Sri Lanka · Grade 11 · Practice Sheet 43

1. 1.

   In a triangle, a = 14, b = 5 and the included angle C = 70°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

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

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2. 2.

   An object has mass 151.7 g and volume 37 cm³. Find its density.

   Formula:Density

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

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3. 3.

   Find the force needed to accelerate a 12 kg mass at 7.2 m/s².

   Formula:Newton's Second Law

   $F = ma$

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4. 4.

   A wave has frequency 870 Hz and wavelength 3.3 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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5. 5.

   Find the momentum of a 15 kg object moving at 9 m/s.

   Formula:Momentum

   $p = mv$

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6. 6.

   Find the gravitational potential energy of a 10 kg object raised 28 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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7. 7.

   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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8. 8.

   Find the gravitational potential energy of a 7 kg object raised 17 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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9. 9.

   An object with initial velocity 4 m/s accelerates at 1.7 m/s² for 3 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

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10. 10.

    Find the sum of the first 8 terms of an arithmetic series with first term a = 9 and common difference d = 7.

    Formula:Sum of an Arithmetic Series

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

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11. 11.

    A wave has frequency 159 Hz and wavelength 0.32 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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12. 12.

    Find the force needed to accelerate a 53 kg mass at 5 m/s².

    Formula:Newton's Second Law

    $F = ma$

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13. 13.

    Find the gravitational potential energy of a 30 kg object raised 19 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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14. 14.

    A right-angled triangle has legs of 4 cm and 4 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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15. 15.

    A 40 kg object moves at 13 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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16. 16.

    Find the population standard deviation of: 19, 9, 15, 18, 9 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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17. 17.

    An object with initial velocity 15 m/s accelerates at 1.2 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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18. 18.

    Find the sum of the first 16 terms of an arithmetic series with first term a = 5 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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19. 19.

    Find the gravitational potential energy of a 39 kg object raised 16 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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20. 20.

    A wave has frequency 562 Hz and wavelength 0.81 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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