Italy · Classe 12 · Practice Sheet 11

1. 1.

   A device runs at 138 V drawing 8.9 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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2. 2.

   Find the sum of the first 15 terms of an arithmetic series with first term a = 9 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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3. 3.

   A current of 4.3 A flows through a 58 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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4. 4.

   Find the sum of the first 12 terms of an arithmetic series with first term a = 9 and common difference d = 6.

   Formula:Sum of an Arithmetic Series

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

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5. 5.

   A cone has base radius 7 cm and height 17 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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6. 6.

   A 5 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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7. 7.

   A wave has frequency 243 Hz and wavelength 0.42 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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8. 8.

   An object with initial velocity 12 m/s accelerates at 1.6 m/s² for 2 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

   $s = ut + \tfrac{1}{2}at^2$

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9. 9.

   A body starts at 17 m/s and accelerates at 3.5 m/s² for 7 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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10. 10.

    A current of 2.9 A flows through a 38 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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11. 11.

    A wave has frequency 222 Hz and wavelength 4.28 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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12. 12.

    A population of 1,200 grows 5% per year. Find its size after 3 years (nearest whole number).

    Formula:Exponential Growth

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

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13. 13.

    A force of 37 N moves an object 30 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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14. 14.

    In a triangle, a = 18, b = 14 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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15. 15.

    Solve using the quadratic formula: x² + 0x − 25 = 0.

    Formula:Quadratic Formula

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

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16. 16.

    In a triangle, a = 10, b = 6 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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17. 17.

    An object with initial velocity 12 m/s accelerates at 2.1 m/s² for 5 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

    $s = ut + \tfrac{1}{2}at^2$

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18. 18.

    Find the sum of the first 3 terms of a geometric series with first term a = 5 and common ratio r = 4.

    Formula:Sum of a Geometric Series

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

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19. 19.

    Find the momentum of a 8 kg object moving at 9 m/s.

    Formula:Momentum

    $p = mv$

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20. 20.

    A population of 8,000 grows 2% per year. Find its size after 2 years (nearest whole number).

    Formula:Exponential Growth

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

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