Czechia · Grade 11 · Practice Sheet 34

1. 1.

   A population of 2,100 grows 3% 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 triangle has sides a = 6 cm and b = 14 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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3. 3.

   A 25 kg object moves at 14 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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4. 4.

   Find the momentum of a 28 kg object moving at 20 m/s.

   Formula:Momentum

   $p = mv$

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5. 5.

   Two masses 4,200 kg and 480 kg are 10 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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6. 6.

   A population of 7,100 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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7. 7.

   Find the volume of a sphere of radius 9 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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8. 8.

   A force of 265 N acts on an area of 5.9 m². Find the pressure.

   Formula:Pressure

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

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9. 9.

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

   Formula:Sum of a Geometric Series

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

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10. 10.

    A force of 104 N moves an object 25 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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11. 11.

    A cylinder has radius 3 cm and height 27 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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12. 12.

    A right-angled triangle has legs of 16 cm and 8 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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13. 13.

    A wave has frequency 46 Hz and wavelength 1.56 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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14. 14.

    Find the momentum of a 2 kg object moving at 6 m/s.

    Formula:Momentum

    $p = mv$

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15. 15.

    Find the population standard deviation of: 3, 8, 14, 9, 4 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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16. 16.

    A wave has frequency 427 Hz and wavelength 0.45 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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17. 17.

    A force of 388 N acts on an area of 0.9 m². Find the pressure.

    Formula:Pressure

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

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18. 18.

    Find the population standard deviation of: 17, 12, 14, 10, 10 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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19. 19.

    A 20 kg object moves at 22 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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20. 20.

    A right-angled triangle has legs of 8 cm and 6 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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