and iii
(c) i and iii
(d) i ii and iii
5. Under what condition is b^n always positive for all values of n?
(a) b > 0
(b) b < 0
(c) b = 0
(d) b ≠ 1
6. \log_a(AB) = Which of the following?
(a) \log_aA\times\log_bB
(b) \log_aA+\log_bB
(c) \log_aA-\log_bB
(d) \log_aA÷\log_bB
7. Which of the following points is located on the x-axis?
(a) (2, 0)
(b) (-3, 5)
(c) (0, 3)
(d) (-2, -2)
8. How many primary methods are there for solving linear equations with two variables?
(a) 2
(b) 3
(c) 4
(d) 5
Based on the following information, answer questions 9 and 10:
9. What is the length of BC?
(a) 9 cm
(b) 29 cm
(c) 39 cm
(d) 49 cm
Class nine math for annual exam part 1
10. What is the value of sin ∠BAC?
(a) \frac{9}{40}
(b) \frac{9}{41}
(c) \frac{40}{41}
(d) \frac{81}{41}
11. If a right-angled triangle is formed with sides of 17 cm, 8 cm, and 15 cm, what will be the length of the hypotenuse?
(a) 8
(b) 13
(c) 17
(d) 23
12. Which of the following distances do the hands of a wall clock traverse?
(a) Linear distance
(b) Perpendicular distance
(c) Angular distance
(d) Parallel distance
13. Dividing a complete rotation by 360 results in what kind of angular distance?
(a) 1′ (minute)
(b) 10° (degree)
(c) 1” (second)
(d) 1c (radian)
14. Mushfiq’s runs in 10 matches are: 56, 30, 26, 37, 78, 65, 28, 48, 54, 16. What is the median of his runs?
(a) 72.5
(b) 42.5
(c) 70
(d) 77.5
15. Last year’s minimum temperature was 11°C, and the temperature range was 33°C. What was the maximum temperature last year?
(a) 42°C
(b) 32°C
(c) 35°C
(d) 44°C
Answer in one word: 1 × 10 = 10
16. If the n-th term, a_n = 1, what type of sequence is it?
17. What is the tenth term of the sequence 0, 1, 1, 2, 3, 5, ……?
18. Write the formula for \log_bb .
19. In a^x = b^x , what is the condition for a = b?
20. In a graph, what does each line of a linear equation represent?
21. In a right-angled triangle, the base and height are named with respect to what?
22. Which type of angle has an undefined measure?
23. In the standard position, what is the value of tan ( \theta \) relative to the point (15, 0)?
24. What is the term for the difference between the central value and other data points?
25. How is the range of measurement represented?
Section B: Short and Descriptive (75 Marks)
1. Answer the following questions: 2 × 13 = 26
(a) In an arithmetic sequence, if the fifth term is 16 and the ninth term is 28, find the first term and common difference.
(b) For a sequence with the sum of the first n terms as n(n + 1), what is the sum of the first 10 terms?
(c) Find the general term of the sequence \frac{1}{2}, \frac{1}{2^2}, \frac{1}{2^3}, \frac{1}{2^4} , …
(d) If \log_{\sqrt8}x = 3\frac{1}{3} , find the value of \( x \).
(e) Show that an earthquake measuring 8 on the Richter scale is 1000 times stronger than one measuring 5.
(f) Verify the solvability of the equations x + y = p + q and px - qy = p^2 - q^2 .
(g) Determine the nature of the roots of the equation x^2 - 3 and solve it.
(g) \Delta ABC is a right-angled triangle with \angle B = 90^\circ , AC = 13 cm, BC = 12 cm, and \angle BAC = \theta . Find the value of \sin \theta .
(h) What is the value of \cot 90^\circ \cdot \tan 0^\circ \cdot \sec 30^\circ \cdot \csc 60^\circ ?
(i) Express 270^\circ in radians.
(j) Express the point P(1, -3) in terms of (r, \theta) .
(k) Find the range of the data set 48, 70, 58, 40, 43, 55, 63, 46, 56, 44 .
(l) If the arithmetic mean of the data series 50, 60, 45, 35, 75, 85, 90 is 62.86 , find the mean deviation.
2. Observe the following sequences:
(i) 1 − 3 + 9 − 27 + …..
and (ii) 54 + 18 + 6 + … + \frac{2}{81}
(a) Find the sum of the first 7 terms of sequence (i). 3
(b) Find the sum of sequence (ii). 4
3. Anika and Mim are two sisters. Their parents decide to give them pocket money for 10 days using two different methods. On the first day, both Anika and Mim receive 2 taka each. Anika receives double the previous day’s amount each day, while Mim receives 2 taka more than the previous day.
(a) Determine who receives more pocket money on the fifth day, Anika or Mim. 3
(b) Verify whether Anika receives 18 times more total pocket money than Mim over the first 10 days. 4
4. M=4^{2p+1} and L=\frac{q^{x+1}}{(q^x)^{x-1}} \div \frac{(3q)^{x+1}}{(q^{x-1})^{x+1}} \div q^{-2}
(a) If M = 128 , find the value of p . 3
(b) If q = 3 , what is the value of L ? 4
5. The intensity of sound emitted from a motorcycle is 3.52 \times 10^{-5} W per square meter. An autorickshaw emits 60 decibels of sound, and a rickshaw emits 50 decibels of sound.
(a) How many decibels of sound are emitted from the motorcycle? 2
(b) What is the intensity of sound emitted per square meter from the autorickshaw? 2
(c) Compare the sound intensity between the autorickshaw and the rickshaw. 3
6. Kona bought 5 guava saplings and 4 lemon saplings for 410 taka at a tree fair. Raju bought 4 guava saplings and 5 lemon saplings at the same rate for 400 taka. The price of each lemon sapling is 10 taka less than each guava sapling.
(a) Form a system of equations based on the given information. 1
(b) Solve the system of equations obtained in (a) using the cross-multiplication method. 3
(c) Solve the system of equations obtained in (a) using the elimination method. 3
7. A fruit seller bought mangoes at 20 taka each and bananas at 10 taka each, spending a total of 1000 taka. He sold each mango and banana at a profit of 2 taka, making a total profit of 120 taka.
(a) Form two equations based on the information provided. 3
(b) How many mangoes and bananas did the fruit seller buy? 4
8. A student was standing at point P in front of a tower. The angle of elevation to the top of the tower from point P is 30°. Moving 50 meters closer to the tower to point Q, the angle of elevation becomes 45°.
(a) Represent the information with a diagram. 3
(b) Find the height of the tower. 4
9. Noyon went on a trip with his family from Dhaka to Cox’s Bazar in their own car. The radius of their car’s wheels is 0.6 meters, and the radius of the Earth is 6440 km.
(a) If Dhaka and Cox’s Bazar subtend an angle of 20° at the Earth’s center, find the distance between them. 3
(b) How many rotations will the car’s wheels make to cover the total distance from Dhaka to Cox’s Bazar? 4
10. Shakib’s runs in eight matches are as follows:
72, 55, 100, 67, 82, 40, 76, 80
(a) Calculate Shakib’s average runs. 2
(b) Show that Shakib’s median runs are higher than his average runs. 2
(c) Find the mean deviation from the median.
11. The run data of two batsmen over 6 matches is as follows:
| Tamim’s runs | 45 | 75 | 100 | 25 | 65 | 55 |
| Soumya’s runs | 102 | 20 | 85 | 35 | 10 | 35 |
(a) Calculate the range of runs for both batsmen. 2
(b) Find the mean, median, and mode of Tamim’s runs. 2
(c) Calculate the mean deviation from the mean, median, and mode for Tamim’s runs. 3
