France · Classe 11 · Practice Sheet 30

1. 1.

   A cylinder has radius 13 cm and height 9 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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2. 2.

   Two masses 7,900 kg and 160 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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3. 3.

   Find the sum of the first 5 terms of an arithmetic series with first term a = 6 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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4. 4.

   A cylinder has radius 9 cm and height 14 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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5. 5.

   A body starts at 3 m/s and accelerates at 1.5 m/s² for 4 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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6. 6.

   A device runs at 183 V drawing 2.4 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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7. 7.

   In a triangle, a = 6, b = 9 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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8. 8.

   A force of 29 N moves an object 39 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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9. 9.

   Solve using the quadratic formula: x² + 7x + 6 = 0.

   Formula:Quadratic Formula

   $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

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10. 10.

    Find the gravitational potential energy of a 22 kg object raised 10 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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11. 11.

    Two masses 1,900 kg and 170 kg are 10 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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12. 12.

    An object has mass 162 g and volume 30 cm³. Find its density.

    Formula:Density

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

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13. 13.

    A current of 7.7 A flows through a 24 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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14. 14.

    A body starts at 6 m/s and accelerates at 5.1 m/s² for 10 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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15. 15.

    A current of 1.6 A flows through a 11 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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16. 16.

    An object has mass 378.4 g and volume 44 cm³. Find its density.

    Formula:Density

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

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17. 17.

    Find the force needed to accelerate a 5 kg mass at 5.9 m/s².

    Formula:Newton's Second Law

    $F = ma$

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18. 18.

    Find the momentum of a 44 kg object moving at 4 m/s.

    Formula:Momentum

    $p = mv$

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19. 19.

    Solve using the quadratic formula: x² − 9x + 20 = 0.

    Formula:Quadratic Formula

    $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

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20. 20.

    €2,500 is invested at 3% 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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