Netherlands · Year 11 · Practice Sheet 44

1. 1.

   A cylinder has radius 14 cm and height 25 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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2. 2.

   Find the population standard deviation of: 3, 6, 5, 18, 8 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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3. 3.

   Find the sum of the first 4 terms of a geometric series with first term a = 5 and common ratio r = 4.

   Formula:Sum of a Geometric Series

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

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4. 4.

   A cone has base radius 11 cm and height 14 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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5. 5.

   A current of 6.1 A flows through a 8 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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6. 6.

   A force of 222 N acts on an area of 4 m². Find the pressure.

   Formula:Pressure

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

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7. 7.

   A wave has frequency 513 Hz and wavelength 1.83 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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8. 8.

   Find the population standard deviation of: 15, 12, 20, 13, 19 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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9. 9.

   A triangle has sides a = 13 cm and b = 20 cm with an included angle C = 30°. 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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10. 10.

    A force of 168 N acts on an area of 2.8 m². Find the pressure.

    Formula:Pressure

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

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11. 11.

    An object has mass 220.8 g and volume 46 cm³. Find its density.

    Formula:Density

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

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12. 12.

    A device runs at 7 V drawing 2.1 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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13. 13.

    A force of 71 N moves an object 33 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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14. 14.

    In a triangle, a = 5, b = 9 and the included angle C = 100°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

    $c = \sqrt{a^2 + b^2 - 2ab\cos C}$

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15. 15.

    Find the force needed to accelerate a 12 kg mass at 0.7 m/s².

    Formula:Newton's Second Law

    $F = ma$

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16. 16.

    A device runs at 97 V drawing 1.8 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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17. 17.

    €3,200 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 device runs at 145 V drawing 8.9 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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19. 19.

    Two masses 5,400 kg and 250 kg are 5 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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20. 20.

    A cylinder has radius 8 cm and height 20 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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