Hungary · Grade 12 · Practice Sheet 27

1. 1.

   Find the force needed to accelerate a 29 kg mass at 3.9 m/s².

   Formula:Newton's Second Law

   $F = ma$

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2. 2.

   A force of 10 N moves an object 25 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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3. 3.

   A device runs at 229 V drawing 7.8 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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4. 4.

   A 10 kg object moves at 11 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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5. 5.

   A triangle has sides a = 6 cm and b = 19 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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6. 6.

   In a triangle, a = 18, b = 7 and the included angle C = 40°. 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 cone has base radius 11 cm and height 24 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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8. 8.

   A 21 kg object moves at 11 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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9. 9.

   A device runs at 138 V drawing 2.3 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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10. 10.

    Two masses 5,900 kg and 860 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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11. 11.

    In a triangle, a = 5, b = 12 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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12. 12.

    A device runs at 211 V drawing 9.4 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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13. 13.

    Find the force needed to accelerate a 60 kg mass at 8.6 m/s².

    Formula:Newton's Second Law

    $F = ma$

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14. 14.

    A wave has frequency 628 Hz and wavelength 0.59 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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15. 15.

    A population of 5,200 grows 8% per year. Find its size after 6 years (nearest whole number).

    Formula:Exponential Growth

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

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16. 16.

    Find the population standard deviation of: 12, 5, 4, 19, 18 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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17. 17.

    In a triangle, a = 17, b = 9 and the included angle C = 40°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

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

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18. 18.

    A cone has base radius 10 cm and height 7 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.

    A wave has frequency 302 Hz and wavelength 1.64 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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20. 20.

    Find the gravitational potential energy of a 3 kg object raised 3 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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