Uganda · Grade 11 · Practice Sheet 3

1. 1.

   A body starts at 12 m/s and accelerates at 1.1 m/s² for 7 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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2. 2.

   A triangle has sides a = 12 cm and b = 13 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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3. 3.

   Find the force needed to accelerate a 28 kg mass at 3.8 m/s².

   Formula:Newton's Second Law

   $F = ma$

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4. 4.

   A wave has frequency 100 Hz and wavelength 1.8 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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5. 5.

   Find the population standard deviation of: 20, 20, 11, 9, 20 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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6. 6.

   Find the sum of the first 8 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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7. 7.

   Two masses 4,400 kg and 310 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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8. 8.

   A 19 kg object moves at 15 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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9. 9.

   A population of 7,600 grows 10% per year. Find its size after 5 years (nearest whole number).

   Formula:Exponential Growth

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

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10. 10.

    A triangle has sides a = 11 cm and b = 9 cm with an included angle C = 90°. 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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11. 11.

    A device runs at 195 V drawing 8.2 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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12. 12.

    A cone has base radius 9 cm and height 21 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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13. 13.

    Find the gravitational potential energy of a 11 kg object raised 31 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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14. 14.

    USh 3,700 is invested at 8% compound interest per annum for 4 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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15. 15.

    A force of 160 N acts on an area of 1.6 m². Find the pressure.

    Formula:Pressure

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

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16. 16.

    A force of 70 N moves an object 12 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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17. 17.

    An object with initial velocity 14 m/s accelerates at 2.7 m/s² for 5 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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18. 18.

    Find the momentum of a 53 kg object moving at 10 m/s.

    Formula:Momentum

    $p = mv$

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19. 19.

    Find the population standard deviation of: 8, 6, 14, 3, 16 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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20. 20.

    A 10 kg object moves at 16 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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