Taiwan · Grade 12 · Practice Sheet 26

1. 1.

   A wave has frequency 175 Hz and wavelength 4.47 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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2. 2.

   A current of 3.8 A flows through a 8 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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3. 3.

   Find the momentum of a 22 kg object moving at 14 m/s.

   Formula:Momentum

   $p = mv$

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4. 4.

   A 14 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.

   Find the sum of the first 15 terms of an arithmetic series with first term a = 5 and common difference d = 6.

   Formula:Sum of an Arithmetic Series

   $S_n = \tfrac{n}{2}\left(2a + (n-1)d\right)$

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6. 6.

   An object with initial velocity 13 m/s accelerates at 2.2 m/s² for 4 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

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7. 7.

   Find the volume of a sphere of radius 4 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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8. 8.

   A force of 176 N acts on an area of 1.4 m². Find the pressure.

   Formula:Pressure

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

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9. 9.

   Solve using the quadratic formula: x² − 9x + 18 = 0.

   Formula:Quadratic Formula

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

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10. 10.

    A force of 120 N moves an object 11 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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11. 11.

    A population of 1,600 grows 5% 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 gravitational potential energy of a 24 kg object raised 37 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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13. 13.

    Find the population standard deviation of: 12, 18, 16, 16, 13 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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14. 14.

    A body starts at 12 m/s and accelerates at 1.8 m/s² for 12 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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15. 15.

    A 31 kg object moves at 4 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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16. 16.

    Find the sum of the first 12 terms of an arithmetic series with first term a = 8 and common difference d = 1.

    Formula:Sum of an Arithmetic Series

    $S_n = \tfrac{n}{2}\left(2a + (n-1)d\right)$

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17. 17.

    Find the population standard deviation of: 15, 19, 5, 5, 7 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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18. 18.

    A device runs at 89 V drawing 5.7 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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19. 19.

    Find the momentum of a 36 kg object moving at 28 m/s.

    Formula:Momentum

    $p = mv$

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20. 20.

    A force of 371 N acts on an area of 7.3 m². Find the pressure.

    Formula:Pressure

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

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