Italy · Classe 12 · Practice Sheet 1

1. 1.

   Find the force needed to accelerate a 60 kg mass at 5.1 m/s².

   Formula:Newton's Second Law

   $F = ma$

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2. 2.

   A force of 165 N acts on an area of 1.5 m². Find the pressure.

   Formula:Pressure

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

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3. 3.

   A triangle has sides a = 10 cm and b = 19 cm with an included angle C = 30°. 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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4. 4.

   Find the momentum of a 17 kg object moving at 15 m/s.

   Formula:Momentum

   $p = mv$

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5. 5.

   A current of 6.4 A flows through a 44 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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6. 6.

   Two masses 2,800 kg and 190 kg are 7 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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7. 7.

   Solve using the quadratic formula: x² − 2x − 3 = 0.

   Formula:Quadratic Formula

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

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8. 8.

   A wave has frequency 543 Hz and wavelength 3.36 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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9. 9.

   Find the gravitational potential energy of a 26 kg object raised 7 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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10. 10.

    A device runs at 156 V drawing 8.2 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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11. 11.

    Find the population standard deviation of: 12, 9, 16, 2, 15 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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12. 12.

    A body starts at 8 m/s and accelerates at 4.4 m/s² for 6 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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13. 13.

    A population of 5,300 grows 10% per year. Find its size after 5 years (nearest whole number).

    Formula:Exponential Growth

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

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14. 14.

    A force of 28 N moves an object 3 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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15. 15.

    €3,500 is invested at 4% compound interest per annum for 2 years. Find the final amount (to 2 d.p.).

    Formula:Compound Interest

    $A = P\left(1 + \dfrac{r}{100}\right)^{t}$

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16. 16.

    Find the sum of the first 3 terms of a geometric series with first term a = 2 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.

    €2,500 is invested at 4% compound interest per annum for 4 years. Find the final amount (to 2 d.p.).

    Formula:Compound Interest

    $A = P\left(1 + \dfrac{r}{100}\right)^{t}$

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18. 18.

    Solve using the quadratic formula: x² − 1x − 6 = 0.

    Formula:Quadratic Formula

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

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19. 19.

    Find the momentum of a 58 kg object moving at 20 m/s.

    Formula:Momentum

    $p = mv$

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20. 20.

    Find the gravitational potential energy of a 30 kg object raised 24 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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