Italy · Classe 12 · Practice Sheet 17

1. 1.

   Find the force needed to accelerate a 13 kg mass at 0.6 m/s².

   Formula:Newton's Second Law

   $F = ma$

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2. 2.

   In a triangle, a = 10, b = 15 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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3. 3.

   A force of 279 N acts on an area of 3.8 m². Find the pressure.

   Formula:Pressure

   $P = \dfrac{F}{A}$

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4. 4.

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

   Formula:Sum of a Geometric Series

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

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5. 5.

   A population of 2,900 grows 10% per year. Find its size after 8 years (nearest whole number).

   Formula:Exponential Growth

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

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6. 6.

   Find the gravitational potential energy of a 34 kg object raised 4 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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7. 7.

   Find the force needed to accelerate a 39 kg mass at 2.2 m/s².

   Formula:Newton's Second Law

   $F = ma$

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8. 8.

   A force of 37 N moves an object 12 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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9. 9.

   A device runs at 10 V drawing 9 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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10. 10.

    A force of 92 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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11. 11.

    In a triangle, a = 11, b = 14 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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12. 12.

    Find the force needed to accelerate a 32 kg mass at 1.9 m/s².

    Formula:Newton's Second Law

    $F = ma$

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13. 13.

    Find the momentum of a 46 kg object moving at 30 m/s.

    Formula:Momentum

    $p = mv$

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14. 14.

    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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15. 15.

    A population of 3,000 grows 10% per year. Find its size after 3 years (nearest whole number).

    Formula:Exponential Growth

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

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16. 16.

    Find the sum of the first 5 terms of a geometric series with first term a = 7 and common ratio r = 3.

    Formula:Sum of a Geometric Series

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

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17. 17.

    Find the population standard deviation of: 17, 2, 20, 13, 12 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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18. 18.

    Find the momentum of a 34 kg object moving at 20 m/s.

    Formula:Momentum

    $p = mv$

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19. 19.

    A force of 40 N moves an object 24 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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20. 20.

    A triangle has sides a = 12 cm and b = 14 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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