Taiwan · Grade 10 · Practice Sheet 15

1. 1.

   Find the gravitational potential energy of a 30 kg object raised 21 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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2. 2.

   A device runs at 37 V drawing 8.1 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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3. 3.

   Find the sum of the first 17 terms of an arithmetic series with first term a = 11 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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4. 4.

   Solve using the quadratic formula: x² − 10x + 24 = 0.

   Formula:Quadratic Formula

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

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5. 5.

   Find the momentum of a 42 kg object moving at 10 m/s.

   Formula:Momentum

   $p = mv$

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6. 6.

   A force of 107 N moves an object 14 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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7. 7.

   Solve for x: 2x + 19 = 35.

   Formula:Solving a Linear Equation

   $x = \dfrac{c - b}{a}$

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8. 8.

   Find the gravitational potential energy of a 41 kg object raised 35 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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9. 9.

   Find the sum of the first 9 terms of an arithmetic series with first term a = 11 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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10. 10.

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

    A force of 108 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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12. 12.

    A value changes from 44 to 45. Find the percentage change (to 2 d.p.).

    Formula:Percentage Change

    $\%\,\text{change} = \dfrac{\text{new} - \text{old}}{\text{old}} \times 100$

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13. 13.

    A 21 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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14. 14.

    A wave has frequency 349 Hz and wavelength 4.31 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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15. 15.

    Find the gravitational potential energy of a 7 kg object raised 22 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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16. 16.

    A device runs at 106 V drawing 3.9 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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17. 17.

    Find the momentum of a 41 kg object moving at 27 m/s.

    Formula:Momentum

    $p = mv$

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18. 18.

    A force of 187 N acts on an area of 9.5 m². Find the pressure.

    Formula:Pressure

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

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19. 19.

    A 24 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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20. 20.

    A wave has frequency 270 Hz and wavelength 3.81 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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