Mongolia · Grade 12 · Practice Sheet 25

1. 1.

   A force of 192 N acts on an area of 9.5 m². Find the pressure.

   Formula:Pressure

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

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2. 2.

   A 21 kg object moves at 12 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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3. 3.

   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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4. 4.

   Find the force needed to accelerate a 11 kg mass at 2.7 m/s².

   Formula:Newton's Second Law

   $F = ma$

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5. 5.

   Find the gravitational potential energy of a 2 kg object raised 32 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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6. 6.

   Find the population standard deviation of: 8, 7, 17, 14, 5 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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7. 7.

   A force of 298 N acts on an area of 1 m². Find the pressure.

   Formula:Pressure

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

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8. 8.

   Find the population standard deviation of: 13, 9, 7, 18, 5 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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9. 9.

   Find the force needed to accelerate a 23 kg mass at 2.8 m/s².

   Formula:Newton's Second Law

   $F = ma$

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10. 10.

    Find the sum of the first 14 terms of an arithmetic series with first term a = 10 and common difference d = 5.

    Formula:Sum of an Arithmetic Series

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

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11. 11.

    Find the population standard deviation of: 19, 5, 9, 19, 19 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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12. 12.

    A current of 5 A flows through a 44 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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13. 13.

    Find the sum of the first 8 terms of an arithmetic series with first term a = 3 and common difference d = 5.

    Formula:Sum of an Arithmetic Series

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

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14. 14.

    A force of 379 N acts on an area of 7.4 m². Find the pressure.

    Formula:Pressure

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

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15. 15.

    A wave has frequency 464 Hz and wavelength 4.84 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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16. 16.

    Two masses 8,300 kg and 560 kg are 15 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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17. 17.

    ₮1,400 is invested at 5% compound interest per annum for 3 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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18. 18.

    An object with initial velocity 1 m/s accelerates at 3.1 m/s² for 10 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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19. 19.

    ₮2,400 is invested at 6% compound interest per annum for 3 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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20. 20.

    Find the momentum of a 56 kg object moving at 10 m/s.

    Formula:Momentum

    $p = mv$

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