Netherlands · Year 11 · Practice Sheet 32

1. 1.

   Find the population standard deviation of: 9, 18, 20, 8, 11 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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2. 2.

   Find the gravitational potential energy of a 14 kg object raised 39 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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3. 3.

   €3,100 is invested at 6% 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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4. 4.

   A force of 147 N acts on an area of 1.5 m². Find the pressure.

   Formula:Pressure

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

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5. 5.

   An object with initial velocity 12 m/s accelerates at 4.1 m/s² for 8 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

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6. 6.

   An object has mass 123 g and volume 41 cm³. Find its density.

   Formula:Density

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

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7. 7.

   Two masses 2,600 kg and 600 kg are 9 m apart. Find the gravitational force between them. (G = 6.674×10⁻¹¹)

   Formula:Newton’s Law of Gravitation

   $F = G\dfrac{m_1 m_2}{r^2}$

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8. 8.

   Find the momentum of a 52 kg object moving at 26 m/s.

   Formula:Momentum

   $p = mv$

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9. 9.

   Find the gravitational potential energy of a 37 kg object raised 16 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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10. 10.

    In a triangle, a = 18, 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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11. 11.

    Find the population standard deviation of: 10, 14, 13, 9, 5 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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12. 12.

    Find the gravitational potential energy of a 6 kg object raised 24 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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13. 13.

    A force of 84 N acts on an area of 8.5 m². Find the pressure.

    Formula:Pressure

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

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14. 14.

    Find the sum of the first 8 terms of a geometric series with first term a = 5 and common ratio r = 2.

    Formula:Sum of a Geometric Series

    $S_n = \dfrac{a(r^{n} - 1)}{r - 1}$

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15. 15.

    An object has mass 54.6 g and volume 21 cm³. Find its density.

    Formula:Density

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

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16. 16.

    A device runs at 233 V drawing 0.5 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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17. 17.

    Find the population standard deviation of: 20, 14, 18, 6, 4 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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18. 18.

    A cone has base radius 2 cm and height 15 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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19. 19.

    A right-angled triangle has legs of 18 cm and 7 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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20. 20.

    Find the sum of the first 8 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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