9th Class Mathematics First half Book Paper

Q1. Multiple choice questions (Attempt all · 48 × 0.75 = 36)

1. For three sets, the central region of a Venn diagram represents:
   1. A ∪ B ∪ C
   2. A ∩ B ∩ C
   3. A − B
   4. A′
2. 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
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. Which one is the standard form of linear equation?
   1. $ax^2 + b = 0$
   2. ax + b = -c
   3. ax + b > 0
   4. ax + b = 0
5. log 125 can be written as:
   1. log 5
   2. 2 log 5
   3. 3 log 5
   4. 5 log 3
6. If a.b = 1, what is be called?
   1. multiplicative inverse of a
   2. additive identiy
   3. multiplicative identity
   4. self-multiplicative inverse
7. An ordered pair is written as:
   1. {a, b}
   2. (a, b)
   3. [a, b]
   4. a + b
8. To convert degrees into radians, multiply by:
   1. π/180
   2. 180/π
   3. 60
   4. 360
9. a/b + c/b equals:
   1. (a + c)/b
   2. (a + c)/2b
   3. ac/b
   4. a+c
10. The symbol “>” means:
    1. Less than
    2. Greater than
    3. Equal to
    4. Not equal to only
11. 5 log 2 - 2 log 5 is
    1. $\frac{(\log 2)^5}{(\log 5)^2}$
    2. $\frac{\log 2^5}{\log 5^2}$
    3. $\frac{\log 2^2}{\log 5^5}$
    4. $\frac{5}{2}log\frac{2}{5}$
12. Which of the following sets have the closure propetry w.r.t. multiplication?
    1. { -1 , -2 }
    2. { 0 , -1 }
    3. { 0 , 1 }
    4. ${ 1 , \sqrt{2} }$
13. The Venn diagram is used to represent:
    1. Numbers only
    2. Relations between sets
    3. Equations only
    4. Angles
14. Bearing of South is:
    1. 090°
    2. 180°
    3. 270°
    4. 360°
15. √(x²) is:
    1. x only
    2. ±x
    3. x²
    4. 2x
16. Solve: 2 < x < 6
    1. x < 2 or x > 6
    2. 2 < x < 6
    3. x ≤ 2
    4. x ≥ 6
17. Logarithmic methods are especially useful when numbers are:
    1. Very small or very large
    2. Equal to zero only
    3. Negative only
    4. Whole numbers only
18. A person walks 3.5 km/h for 12 hours. The total distance is:
    1. 36 km
    2. 40 km
    3. 42 km
    4. 45 km
19. If 52 people speak Arabic and 112 speak French, those who speak both are represented by:
    1. A ∪ F
    2. A ∩ F
    3. A − F
    4. F′
20. 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
21. The HCF–LCM relation is useful for finding:
    1. An unknown polynomial
    2. Angles only
    3. Logarithms only
    4. Coordinates only
22. Which one is the solution of $2(x + 6) \leq 3 (x + 4)$?
    1. $x \leq 0$
    2. $x \geq 0$
    3. $x \leq 24$
    4. $x \geq 24$
23. Scientific notation of 6.25 is:
    1. 6.25 × 10⁰
    2. 0.625 × 10¹
    3. 62.5 × 10⁻¹
    4. All represent same value, but standard form is A
24. $\sqrt[m]{\sqrt[n]{a}} = \ldots\ldots$
    1. $\sqrt[mn]{a}$
    2. $\sqrt[m+n]{a}$
    3. $\sqrt[m-n]{a}$
    4. $\sqrt[n]{\sqrt[m]{a}}$
25. The set containing all elements of A and B is called:
    1. Intersection
    2. Union
    3. Difference
    4. Complement
26. $- 3 - 3tan^2θ = ?$
    1. $3cosec^2θ$
    2. $-3cosec^2θ$
    3. $-3sec^2θ$
    4. $3sec^2θ$
27. x (2a + 3b + 7) + x (2a + 3b + 5) equals
    1. 2 x (2a + 3b + 6)
    2. 4 x (2a + 3b + 6)
    3. x (2a + 3b + 7)(2a + 3b + 5)
    4. (x + x) (2a + 3b + 12)
28. Which one is a strict inequality?
    1. $x + 3 \neq 0$
    2. 12x > 5
    3. $2y - 3 \leq 0$
    4. $4x + 5 \geq 0$
29. $log_b g^h$ is
    1. $g log_b h$
    2. $log_b (gh)$
    3. $(log_b g) × h$
    4. $h log_b g$
30. The expression $a^{1/2}$ is equivalent to:
    1. a²
    2. √a
    3. 1/a
    4. 2a
31. In the ordered pair (a, b), a is called the:
    1. Second element
    2. First element
    3. Range
    4. Relation
32. One degree is equal to:
    1. 30′
    2. 60′
    3. 90′
    4. 120′
33. 27x³ − 64 is:
    1. (3x)³ − 4³
    2. 27(x − 64)
    3. (27x)³ − 4³
    4. 3x³ − 4³
34. Solve: 3 − x ≥ 0
    1. x ≥ 3
    2. x ≤ 3
    3. x > 3
    4. x < −3
35. Which logarithm is undefined in the real number system?
    1. log₂8
    2. log₅1
    3. log₃(−9)
    4. log₇49
36. $\text{If } z < 0 \text{ and } x < y \Rightarrow \text{ then:}$
    1. $\ xz < yz$
    2. $\ xz > yz$
    3. $\ xz = yz$
    4. $\ xz \leq yz$
37. If n(A) = 23, n(A ∪ B) = 44 and n(A ∩ B) = 2, then n(B) is:
    1. 19
    2. 21
    3. 23
    4. 25
38. Angle of elevation and corresponding angle of depression between parallel horizontals are:
    1. Complementary
    2. Equal
    3. Supplementary
    4. Always 90°
39. 8a³ + b³ can be written as:
    1. (2a)³ + b³
    2. 2a³ + b³
    3. (8a)³ + b³
    4. a³ + (2b)³
40. Which property is used when the same number is added to both sides of an equation?
    1. Addition property
    2. Multiplication property
    3. Division property
    4. Transitive property
41. If log₅25 = 2, then in exponential form:
    1. 2⁵ = 25
    2. 5² = 25
    3. 25² = 5
    4. 5² = 10
42. $\left(\frac{25}{16}\right)^{-\frac{1}{2}}$
    1. $\frac{5}{4}$
    2. $\frac{4}{5}$
    3. $\frac{-5}{4}$
    4. $\frac{-4}{5}$
43. If R = {(1,2),(2,3)}, then R⁻¹ is:
    1. {(1,2),(2,3)}
    2. {(2,1),(3,2)}
    3. {(1,3),(2,2)}
    4. {(3,1),(2,2)}
44. Area of a sector is:
    1. rθ
    2. ½r²θ
    3. πr²
    4. 2πr
45. 4x² + 12x + 9 is:
    1. (2x + 3)²
    2. (2x − 3)²
    3. (4x + 3)²
    4. (x + 9)²
46. The equation: ∣x∣=k,k>0
    1. No solution
    2. One solution
    3. Two solutions
    4. Infinite solutions
47. $\log_b M-\log_b N \text{ is}$
    1. $\frac{\log_b M}{\log_b N}$
    2. $\log_b\left(\frac{M}{N}\right)$
    3. $\log_N M$
    4. $\frac{\log_b N}{\log_b M}$
48. Which property does NOT generally hold for subtraction?
    1. Closure
    2. Commutative
    3. Distributive
    4. Associative under addition