Mongolia · Grade 12 · Practice Sheet 11

1. 1.

   Find the gravitational potential energy of a 26 kg object raised 23 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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2. 2.

   A 22 kg object moves at 20 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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3. 3.

   A force of 301 N acts on an area of 8.5 m². Find the pressure.

   Formula:Pressure

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

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4. 4.

   A device runs at 118 V drawing 7.1 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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5. 5.

   Find the momentum of a 43 kg object moving at 30 m/s.

   Formula:Momentum

   $p = mv$

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6. 6.

   An object with initial velocity 12 m/s accelerates at 3.9 m/s² for 6 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

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7. 7.

   A cone has base radius 5 cm and height 16 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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8. 8.

   A current of 1.4 A flows through a 4 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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9. 9.

   A body starts at 18 m/s and accelerates at 3.5 m/s² for 9 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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10. 10.

    Solve using the quadratic formula: x² − 5x + 6 = 0.

    Formula:Quadratic Formula

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

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11. 11.

    A population of 3,000 grows 3% per year. Find its size after 2 years (nearest whole number).

    Formula:Exponential Growth

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

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12. 12.

    Find the force needed to accelerate a 18 kg mass at 8.9 m/s².

    Formula:Newton's Second Law

    $F = ma$

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13. 13.

    Two masses 4,100 kg and 820 kg are 13 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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14. 14.

    ₮1,400 is invested at 6% 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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15. 15.

    Find the population standard deviation of: 14, 9, 9, 9, 7 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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16. 16.

    A device runs at 231 V drawing 4.6 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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17. 17.

    Find the momentum of a 42 kg object moving at 10 m/s.

    Formula:Momentum

    $p = mv$

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18. 18.

    A population of 8,600 grows 2% per year. Find its size after 7 years (nearest whole number).

    Formula:Exponential Growth

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

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19. 19.

    A 35 kg object moves at 9 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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20. 20.

    An object with initial velocity 8 m/s accelerates at 2 m/s² for 6 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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