Algeria · Grade 11 · Practice Sheet 17

1. 1.

   Two masses 8,100 kg and 740 kg are 14 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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2. 2.

   In a triangle, a = 12, b = 10 and the included angle C = 60°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

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

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3. 3.

   Find the momentum of a 34 kg object moving at 18 m/s.

   Formula:Momentum

   $p = mv$

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4. 4.

   Two masses 8,200 kg and 890 kg are 6 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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5. 5.

   Find the sum of the first 4 terms of a geometric series with first term a = 1 and common ratio r = 3.

   Formula:Sum of a Geometric Series

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

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6. 6.

   Find the population standard deviation of: 3, 4, 4, 11, 11 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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7. 7.

   A body starts at 12 m/s and accelerates at 4.7 m/s² for 11 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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8. 8.

   Find the sum of the first 6 terms of an arithmetic series with first term a = 10 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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9. 9.

   A cone has base radius 12 cm and height 18 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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10. 10.

    Solve using the quadratic formula: x² − 5x + 4 = 0.

    Formula:Quadratic Formula

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

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11. 11.

    A force of 75 N moves an object 13 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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12. 12.

    An object has mass 79.2 g and volume 22 cm³. Find its density.

    Formula:Density

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

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13. 13.

    Find the momentum of a 27 kg object moving at 16 m/s.

    Formula:Momentum

    $p = mv$

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14. 14.

    A cone has base radius 9 cm and height 17 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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15. 15.

    A current of 6.6 A flows through a 46 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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16. 16.

    A force of 10 N moves an object 10 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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17. 17.

    A device runs at 190 V drawing 10 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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18. 18.

    A cylinder has radius 3 cm and height 22 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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19. 19.

    Find the force needed to accelerate a 35 kg mass at 4.4 m/s².

    Formula:Newton's Second Law

    $F = ma$

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20. 20.

    Find the sum of the first 6 terms of a geometric series with first term a = 6 and common ratio r = 2.

    Formula:Sum of a Geometric Series

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

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