Ireland · Year 12 · Practice Sheet 15

1. 1.

   Find the gravitational potential energy of a 46 kg object raised 4 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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2. 2.

   A current of 1.2 A flows through a 13 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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3. 3.

   A 15 kg object moves at 21 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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4. 4.

   Solve using the quadratic formula: x² + 3x − 4 = 0.

   Formula:Quadratic Formula

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

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5. 5.

   A triangle has sides a = 5 cm and b = 8 cm with an included angle C = 45°. 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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6. 6.

   Find the momentum of a 42 kg object moving at 11 m/s.

   Formula:Momentum

   $p = mv$

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7. 7.

   A force of 144 N acts on an area of 6 m². Find the pressure.

   Formula:Pressure

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

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8. 8.

   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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9. 9.

   A wave has frequency 277 Hz and wavelength 4.51 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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10. 10.

    In a triangle, a = 18, b = 13 and the included angle C = 100°. 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 7 V drawing 0.6 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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12. 12.

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

    Formula:Quadratic Formula

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

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13. 13.

    A triangle has sides a = 19 cm and b = 18 cm with an included angle C = 60°. 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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14. 14.

    Find the sum of the first 5 terms of an arithmetic series with first term a = 7 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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15. 15.

    A device runs at 100 V drawing 1 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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16. 16.

    Find the gravitational potential energy of a 23 kg object raised 3 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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17. 17.

    Find the population standard deviation of: 7, 6, 20, 9, 11 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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18. 18.

    Find the gravitational potential energy of a 30 kg object raised 3 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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19. 19.

    Find the sum of the first 8 terms of a geometric series with first term a = 8 and common ratio r = 3.

    Formula:Sum of a Geometric Series

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

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20. 20.

    A population of 7,800 grows 5% per year. Find its size after 8 years (nearest whole number).

    Formula:Exponential Growth

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

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