Belgium · Year 12 · Practice Sheet 24

1. 1.

   A device runs at 155 V drawing 3.3 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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2. 2.

   A 31 kg object moves at 2 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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3. 3.

   Find the gravitational potential energy of a 11 kg object raised 33 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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4. 4.

   Find the sum of the first 6 terms of an arithmetic series with first term a = 3 and common difference d = 7.

   Formula:Sum of an Arithmetic Series

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

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5. 5.

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

   Formula:Sum of a Geometric Series

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

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6. 6.

   A device runs at 62 V drawing 0.3 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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7. 7.

   €4,000 is invested at 3% compound interest per annum for 5 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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8. 8.

   A force of 282 N acts on an area of 9.8 m². Find the pressure.

   Formula:Pressure

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

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9. 9.

   Find the sum of the first 4 terms of a geometric series with first term a = 6 and common ratio r = 3.

   Formula:Sum of a Geometric Series

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

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10. 10.

    Find the momentum of a 8 kg object moving at 13 m/s.

    Formula:Momentum

    $p = mv$

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11. 11.

    A population of 2,400 grows 2% per year. Find its size after 8 years (nearest whole number).

    Formula:Exponential Growth

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

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12. 12.

    Find the gravitational potential energy of a 27 kg object raised 14 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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13. 13.

    Solve using the quadratic formula: x² − 1x − 20 = 0.

    Formula:Quadratic Formula

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

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14. 14.

    Find the sum of the first 11 terms of an arithmetic series with first term a = 7 and common difference d = 4.

    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 44 V drawing 5.6 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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16. 16.

    A force of 124 N acts on an area of 0.5 m². Find the pressure.

    Formula:Pressure

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

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17. 17.

    Find the gravitational potential energy of a 17 kg object raised 11 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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18. 18.

    Find the population standard deviation of: 15, 8, 6, 9, 11 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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19. 19.

    Find the sum of the first 7 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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20. 20.

    Find the population standard deviation of: 20, 12, 10, 19, 16 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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