Egypt · Grade 11 · Practice Sheet 29

1. 1.

   Find the volume of a sphere of radius 5 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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2. 2.

   Find the sum of the first 17 terms of an arithmetic series with first term a = 11 and common difference d = 1.

   Formula:Sum of an Arithmetic Series

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

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3. 3.

   A current of 3.1 A flows through a 24 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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4. 4.

   Find the population standard deviation of: 6, 5, 18, 19, 5 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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5. 5.

   Find the momentum of a 11 kg object moving at 12 m/s.

   Formula:Momentum

   $p = mv$

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6. 6.

   A wave has frequency 128 Hz and wavelength 1.8 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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7. 7.

   A force of 173 N acts on an area of 2.9 m². Find the pressure.

   Formula:Pressure

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

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8. 8.

   E£ 1,900 is invested at 6% compound interest per annum for 2 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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9. 9.

   An object has mass 60.2 g and volume 43 cm³. Find its density.

   Formula:Density

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

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10. 10.

    A triangle has sides a = 5 cm and b = 20 cm with an included angle C = 90°. 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.

    A population of 7,800 grows 2% per year. Find its size after 2 years (nearest whole number).

    Formula:Exponential Growth

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

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12. 12.

    A triangle has sides a = 5 cm and b = 16 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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13. 13.

    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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14. 14.

    Find the sum of the first 11 terms of an arithmetic series with first term a = 12 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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15. 15.

    A device runs at 59 V drawing 6.8 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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16. 16.

    Find the sum of the first 17 terms of an arithmetic series with first term a = 11 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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17. 17.

    A 25 kg object moves at 12 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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18. 18.

    A device runs at 162 V drawing 9.4 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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19. 19.

    A population of 1,000 grows 2% per year. Find its size after 3 years (nearest whole number).

    Formula:Exponential Growth

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

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20. 20.

    A right-angled triangle has legs of 3 cm and 11 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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