Romania · Grade 11 · Practice Sheet 30

1. 1.

   A population of 4,600 grows 5% per year. Find its size after 6 years (nearest whole number).

   Formula:Exponential Growth

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

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2. 2.

   A device runs at 153 V drawing 2.4 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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3. 3.

   A force of 334 N acts on an area of 3.8 m². Find the pressure.

   Formula:Pressure

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

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4. 4.

   An object has mass 142.5 g and volume 25 cm³. Find its density.

   Formula:Density

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

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5. 5.

   A device runs at 44 V drawing 7.2 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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6. 6.

   Find the sum of the first 13 terms of an arithmetic series with first term a = 1 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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7. 7.

   Find the population standard deviation of: 12, 2, 14, 19, 6 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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8. 8.

   A body starts at 7 m/s and accelerates at 2.1 m/s² for 7 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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9. 9.

   A wave has frequency 728 Hz and wavelength 3.31 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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10. 10.

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

    Formula:Quadratic Formula

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

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11. 11.

    Find the momentum of a 51 kg object moving at 27 m/s.

    Formula:Momentum

    $p = mv$

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12. 12.

    Two masses 4,000 kg and 410 kg are 7 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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13. 13.

    Find the gravitational potential energy of a 44 kg object raised 20 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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14. 14.

    An object with initial velocity 14 m/s accelerates at 3.6 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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15. 15.

    An object has mass 92.4 g and volume 28 cm³. Find its density.

    Formula:Density

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

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16. 16.

    A right-angled triangle has legs of 7 cm and 5 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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17. 17.

    lei 2,800 is invested at 5% compound interest per annum for 4 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.

    Find the volume of a sphere of radius 10 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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19. 19.

    A cone has base radius 12 cm and height 18 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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20. 20.

    A wave has frequency 474 Hz and wavelength 4.78 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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