Australia · Year 11 · Practice Sheet 31

1. 1.

   A force of 21 N moves an object 22 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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2. 2.

   Find the sum of the first 15 terms of an arithmetic series with first term a = 5 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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3. 3.

   Find the population standard deviation of: 16, 8, 8, 5, 2 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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4. 4.

   A right-angled triangle has legs of 20 cm and 18 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

   $c = \sqrt{a^2 + b^2}$

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5. 5.

   A force of 109 N moves an object 23 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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6. 6.

   An object with initial velocity 2 m/s accelerates at 4.1 m/s² for 5 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

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7. 7.

   A force of 17 N moves an object 27 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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8. 8.

   A force of 374 N acts on an area of 0.9 m². Find the pressure.

   Formula:Pressure

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

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9. 9.

   A right-angled triangle has legs of 14 cm and 16 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

   $c = \sqrt{a^2 + b^2}$

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10. 10.

    A body starts at 2 m/s and accelerates at 1 m/s² for 9 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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11. 11.

    A triangle has sides a = 9 cm and b = 19 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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12. 12.

    A right-angled triangle has legs of 14 cm and 17 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

    $c = \sqrt{a^2 + b^2}$

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13. 13.

    Find the population standard deviation of: 3, 12, 13, 8, 14 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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14. 14.

    A wave has frequency 439 Hz and wavelength 0.92 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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15. 15.

    Solve using the quadratic formula: x² + 3x − 18 = 0.

    Formula:Quadratic Formula

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

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16. 16.

    Find the force needed to accelerate a 28 kg mass at 8.3 m/s².

    Formula:Newton's Second Law

    $F = ma$

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17. 17.

    A force of 37 N moves an object 22 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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18. 18.

    A device runs at 76 V drawing 7.5 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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19. 19.

    A cylinder has radius 4 cm and height 28 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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20. 20.

    A wave has frequency 888 Hz and wavelength 3.61 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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