Thailand · Grade 11 · Practice Sheet 6

1. 1.

   A cone has base radius 2 cm and height 20 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

   $V = \tfrac{1}{3} \pi r^2 h$

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2. 2.

   A population of 4,100 grows 5% per year. Find its size after 6 years (nearest whole number).

   Formula:Exponential Growth

   $N = N_0 (1 + r)^{t}$

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3. 3.

   Find the force needed to accelerate a 5 kg mass at 3.7 m/s².

   Formula:Newton's Second Law

   $F = ma$

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4. 4.

   A population of 7,700 grows 5% per year. Find its size after 3 years (nearest whole number).

   Formula:Exponential Growth

   $N = N_0 (1 + r)^{t}$

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5. 5.

   A 7 kg object moves at 18 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

   $KE = \tfrac{1}{2} m v^2$

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6. 6.

   A wave has frequency 173 Hz and wavelength 3.14 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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7. 7.

   In a triangle, a = 17, b = 7 and the included angle C = 60°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

   $c = \sqrt{a^2 + b^2 - 2ab\cos C}$

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8. 8.

   Find the momentum of a 32 kg object moving at 24 m/s.

   Formula:Momentum

   $p = mv$

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9. 9.

   Two masses 6,000 kg and 150 kg are 8 m apart. Find the gravitational force between them. (G = 6.674×10⁻¹¹)

   Formula:Newton’s Law of Gravitation

   $F = G\dfrac{m_1 m_2}{r^2}$

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10. 10.

    Find the gravitational potential energy of a 35 kg object raised 2 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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11. 11.

    An object has mass 70.5 g and volume 47 cm³. Find its density.

    Formula:Density

    $\rho = \dfrac{m}{V}$

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12. 12.

    A cone has base radius 11 cm and height 6 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

    $V = \tfrac{1}{3} \pi r^2 h$

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13. 13.

    Find the momentum of a 9 kg object moving at 25 m/s.

    Formula:Momentum

    $p = mv$

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14. 14.

    Find the volume of a sphere of radius 3 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

    $V = \tfrac{4}{3} \pi r^3$

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15. 15.

    A current of 5.2 A flows through a 24 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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16. 16.

    A wave has frequency 497 Hz and wavelength 2.5 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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17. 17.

    An object with initial velocity 8 m/s accelerates at 2.4 m/s² for 9 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

    $s = ut + \tfrac{1}{2}at^2$

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18. 18.

    A right-angled triangle has legs of 9 cm and 20 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

    $c = \sqrt{a^2 + b^2}$

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19. 19.

    A force of 35 N moves an object 5 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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20. 20.

    A wave has frequency 554 Hz and wavelength 3.52 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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