Romania · Grade 11 · Practice Sheet 21

1. 1.

   A force of 24 N moves an object 12 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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2. 2.

   Two masses 1,000 kg and 170 kg are 7 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 14 terms of an arithmetic series with first term a = 5 and common difference d = 3.

   Formula:Sum of an Arithmetic Series

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

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4. 4.

   A force of 108 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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5. 5.

   A device runs at 118 V drawing 4.6 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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6. 6.

   In a triangle, a = 16, b = 17 and the included angle C = 70°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

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

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7. 7.

   A triangle has sides a = 7 cm and b = 15 cm with an included angle C = 90°. Find its area (to 2 d.p.).

   Formula:Area of a Triangle (Sine Rule)

   $A = \tfrac{1}{2} ab\sin C$

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8. 8.

   Find the volume of a sphere of radius 6 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

   $V = \tfrac{4}{3} \pi r^3$

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9. 9.

   Find the sum of the first 14 terms of an arithmetic series with first term a = 6 and common difference d = 3.

   Formula:Sum of an Arithmetic Series

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

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10. 10.

    Find the population standard deviation of: 7, 8, 11, 11, 10 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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11. 11.

    Solve using the quadratic formula: x² + 4x − 12 = 0.

    Formula:Quadratic Formula

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

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12. 12.

    In a triangle, a = 13, b = 13 and the included angle C = 70°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

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

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13. 13.

    A force of 500 N acts on an area of 2.8 m². Find the pressure.

    Formula:Pressure

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

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14. 14.

    Find the volume of a sphere of radius 3 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

    $V = \tfrac{4}{3} \pi r^3$

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15. 15.

    A force of 166 N acts on an area of 6.4 m². Find the pressure.

    Formula:Pressure

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

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16. 16.

    Two masses 1,600 kg and 390 kg are 4 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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17. 17.

    A current of 7.4 A flows through a 60 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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18. 18.

    Find the force needed to accelerate a 37 kg mass at 4.8 m/s².

    Formula:Newton's Second Law

    $F = ma$

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19. 19.

    An object with initial velocity 8 m/s accelerates at 1.3 m/s² for 4 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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20. 20.

    A force of 69 N acts on an area of 5.1 m². Find the pressure.

    Formula:Pressure

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

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