Kenya · Grade 12 · Practice Sheet 26

1. 1.

   A wave has frequency 63 Hz and wavelength 1.14 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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2. 2.

   Two masses 5,300 kg and 400 kg are 8 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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3. 3.

   Find the sum of the first 7 terms of a geometric series with first term a = 6 and common ratio r = 3.

   Formula:Sum of a Geometric Series

   $S_n = \dfrac{a(r^{n} - 1)}{r - 1}$

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4. 4.

   A force of 20 N moves an object 14 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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5. 5.

   Find the gravitational potential energy of a 45 kg object raised 15 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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6. 6.

   An object with initial velocity 6 m/s accelerates at 3.8 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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7. 7.

   Find the sum of the first 20 terms of an arithmetic series with first term a = 6 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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8. 8.

   A force of 76 N moves an object 20 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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9. 9.

   A wave has frequency 184 Hz and wavelength 3.14 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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10. 10.

    A force of 285 N acts on an area of 1.7 m². Find the pressure.

    Formula:Pressure

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

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11. 11.

    Find the gravitational potential energy of a 49 kg object raised 33 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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12. 12.

    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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13. 13.

    A population of 3,800 grows 8% per year. Find its size after 7 years (nearest whole number).

    Formula:Exponential Growth

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

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14. 14.

    A force of 216 N acts on an area of 6.4 m². Find the pressure.

    Formula:Pressure

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

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15. 15.

    KSh 4,000 is invested at 3% 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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16. 16.

    Find the momentum of a 46 kg object moving at 7 m/s.

    Formula:Momentum

    $p = mv$

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17. 17.

    Two masses 5,600 kg and 280 kg are 3 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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18. 18.

    A wave has frequency 320 Hz and wavelength 3.64 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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19. 19.

    Find the momentum of a 45 kg object moving at 3 m/s.

    Formula:Momentum

    $p = mv$

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20. 20.

    Find the population standard deviation of: 5, 17, 20, 17, 3 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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