Ireland · Year 12 · Practice Sheet 39

1. 1.

   Two masses 2,100 kg and 810 kg are 8 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.

   An object with initial velocity 8 m/s accelerates at 2.5 m/s² for 7 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

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3. 3.

   Find the sum of the first 14 terms of an arithmetic series with first term a = 8 and common difference d = 7.

   Formula:Sum of an Arithmetic Series

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

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4. 4.

   Find the volume of a sphere of radius 8 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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5. 5.

   A force of 90 N moves an object 15 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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6. 6.

   Find the gravitational potential energy of a 50 kg object raised 31 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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7. 7.

   Find the momentum of a 31 kg object moving at 20 m/s.

   Formula:Momentum

   $p = mv$

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8. 8.

   A force of 11 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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9. 9.

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

   Formula:Quadratic Formula

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

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10. 10.

    In a triangle, a = 18, b = 5 and the included angle C = 110°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

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

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11. 11.

    Find the volume of a sphere of radius 5 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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12. 12.

    A current of 3.5 A flows through a 51 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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13. 13.

    Two masses 4,100 kg and 400 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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14. 14.

    Find the sum of the first 13 terms of an arithmetic series with first term a = 10 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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15. 15.

    A triangle has sides a = 13 cm and b = 8 cm with an included angle C = 120°. 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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16. 16.

    A force of 49 N moves an object 32 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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17. 17.

    A triangle has sides a = 20 cm and b = 17 cm with an included angle C = 60°. 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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18. 18.

    A cone has base radius 9 cm and height 15 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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19. 19.

    Find the momentum of a 56 kg object moving at 11 m/s.

    Formula:Momentum

    $p = mv$

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20. 20.

    A wave has frequency 21 Hz and wavelength 1.53 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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