Ireland · Year 11 · Practice Sheet 47

1. 1.

   A wave has frequency 64 Hz and wavelength 4.04 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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2. 2.

   Find the gravitational potential energy of a 25 kg object raised 29 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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3. 3.

   A 15 kg object moves at 23 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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4. 4.

   Find the sum of the first 7 terms of a geometric series with first term a = 2 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.

   An object has mass 70 g and volume 50 cm³. Find its density.

   Formula:Density

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

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6. 6.

   A cone has base radius 9 cm and height 13 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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7. 7.

   A body starts at 18 m/s and accelerates at 5.1 m/s² for 3 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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8. 8.

   A force of 49 N moves an object 2 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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9. 9.

   A current of 7.1 A flows through a 4 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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10. 10.

    A body starts at 14 m/s and accelerates at 2.6 m/s² for 6 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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11. 11.

    Find the volume of a sphere of radius 3 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

    $V = \tfrac{4}{3} \pi r^3$

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12. 12.

    A force of 85 N moves an object 6 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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13. 13.

    Solve using the quadratic formula: x² + 4x − 12 = 0.

    Formula:Quadratic Formula

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

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14. 14.

    A triangle has sides a = 14 cm and b = 13 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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15. 15.

    A body starts at 6 m/s and accelerates at 3.7 m/s² for 8 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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16. 16.

    A population of 7,500 grows 2% per year. Find its size after 5 years (nearest whole number).

    Formula:Exponential Growth

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

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17. 17.

    A force of 40 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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18. 18.

    A wave has frequency 453 Hz and wavelength 3.66 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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19. 19.

    Find the population standard deviation of: 15, 10, 11, 10, 5 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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20. 20.

    A wave has frequency 160 Hz and wavelength 3.29 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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