Kuwait · Grade 11 · Practice Sheet 6

1. 1.

   A cone has base radius 8 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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2. 2.

   A force of 13 N moves an object 11 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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3. 3.

   In a triangle, a = 8, b = 8 and the included angle C = 100°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

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

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4. 4.

   Find the momentum of a 7 kg object moving at 28 m/s.

   Formula:Momentum

   $p = mv$

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5. 5.

   An object with initial velocity 3 m/s accelerates at 3.3 m/s² for 8 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

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6. 6.

   A force of 113 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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7. 7.

   A cylinder has radius 2 cm and height 12 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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8. 8.

   Find the sum of the first 11 terms of an arithmetic series with first term a = 11 and common difference d = 8.

   Formula:Sum of an Arithmetic Series

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

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9. 9.

   A device runs at 16 V drawing 2.7 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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10. 10.

    A current of 5.2 A flows through a 5 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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11. 11.

    Find the force needed to accelerate a 38 kg mass at 5.4 m/s².

    Formula:Newton's Second Law

    $F = ma$

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12. 12.

    Two masses 6,200 kg and 410 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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13. 13.

    An object has mass 158.4 g and volume 18 cm³. Find its density.

    Formula:Density

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

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14. 14.

    A device runs at 45 V drawing 7.9 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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15. 15.

    Find the force needed to accelerate a 42 kg mass at 8.3 m/s².

    Formula:Newton's Second Law

    $F = ma$

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16. 16.

    A 19 kg object moves at 7 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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17. 17.

    Two masses 5,700 kg and 250 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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18. 18.

    Find the sum of the first 18 terms of an arithmetic series with first term a = 6 and common difference d = 2.

    Formula:Sum of an Arithmetic Series

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

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19. 19.

    Find the sum of the first 4 terms of a geometric series with first term a = 2 and common ratio r = 2.

    Formula:Sum of a Geometric Series

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

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20. 20.

    Find the force needed to accelerate a 18 kg mass at 8.9 m/s².

    Formula:Newton's Second Law

    $F = ma$

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