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Federal (FBISE) · Quarter book test · Free

9th Class Mathematics 2nd Quarter Book Paper

40 marks · 1 hour · 28 questions. Covers: 04. Factorization and Algebraic Manipulation, 05. Linear Equations and Inequalities, 06. Trigonometry and Bearing.

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9th Class Mathematics 2nd Quarter Book Paper

9th Class · Mathematics · Federal (FBISE)

Name: ____________Roll No: ________Class/Section: ________Date: ________Total marks: 40Time: 1 hour

Q1. Multiple choice questions (Attempt all · 12 × 1 = 12)

  1. If a tower is 100 m high and tan θ = 1, horizontal distance from tower is:
    1. 50 m
    2. 100 m
    3. 150 m
    4. 200 m
  2. Which one is the standard form of linear equation?
    1. ax2+b=0ax^2 + b = 0
    2. ax + b = -c
    3. ax + b > 0
    4. ax + b = 0
  3. x² − 9 can be factorized as:
    1. (x − 3)(x + 3)
    2. (x − 9)(x + 1)
    3. (x − 3)²
    4. (x + 3)²
  4. To convert degrees into radians, multiply by:
    1. π/180
    2. 180/π
    3. 60
    4. 360
  5. The symbol “>” means:
    1. Less than
    2. Greater than
    3. Equal to
    4. Not equal to only
  6. a/b + c/b equals:
    1. (a + c)/b
    2. (a + c)/2b
    3. ac/b
    4. a+c
  7. Bearing of South is:
    1. 090°
    2. 180°
    3. 270°
    4. 360°
  8. Solve: 2 < x < 6
    1. x < 2 or x > 6
    2. 2 < x < 6
    3. x ≤ 2
    4. x ≥ 6
  9. √(x²) is:
    1. x only
    2. ±x
    3. x²
    4. 2x
  10. A bearing of 050° means:
    1. 50° clockwise from north
    2. 50° clockwise from south
    3. 50° anticlockwise from east
    4. 50° clockwise from west
  11. Which one is the solution of 2(x+6) ≤3(x+4)2(x + 6) \leq 3 (x + 4)?
    1. x ≤0x \leq 0
    2. x ≥ 0x \geq 0
    3. x ≤24x \leq 24
    4. x ≥ 24x \geq 24
  12. The HCF–LCM relation is useful for finding:
    1. An unknown polynomial
    2. Angles only
    3. Logarithms only
    4. Coordinates only

Q2. Short questions (Attempt any 8 of 12 · 8 × 2 = 16)

  1. Factorize the following polynomial. 2x2y3−6x2y2+2xy32x^2y^3 - 6x^2y^2 + 2xy^3
  2. Check whether the given value of each variable satisfies the inequality. 4−2x≤9;x=−34 - 2x \leq 9; x = -3
  3. Convert in radian. Use π= 3.1416. 60∘60^\circ
  4. Find the mission factor in the following. (5x2+12x−9)=()(x+3)(5x^2 + 12x - 9) = ( ) (x + 3)
  5. Solve the following. 5−∣5y+1∣=−95 -|5y + 1| = -9
  6. Find value of θ for the following question in the interval 0≤θ≤π2 0 \leq θ \leq \frac {\pi}{2}. sec⁡2θ−2tan⁡2θ=0 {\sec^2\theta - 2\tan^2\theta} = 0
  7. Simplify the following (where the expression in the denominator are non-zero)12x−3y−x+y4x2−9y2\frac{1}{2x - 3y} - \frac{x + y}{4x^2 - 9y^2}
  8. Reduce the radical equation into simple linear equation then find their solution. In case of extraneous solution, write ϕ for solution set. 12−y+1=14 12 -\sqrt{y + 1} = 14
  9. Convert in radian. Write the answer in term of π. 120∘120^\circ
  10. Factorize the following polynomial. m2−2m−15m^2 - 2m - 15
  11. Solve the following inequalities. 3x−2<7,x∈N3x - 2 < 7, x \in N
  12. Find radian measure of the central angle of a circular sector for the following data. A=100 cm2, ℓ=10 cmA = 100\, \text{cm}^2, \, \ell = 10\, \text{cm}

Q3. Long questions (Attempt any 3 of 4 · 3 × 4 = 12)

  1. The area of a right triangle is 50 cm². One of its angles is 45⁰. Find the lengths of the sides and hypotenuse of the triangle.
  2. Find the HCF of the following by division method. 2x3+6x2+x+3,3x3+9x2−2x−6,x3+3x2+2x+6 2x^3 + 6x^2 + x + 3, 3x^3 + 9x^2 - 2x - 6, x^3 + 3x^2 + 2x + 6
  3. Solve the following. 5x−4−410\frac{\sqrt{5x - 4} - 4}{10}
  4. Prove the relation by using basic trigonometric identities. sec2θ+cosec2θ=sec2θcosec2θsec^2 θ + cosec^2 θ = sec^2 θ cosec^2 θ