Kenya · Grade 11 · Practice Sheet 3

1. 1.

   Find the momentum of a 53 kg object moving at 9 m/s.

   Formula:Momentum

   $p = mv$

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2. 2.

   Find the sum of the first 12 terms of an arithmetic series with first term a = 3 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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3. 3.

   A wave has frequency 387 Hz and wavelength 1.75 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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4. 4.

   An object with initial velocity 3 m/s accelerates at 3.4 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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5. 5.

   A wave has frequency 114 Hz and wavelength 1.1 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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6. 6.

   Two masses 1,900 kg and 710 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 32 kg object moves at 17 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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8. 8.

   KSh 500 is invested at 3% 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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9. 9.

   A triangle has sides a = 12 cm and b = 5 cm with an included angle C = 45°. Find its area (to 2 d.p.).

   Formula:Area of a Triangle (Sine Rule)

   $A = \tfrac{1}{2} ab\sin C$

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10. 10.

    In a triangle, a = 18, b = 11 and the included angle C = 80°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

    $c = \sqrt{a^2 + b^2 - 2ab\cos C}$

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11. 11.

    A population of 5,400 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.

    A device runs at 55 V drawing 1.4 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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13. 13.

    An object has mass 34.2 g and volume 9 cm³. Find its density.

    Formula:Density

    $\rho = \dfrac{m}{V}$

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14. 14.

    A 7 kg object moves at 23 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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15. 15.

    Find the momentum of a 30 kg object moving at 3 m/s.

    Formula:Momentum

    $p = mv$

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16. 16.

    An object with initial velocity 4 m/s accelerates at 4 m/s² for 7 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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17. 17.

    Find the force needed to accelerate a 59 kg mass at 1.8 m/s².

    Formula:Newton's Second Law

    $F = ma$

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18. 18.

    A device runs at 119 V drawing 8.3 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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19. 19.

    An object with initial velocity 15 m/s accelerates at 4.1 m/s² for 6 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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20. 20.

    Find the volume of a sphere of radius 7 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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