Egypt · Grade 11 · Practice Sheet 39

1. 1.

   A population of 7,400 grows 5% per year. Find its size after 8 years (nearest whole number).

   Formula:Exponential Growth

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

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2. 2.

   A 21 kg object moves at 3 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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3. 3.

   Find the force needed to accelerate a 45 kg mass at 8.8 m/s².

   Formula:Newton's Second Law

   $F = ma$

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4. 4.

   Find the gravitational potential energy of a 26 kg object raised 17 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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5. 5.

   A cone has base radius 4 cm and height 19 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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6. 6.

   A right-angled triangle has legs of 14 cm and 4 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

   $c = \sqrt{a^2 + b^2}$

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7. 7.

   Two masses 5,400 kg and 180 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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8. 8.

   Find the momentum of a 40 kg object moving at 15 m/s.

   Formula:Momentum

   $p = mv$

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9. 9.

   Find the gravitational potential energy of a 41 kg object raised 6 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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10. 10.

    Find the sum of the first 18 terms of an arithmetic series with first term a = 2 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.

    A force of 301 N acts on an area of 4.6 m². Find the pressure.

    Formula:Pressure

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

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12. 12.

    A wave has frequency 146 Hz and wavelength 0.21 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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13. 13.

    Find the sum of the first 14 terms of an arithmetic series with first term a = 12 and common difference d = 6.

    Formula:Sum of an Arithmetic Series

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

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14. 14.

    A body starts at 6 m/s and accelerates at 2.2 m/s² for 5 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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15. 15.

    A device runs at 99 V drawing 4.5 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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16. 16.

    A wave has frequency 358 Hz and wavelength 2.8 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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17. 17.

    Find the momentum of a 56 kg object moving at 6 m/s.

    Formula:Momentum

    $p = mv$

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18. 18.

    Two masses 3,700 kg and 220 kg are 16 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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19. 19.

    A 29 kg object moves at 3 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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20. 20.

    Find the force needed to accelerate a 41 kg mass at 0.9 m/s².

    Formula:Newton's Second Law

    $F = ma$

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