Italy · Classe 11 · Practice Sheet 47

1. 1.

   A force of 241 N acts on an area of 1.6 m². Find the pressure.

   Formula:Pressure

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

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2. 2.

   A wave has frequency 63 Hz and wavelength 2.45 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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3. 3.

   A population of 4,300 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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4. 4.

   A cylinder has radius 3 cm and height 6 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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5. 5.

   Find the force needed to accelerate a 31 kg mass at 6.3 m/s².

   Formula:Newton's Second Law

   $F = ma$

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6. 6.

   In a triangle, a = 8, b = 5 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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7. 7.

   Find the population standard deviation of: 12, 7, 19, 8, 4 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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8. 8.

   €1,700 is invested at 8% 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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9. 9.

   Find the sum of the first 4 terms of a geometric series with first term a = 1 and common ratio r = 2.

   Formula:Sum of a Geometric Series

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

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10. 10.

    In a triangle, a = 15, b = 18 and the included angle C = 50°. 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 device runs at 171 V drawing 1.2 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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12. 12.

    A body starts at 15 m/s and accelerates at 1.2 m/s² for 5 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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13. 13.

    A force of 132 N acts on an area of 6.8 m². Find the pressure.

    Formula:Pressure

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

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14. 14.

    A force of 25 N moves an object 13 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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15. 15.

    Find the momentum of a 58 kg object moving at 3 m/s.

    Formula:Momentum

    $p = mv$

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16. 16.

    A wave has frequency 481 Hz and wavelength 4.24 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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17. 17.

    A device runs at 100 V drawing 3.7 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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18. 18.

    A 12 kg object moves at 20 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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19. 19.

    A device runs at 35 V drawing 5.5 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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20. 20.

    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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