Vietnam · Grade 12 · Practice Sheet 7

1. 1.

   A force of 51 N moves an object 5 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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2. 2.

   A body starts at 7 m/s and accelerates at 4 m/s² for 11 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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3. 3.

   Solve using the quadratic formula: x² + 3x − 10 = 0.

   Formula:Quadratic Formula

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

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4. 4.

   Find the gravitational potential energy of a 39 kg object raised 10 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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5. 5.

   A cone has base radius 9 cm and height 8 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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6. 6.

   Two masses 1,900 kg and 560 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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7. 7.

   A current of 7.7 A flows through a 22 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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8. 8.

   Find the force needed to accelerate a 6 kg mass at 7.9 m/s².

   Formula:Newton's Second Law

   $F = ma$

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9. 9.

   A force of 46 N moves an object 23 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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10. 10.

    An object with initial velocity 7 m/s accelerates at 1.2 m/s² for 8 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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11. 11.

    A population of 8,600 grows 2% per year. Find its size after 6 years (nearest whole number).

    Formula:Exponential Growth

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

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12. 12.

    Find the population standard deviation of: 15, 11, 5, 8, 11 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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13. 13.

    Find the sum of the first 17 terms of an arithmetic series with first term a = 9 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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14. 14.

    Find the momentum of a 17 kg object moving at 21 m/s.

    Formula:Momentum

    $p = mv$

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15. 15.

    VND 900 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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16. 16.

    Find the momentum of a 11 kg object moving at 25 m/s.

    Formula:Momentum

    $p = mv$

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17. 17.

    A force of 53 N moves an object 34 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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18. 18.

    Two masses 6,400 kg and 270 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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19. 19.

    A device runs at 91 V drawing 7.8 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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20. 20.

    A current of 7.2 A flows through a 45 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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