Switzerland · Grade 12 · Practice Sheet 3

1. 1.

   Find the volume of a sphere of radius 2 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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2. 2.

   Find the force needed to accelerate a 22 kg mass at 5.9 m/s².

   Formula:Newton's Second Law

   $F = ma$

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3. 3.

   A wave has frequency 660 Hz and wavelength 3.72 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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4. 4.

   A body starts at 3 m/s and accelerates at 2.6 m/s² for 8 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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5. 5.

   A force of 46 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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6. 6.

   In a triangle, a = 16, b = 10 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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7. 7.

   Find the force needed to accelerate a 38 kg mass at 8.5 m/s².

   Formula:Newton's Second Law

   $F = ma$

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8. 8.

   A body starts at 2 m/s and accelerates at 2.8 m/s² for 9 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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9. 9.

   Find the force needed to accelerate a 16 kg mass at 7.9 m/s².

   Formula:Newton's Second Law

   $F = ma$

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10. 10.

    A force of 8 N moves an object 7 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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11. 11.

    Two masses 4,900 kg and 810 kg are 2 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.

    A current of 2.4 A flows through a 6 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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13. 13.

    Find the momentum of a 50 kg object moving at 14 m/s.

    Formula:Momentum

    $p = mv$

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14. 14.

    Find the sum of the first 6 terms of a geometric series with first term a = 3 and common ratio r = 4.

    Formula:Sum of a Geometric Series

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

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15. 15.

    Two masses 8,700 kg and 900 kg are 16 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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16. 16.

    A cone has base radius 8 cm and height 16 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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17. 17.

    Find the sum of the first 15 terms of an arithmetic series with first term a = 1 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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18. 18.

    Solve using the quadratic formula: x² + 6x + 8 = 0.

    Formula:Quadratic Formula

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

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19. 19.

    A triangle has sides a = 19 cm and b = 20 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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20. 20.

    A 38 kg object moves at 12 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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