Netherlands · Year 12 · Practice Sheet 18

1. 1.

   A force of 292 N acts on an area of 6 m². Find the pressure.

   Formula:Pressure

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

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2. 2.

   Find the volume of a sphere of radius 7 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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3. 3.

   A population of 8,200 grows 3% per year. Find its size after 8 years (nearest whole number).

   Formula:Exponential Growth

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

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4. 4.

   A wave has frequency 508 Hz and wavelength 4.71 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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5. 5.

   A 37 kg object moves at 20 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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6. 6.

   In a triangle, a = 17, b = 10 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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7. 7.

   Find the population standard deviation of: 11, 20, 6, 11, 14 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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8. 8.

   Solve using the quadratic formula: x² − 5x + 6 = 0.

   Formula:Quadratic Formula

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

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9. 9.

   Find the sum of the first 19 terms of an arithmetic series with first term a = 9 and common difference d = 6.

   Formula:Sum of an Arithmetic Series

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

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10. 10.

    A triangle has sides a = 5 cm and b = 11 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.

    An object with initial velocity 5 m/s accelerates at 4.6 m/s² for 10 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

    $s = ut + \tfrac{1}{2}at^2$

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12. 12.

    Find the population standard deviation of: 5, 14, 7, 18, 16 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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13. 13.

    A 6 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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14. 14.

    Find the momentum of a 25 kg object moving at 13 m/s.

    Formula:Momentum

    $p = mv$

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15. 15.

    A current of 7.1 A flows through a 37 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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16. 16.

    Find the momentum of a 30 kg object moving at 15 m/s.

    Formula:Momentum

    $p = mv$

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17. 17.

    A device runs at 25 V drawing 2.3 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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18. 18.

    Solve using the quadratic formula: x² + 6x + 5 = 0.

    Formula:Quadratic Formula

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

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19. 19.

    A force of 39 N moves an object 35 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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20. 20.

    Find the population standard deviation of: 9, 8, 5, 15, 19 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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