Spain · Grado 12 · Practice Sheet 5

1. 1.

   Find the gravitational potential energy of a 41 kg object raised 2 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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2. 2.

   A device runs at 121 V drawing 3.6 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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3. 3.

   Find the momentum of a 14 kg object moving at 2 m/s.

   Formula:Momentum

   $p = mv$

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4. 4.

   Find the sum of the first 6 terms of a geometric series with first term a = 5 and common ratio r = 3.

   Formula:Sum of a Geometric Series

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

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5. 5.

   A force of 55 N moves an object 8 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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6. 6.

   Find the sum of the first 9 terms of an arithmetic series with first term a = 12 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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7. 7.

   A wave has frequency 466 Hz and wavelength 0.78 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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8. 8.

   A current of 0.6 A flows through a 29 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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9. 9.

   A triangle has sides a = 11 cm and b = 5 cm with an included angle C = 90°. 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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10. 10.

    A current of 6.3 A flows through a 26 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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11. 11.

    A 23 kg object moves at 19 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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12. 12.

    A triangle has sides a = 12 cm and b = 14 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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13. 13.

    Find the sum of the first 6 terms of an arithmetic series with first term a = 6 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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14. 14.

    A force of 62 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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15. 15.

    A cone has base radius 10 cm and height 21 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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16. 16.

    A device runs at 223 V drawing 1.1 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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17. 17.

    €2,900 is invested at 3% 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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18. 18.

    A force of 388 N acts on an area of 1.8 m². Find the pressure.

    Formula:Pressure

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

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19. 19.

    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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20. 20.

    Find the sum of the first 20 terms of an arithmetic series with first term a = 8 and common difference d = 2.

    Formula:Sum of an Arithmetic Series

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

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