BAF Shaheen College Dhaka Creative Part

BAF Shaheen College Dhaka

Practice Half Yearly Exam 2020 Class: IX (English Version) Subject: General Mathematics

(Instruction: Answer 02 sets from Part-A, 02 sets from Part-B, 02 sets from Part-C and 01 set from Part-D) Creative Part

Time: 02 Hours 30 minutes Marks: 70 Part A (Algebra)

1. 2 and √2 are two numbers.

a) Define rational numbers with an example.

b) Is √2 a rational number? Explain the reason behind your answer.

c) Write two rational and two irrational numbers between 2 and √2 ?

2 4 4 2. 𝑓(𝑥) = 𝑥²+ 4𝑥 + 3

𝐴 = {𝑥𝜖 𝑵 ∶ 𝑥 𝑜𝑑𝑑 𝑛𝑢𝑚𝑏𝑒𝑟𝑠 𝑎𝑛𝑑 𝑥 < 6}

𝐵 = {𝑥𝜖 𝑵 ∶ 𝑥 𝑓𝑎𝑐𝑡𝑜𝑟𝑠 𝑜𝑓 21}

𝐶 = {𝑥𝜖 𝑵 ∶ 𝑥 𝑖𝑠 𝑎 𝑚𝑢𝑙𝑡𝑖𝑝𝑙𝑒 𝑜𝑓 7 𝑎𝑛𝑑 𝑥 < 35}

a) Find the value of 𝑓(0) 𝑎𝑛𝑑 𝑓(−1)

b) If the number of elements in A is n then show that P(A) has 2^𝑛 number of elements.

c) Show that 𝐴 × (𝐵 ∩ 𝐶) = (𝐴 × 𝐵) ∩ (𝐴 × 𝐶).

2 4 4 3. If 𝑥 = √5 + √6

a) Find the value of _𝑥¹.

b) What is the value of ^𝑥6_𝑥⁻¹₃ . c) Prove that, 𝑥⁶−_𝑥¹₆ = 1932√30 .

2 4 4 Part- B (Trigonometry and Mensuration)

4. Sin A=3/4

a) Draw the diagram of the triangle which satisfies the stem.

b) Find the value of Cos A and Tan A c) Prove that, _{𝐶𝑜𝑠𝑒𝑐 𝐴} ^{Sin 𝐴} +^{𝐶𝑜𝑠 𝐴}_{𝑆𝑒𝑐 𝐴} = 1

2 4 4 5. Using the trigonometric equation-

a) Find the value of sec²𝜃 − tan²𝜃 . b) Show that, ^{√1−𝑠𝑖𝑛𝜃}_{√1+𝑠𝑖𝑛𝜃}(𝑠𝑒𝑐𝜃 + 𝑡𝑎𝑛𝜃) = 1.

c) If 𝑠𝑒𝑐𝜃 + 𝑡𝑎𝑛𝜃 =⁵₂, then show that, 𝑠𝑒𝑐𝜃 − 𝑡𝑎𝑛𝜃 =²₅.

2 4 4 6. The hypotenuse of a right angle triangle is 13m. The height of the triangle is ¹²₅ times of the base.

a) Present the given information in a diagram.

b) What is the area of that triangle?

c) If a triangle has sides a=5m, b=4m and perimeter of 12m draw the triangle and find the area of this triangle.

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Part- C (Geometry)

7. The base of a triangle a= 5cm, adjacent acute angle ∠𝑥 = 40° and the difference of the other two sides is b=2cm.

a) Present the given information in figure.

b) Construct the triangle with your description of construction.

c) Draw a right angled triangle whose one of the right angle adjacent sides is ‘a’ and the difference of the hypotenuse and other side is ‘b’. Give necessary description of construction.

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8. The base adjacent two angles are 60° and 45° and the perimeter is 12 cm.

a) Draw a 135° angle with help of compass and scale.

b) According to stem construct a triangle with proper description.

c) Construct an equilateral triangle whose perimeter is equal to the perimeter of the given triangle. Give proper description of construction.

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9. In ∆𝑃𝑄𝑅, 𝑃𝑂 ⊥ 𝑄𝑅 𝑎𝑛𝑑 𝑃𝑄 = 𝑃𝑅 = 5𝑐𝑚 𝑎𝑛𝑑 𝑂𝑄 = 4𝑐𝑚

a) Find the length of PO.

b) Prove that, OQ=¹₂QR.

c) Prove that, PQ + PR > 2PO.

2 4 4 Part- D (Statistics)

10. The marks obtained by 30 students in annual exam are given-

78, 68, 61, 99, 69, 80, 83, 75, 62, 65,

77, 85, 75, 82, 98, 95, 85, 77, 80, 87,

81, 85, 90, 85. 75, 77, 81, 78, 92, 68.

a) Define arithmetic mean and mode.

b) Create a Frequency distribution table considering 5 as a class interval.

c) Draw a frequency polygon from the above data.

2 4 4 11. The frequency table of marks in Chemistry if given-

Class interval 31-40 41-50 51-60 61-70 71-80 81-90 91-100

Frequency 8 12 20 25 30 15 10

a) Find the lower limit of the mod class of the data.

b) Find median of the data.

c) Draw frequency polygon of the data.

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