France · Classe 10 · Practice Sheet 20

1. 1.

   Find the gravitational potential energy of a 36 kg object raised 18 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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2. 2.

   A cylinder has radius 12 cm and height 7 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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3. 3.

   An object has mass 45 g and volume 9 cm³. Find its density.

   Formula:Density

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

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4. 4.

   A force of 25 N acts on an area of 9.8 m². Find the pressure.

   Formula:Pressure

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

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5. 5.

   Solve using the quadratic formula: x² − 7x + 10 = 0.

   Formula:Quadratic Formula

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

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6. 6.

   A current of 7.3 A flows through a 24 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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7. 7.

   A cylinder has radius 10 cm and height 11 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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8. 8.

   A device runs at 115 V drawing 3.2 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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9. 9.

   Find the gravitational potential energy of a 24 kg object raised 37 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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10. 10.

    A triangle has sides a = 15 cm and b = 6 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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11. 11.

    A wave has frequency 96 Hz and wavelength 0.98 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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12. 12.

    A 29 kg object moves at 11 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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13. 13.

    A force of 17 N moves an object 26 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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14. 14.

    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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15. 15.

    €700 is invested at 5% 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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16. 16.

    Find the force needed to accelerate a 49 kg mass at 8.1 m/s².

    Formula:Newton's Second Law

    $F = ma$

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17. 17.

    €1,600 is invested at 4% compound interest per annum for 3 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 population of 8,000 grows 8% per year. Find its size after 2 years (nearest whole number).

    Formula:Exponential Growth

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

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19. 19.

    A force of 279 N acts on an area of 6.1 m². Find the pressure.

    Formula:Pressure

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

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20. 20.

    Find the sum of the first 6 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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