Uganda · Grade 12 · Practice Sheet 29

1. 1.

   In a triangle, a = 7, b = 8 and the included angle C = 40°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

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

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2. 2.

   USh 2,000 is invested at 8% compound interest per annum for 2 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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3. 3.

   Two masses 1,300 kg and 780 kg are 13 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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4. 4.

   A cone has base radius 5 cm and height 9 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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5. 5.

   A force of 261 N acts on an area of 1.4 m². Find the pressure.

   Formula:Pressure

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

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6. 6.

   Two masses 7,700 kg and 500 kg are 11 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 11 kg object moves at 2 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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8. 8.

   A population of 5,400 grows 5% per year. Find its size after 3 years (nearest whole number).

   Formula:Exponential Growth

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

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9. 9.

   Find the momentum of a 17 kg object moving at 16 m/s.

   Formula:Momentum

   $p = mv$

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10. 10.

    A force of 281 N acts on an area of 0.7 m². Find the pressure.

    Formula:Pressure

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

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11. 11.

    Find the force needed to accelerate a 25 kg mass at 7 m/s².

    Formula:Newton's Second Law

    $F = ma$

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12. 12.

    A wave has frequency 245 Hz and wavelength 4.09 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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13. 13.

    A force of 80 N moves an object 21 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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14. 14.

    A device runs at 54 V drawing 4.6 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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15. 15.

    A current of 3.3 A flows through a 16 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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16. 16.

    A force of 70 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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17. 17.

    Find the force needed to accelerate a 2 kg mass at 7.6 m/s².

    Formula:Newton's Second Law

    $F = ma$

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18. 18.

    A 2 kg object moves at 25 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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19. 19.

    USh 1,000 is invested at 5% 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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20. 20.

    A current of 5.1 A flows through a 22 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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