China · Grade 11 · Practice Sheet 23

1. 1.

   A cylinder has radius 10 cm and height 7 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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2. 2.

   A device runs at 192 V drawing 4.5 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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3. 3.

   Find the population standard deviation of: 6, 6, 12, 20, 8 (to 2 d.p.).

   Formula:Standard Deviation (Population)

   $\sigma = \sqrt{\dfrac{\sum (x - \bar{x})^2}{n}}$

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4. 4.

   Find the force needed to accelerate a 16 kg mass at 8.9 m/s².

   Formula:Newton's Second Law

   $F = ma$

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5. 5.

   Find the gravitational potential energy of a 34 kg object raised 7 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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6. 6.

   Two masses 2,900 kg and 430 kg are 9 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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7. 7.

   Find the gravitational potential energy of a 30 kg object raised 5 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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8. 8.

   An object with initial velocity 1 m/s accelerates at 3.3 m/s² for 10 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

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9. 9.

   Find the momentum of a 43 kg object moving at 7 m/s.

   Formula:Momentum

   $p = mv$

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10. 10.

    Find the gravitational potential energy of a 17 kg object raised 30 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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11. 11.

    ¥2,500 is invested at 5% compound interest per annum for 5 years. Find the final amount (to 2 d.p.).

    Formula:Compound Interest

    $A = P\left(1 + \dfrac{r}{100}\right)^{t}$

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12. 12.

    Two masses 6,200 kg and 760 kg are 14 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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13. 13.

    A force of 190 N acts on an area of 5.2 m². Find the pressure.

    Formula:Pressure

    $P = \dfrac{F}{A}$

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14. 14.

    An object has mass 275 g and volume 50 cm³. Find its density.

    Formula:Density

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

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15. 15.

    A 4 kg object moves at 8 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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16. 16.

    Find the population standard deviation of: 17, 4, 13, 18, 14 (to 2 d.p.).

    Formula:Standard Deviation (Population)

    $\sigma = \sqrt{\dfrac{\sum (x - \bar{x})^2}{n}}$

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17. 17.

    An object with initial velocity 15 m/s accelerates at 3.6 m/s² for 3 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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18. 18.

    A triangle has sides a = 12 cm and b = 17 cm with an included angle C = 45°. Find its area (to 2 d.p.).

    Formula:Area of a Triangle (Sine Rule)

    $A = \tfrac{1}{2} ab\sin C$

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19. 19.

    Solve using the quadratic formula: x² − 1x − 20 = 0.

    Formula:Quadratic Formula

    $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

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20. 20.

    A triangle has sides a = 20 cm and b = 17 cm with an included angle C = 45°. Find its area (to 2 d.p.).

    Formula:Area of a Triangle (Sine Rule)

    $A = \tfrac{1}{2} ab\sin C$

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