Ireland · Year 11 · Practice Sheet 6

1. 1.

   A device runs at 126 V drawing 8.3 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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2. 2.

   Find the momentum of a 35 kg object moving at 20 m/s.

   Formula:Momentum

   $p = mv$

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3. 3.

   An object has mass 155.8 g and volume 41 cm³. Find its density.

   Formula:Density

   $\rho = \dfrac{m}{V}$

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4. 4.

   A triangle has sides a = 5 cm and b = 6 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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5. 5.

   In a triangle, a = 7, b = 11 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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6. 6.

   A device runs at 174 V drawing 0.5 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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7. 7.

   A body starts at 9 m/s and accelerates at 1.3 m/s² for 6 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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8. 8.

   An object with initial velocity 7 m/s accelerates at 1.2 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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9. 9.

   A wave has frequency 471 Hz and wavelength 2.46 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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10. 10.

    Find the sum of the first 6 terms of a geometric series with first term a = 4 and common ratio r = 2.

    Formula:Sum of a Geometric Series

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

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11. 11.

    Find the sum of the first 13 terms of an arithmetic series with first term a = 1 and common difference d = 5.

    Formula:Sum of an Arithmetic Series

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

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12. 12.

    Find the gravitational potential energy of a 12 kg object raised 10 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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13. 13.

    Solve using the quadratic formula: x² − 4x − 5 = 0.

    Formula:Quadratic Formula

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

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14. 14.

    A wave has frequency 423 Hz and wavelength 3.27 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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15. 15.

    Find the sum of the first 18 terms of an arithmetic series with first term a = 1 and common difference d = 1.

    Formula:Sum of an Arithmetic Series

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

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16. 16.

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

    Formula:Sum of a Geometric Series

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

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17. 17.

    A force of 350 N acts on an area of 6.7 m². Find the pressure.

    Formula:Pressure

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

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18. 18.

    A current of 2.4 A flows through a 47 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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19. 19.

    Find the sum of the first 6 terms of a geometric series with first term a = 3 and common ratio r = 2.

    Formula:Sum of a Geometric Series

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

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20. 20.

    In a triangle, a = 11, b = 13 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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