Portugal · Ano 12 · Practice Sheet 1

1. 1.

   Find the momentum of a 17 kg object moving at 27 m/s.

   Formula:Momentum

   $p = mv$

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2. 2.

   A force of 103 N acts on an area of 6.1 m². Find the pressure.

   Formula:Pressure

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

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3. 3.

   A force of 11 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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4. 4.

   Find the momentum of a 42 kg object moving at 25 m/s.

   Formula:Momentum

   $p = mv$

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5. 5.

   Find the force needed to accelerate a 19 kg mass at 4.3 m/s².

   Formula:Newton's Second Law

   $F = ma$

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6. 6.

   €500 is invested at 5% compound interest per annum for 3 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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7. 7.

   A current of 2.2 A flows through a 33 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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8. 8.

   Find the sum of the first 17 terms of an arithmetic series with first term a = 7 and common difference d = 3.

   Formula:Sum of an Arithmetic Series

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

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9. 9.

   In a triangle, a = 16, b = 8 and the included angle C = 80°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

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

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10. 10.

    Find the force needed to accelerate a 13 kg mass at 5.3 m/s².

    Formula:Newton's Second Law

    $F = ma$

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11. 11.

    A wave has frequency 498 Hz and wavelength 3.97 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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12. 12.

    Find the force needed to accelerate a 9 kg mass at 3.8 m/s².

    Formula:Newton's Second Law

    $F = ma$

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13. 13.

    Find the population standard deviation of: 6, 13, 10, 4, 5 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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14. 14.

    Find the volume of a sphere of radius 11 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

    $V = \tfrac{4}{3} \pi r^3$

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15. 15.

    A body starts at 4 m/s and accelerates at 2 m/s² for 8 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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16. 16.

    A population of 2,500 grows 2% per year. Find its size after 7 years (nearest whole number).

    Formula:Exponential Growth

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

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17. 17.

    A device runs at 218 V drawing 10 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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18. 18.

    Find the gravitational potential energy of a 5 kg object raised 34 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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19. 19.

    Find the force needed to accelerate a 28 kg mass at 7.1 m/s².

    Formula:Newton's Second Law

    $F = ma$

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20. 20.

    A wave has frequency 582 Hz and wavelength 1.19 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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