Vietnam · Grade 12 · Practice Sheet 20

1. 1.

   Find the gravitational potential energy of a 11 kg object raised 21 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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2. 2.

   Find the momentum of a 34 kg object moving at 20 m/s.

   Formula:Momentum

   $p = mv$

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3. 3.

   Find the sum of the first 12 terms of an arithmetic series with first term a = 1 and common difference d = 7.

   Formula:Sum of an Arithmetic Series

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

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4. 4.

   A device runs at 103 V drawing 1.3 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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5. 5.

   VND 3,700 is invested at 8% 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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6. 6.

   Find the momentum of a 51 kg object moving at 14 m/s.

   Formula:Momentum

   $p = mv$

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7. 7.

   VND 700 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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8. 8.

   Find the force needed to accelerate a 54 kg mass at 5 m/s².

   Formula:Newton's Second Law

   $F = ma$

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9. 9.

   Two masses 6,100 kg and 350 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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10. 10.

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

    Formula:Sum of an Arithmetic Series

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

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11. 11.

    A force of 330 N acts on an area of 7.1 m². Find the pressure.

    Formula:Pressure

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

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12. 12.

    Solve using the quadratic formula: x² − 7x + 10 = 0.

    Formula:Quadratic Formula

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

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13. 13.

    A 38 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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14. 14.

    A wave has frequency 84 Hz and wavelength 2.4 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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15. 15.

    A device runs at 30 V drawing 9.6 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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16. 16.

    Find the force needed to accelerate a 38 kg mass at 2.6 m/s².

    Formula:Newton's Second Law

    $F = ma$

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17. 17.

    Find the sum of the first 11 terms of an arithmetic series with first term a = 2 and common difference d = 4.

    Formula:Sum of an Arithmetic Series

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

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18. 18.

    A body starts at 6 m/s and accelerates at 2 m/s² for 10 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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19. 19.

    Find the population standard deviation of: 5, 13, 5, 16, 6 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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20. 20.

    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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