Finland · Grade 12 · Practice Sheet 26

1. 1.

   A wave has frequency 589 Hz and wavelength 3.13 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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2. 2.

   A cone has base radius 9 cm and height 12 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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3. 3.

   In a triangle, a = 6, b = 18 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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4. 4.

   Find the gravitational potential energy of a 21 kg object raised 4 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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5. 5.

   Two masses 5,900 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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6. 6.

   Find the sum of the first 4 terms of a geometric series with first term a = 8 and common ratio r = 2.

   Formula:Sum of a Geometric Series

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

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7. 7.

   Find the sum of the first 20 terms of an arithmetic series with first term a = 8 and common difference d = 5.

   Formula:Sum of an Arithmetic Series

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

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8. 8.

   Solve using the quadratic formula: x² + 5x − 6 = 0.

   Formula:Quadratic Formula

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

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9. 9.

   Find the gravitational potential energy of a 30 kg object raised 22 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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10. 10.

    In a triangle, a = 10, b = 7 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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11. 11.

    Find the force needed to accelerate a 24 kg mass at 1.2 m/s².

    Formula:Newton's Second Law

    $F = ma$

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12. 12.

    Two masses 6,200 kg and 240 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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13. 13.

    A wave has frequency 318 Hz and wavelength 0.7 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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14. 14.

    A 39 kg object moves at 22 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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15. 15.

    Find the momentum of a 41 kg object moving at 22 m/s.

    Formula:Momentum

    $p = mv$

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16. 16.

    A force of 98 N moves an object 36 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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17. 17.

    A cone has base radius 7 cm and height 12 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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18. 18.

    A force of 105 N moves an object 33 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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19. 19.

    A body starts at 0 m/s and accelerates at 4.9 m/s² for 4 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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20. 20.

    An object with initial velocity 2 m/s accelerates at 2.3 m/s² for 9 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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