Finland · Grade 12 · Practice Sheet 32

1. 1.

   Find the force needed to accelerate a 58 kg mass at 2.3 m/s².

   Formula:Newton's Second Law

   $F = ma$

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2. 2.

   Two masses 4,900 kg and 730 kg are 3 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 force needed to accelerate a 5 kg mass at 3.4 m/s².

   Formula:Newton's Second Law

   $F = ma$

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4. 4.

   A wave has frequency 412 Hz and wavelength 3.02 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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5. 5.

   Find the gravitational potential energy of a 15 kg object raised 32 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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6. 6.

   Find the population standard deviation of: 3, 3, 17, 5, 16 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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7. 7.

   A device runs at 35 V drawing 6 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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8. 8.

   Find the gravitational potential energy of a 19 kg object raised 25 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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9. 9.

   A device runs at 62 V drawing 8.1 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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10. 10.

    In a triangle, a = 10, b = 6 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.

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

    Formula:Volume of a Cone

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

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12. 12.

    Find the momentum of a 21 kg object moving at 17 m/s.

    Formula:Momentum

    $p = mv$

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13. 13.

    Find the gravitational potential energy of a 2 kg object raised 5 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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14. 14.

    Find the force needed to accelerate a 48 kg mass at 5.6 m/s².

    Formula:Newton's Second Law

    $F = ma$

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15. 15.

    Find the sum of the first 5 terms of an arithmetic series with first term a = 3 and common difference d = 1.

    Formula:Sum of an Arithmetic Series

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

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16. 16.

    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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17. 17.

    A population of 4,800 grows 3% per year. Find its size after 2 years (nearest whole number).

    Formula:Exponential Growth

    $N = N_0 (1 + r)^{t}$

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18. 18.

    A body starts at 19 m/s and accelerates at 4 m/s² for 5 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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19. 19.

    In a triangle, a = 13, b = 11 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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20. 20.

    Find the force needed to accelerate a 10 kg mass at 3.3 m/s².

    Formula:Newton's Second Law

    $F = ma$

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