Mongolia · Grade 12 · Practice Sheet 8

1. 1.

   An object with initial velocity 8 m/s accelerates at 1.3 m/s² for 2 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

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2. 2.

   A cone has base radius 10 cm and height 13 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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3. 3.

   A current of 5.5 A flows through a 51 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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4. 4.

   A 16 kg object moves at 11 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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5. 5.

   A triangle has sides a = 8 cm and b = 11 cm with an included angle C = 30°. 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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6. 6.

   Solve using the quadratic formula: x² + 6x + 8 = 0.

   Formula:Quadratic Formula

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

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7. 7.

   Find the momentum of a 44 kg object moving at 15 m/s.

   Formula:Momentum

   $p = mv$

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8. 8.

   A device runs at 184 V drawing 3.2 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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9. 9.

   Find the momentum of a 17 kg object moving at 7 m/s.

   Formula:Momentum

   $p = mv$

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10. 10.

    ₮3,500 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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11. 11.

    An object with initial velocity 2 m/s accelerates at 2.6 m/s² for 2 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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12. 12.

    A force of 72 N moves an object 39 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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13. 13.

    A device runs at 175 V drawing 1.5 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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14. 14.

    A population of 3,000 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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15. 15.

    Find the gravitational potential energy of a 30 kg object raised 31 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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16. 16.

    Find the population standard deviation of: 17, 14, 4, 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.

    Solve using the quadratic formula: x² − 1x − 12 = 0.

    Formula:Quadratic Formula

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

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18. 18.

    A 35 kg object moves at 21 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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19. 19.

    A body starts at 2 m/s and accelerates at 5.3 m/s² for 11 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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20. 20.

    A wave has frequency 46 Hz and wavelength 1.81 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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