) +5√( - BAF Shaheen College Dhaka

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B A F Shaheen College Dhaka

Practice

Half Yearly Examination- 2020 Class: IX (English Version)

Creative Question Subject: Higher Mathematics

Time:2:35Hours Full marks :50 (Answer 5 questions taking 2 from group A, taking 2 from group B and taking 1 from group C)

Group –A : Algebra 1. f(a)= ^5𝑎−9

𝑎+2

a. Find the value of f(-3) and f(-5). (2) b. Show that f(a) is one-one function, find the domain of the function. (4) c. Find the value of 𝑓⁻¹(a), also find the range of the function f(a). (4) 2. P(x)= -𝑥²+15x+10𝑥³+9 and Q(x)= 𝑥³+𝑥²-6x.

a. Write the P(x) as standard expression of x and find the value of p(-1). (2) b. Factorize P(x). (4) c. Express ^𝑥

2+𝑥−1

𝑄(𝑥) in partial fraction. (4)

3. 6

√(

^2𝑥

𝑥−1

)

+5

√(

^𝑥−1

2𝑥

)

= 13; is an algebraic equation.

a. Taking ^2𝑥

𝑥−1 =𝑎² , write the given equation. (2) b. Solve the obtained equation. (4) c. Verify the correctness of the solution. (4) Group-B: Geometry

4. Sajid draw an angle which is equal to one angle of an equilateral triangle without any protector.

a. What is the measurement of the angle that he draw? Draw it. (2) b. If the base a, the height h, and the angle he draw are given then draw a triangle using the data. (4) c. For the same height and angle if the length of a median is given then draw the triangle. (4) 5. A(2,-4), B=(-4,4)and C=(3,3) are three vertices of a triangle.

a. Draw the triangle on a graph paper (2) b. What type of triangle is it? Justify. (4) c. Find the area of the triangle determining the length of the sides. (4) 6. A quadrilateral ABCD where the value of four vertices are A(0,-1), B(-2,3), C(6,7), D(8,a).

a. Find the area of the triangle ABC considering the points are arranged in anti clockwise. (2) b. If the area of the quadrilateral is 40 square unit then what is the value of a?(a is an integer). (4) c. What type of quadrilateral does it appear to be? Justify your opinion by calculation. (4)

Group-C: Trigonometry

7. The wheel of a car moving from Dhaka to Khulna revolves 720 times in a minute. The radius of the wheel is 0.25 meter.

2

a. Find the circumference of the wheel (2) b. Find the speed of the car. (4) c. If the distance of Dhaka and Khulna subtends 2⁰ angle at the center of the earth, find the time required to go from Dhaka to Khulna (The radius of the earth is 6440 km) (4) 8. Solve the given trigonometric problem.

a. cosA = ¹

2 and sinA is negative. Find the value of sinA and tanA. (2) b. Prove that

√

^{1+𝑐𝑜𝑠𝐴}

1−𝑐𝑜𝑠𝐴 = cosecA+cotA =

√

^{𝑠𝑒𝑐𝐴+1}

𝑠𝑒𝑐𝐴−1 (4) c. Show that :

i. se𝑐⁴A-se𝑐²A=ta𝑛⁴A + ta𝑛²𝐴. (2×2=4) ii. tanA + cotA = secA.cosecA