Tunisia · Grade 11 · Practice Sheet 12

1. 1.

   A wave has frequency 768 Hz and wavelength 4.95 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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2. 2.

   A right-angled triangle has legs of 14 cm and 12 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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3. 3.

   Find the gravitational potential energy of a 19 kg object raised 12 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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4. 4.

   Find the momentum of a 58 kg object moving at 10 m/s.

   Formula:Momentum

   $p = mv$

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5. 5.

   A device runs at 104 V drawing 8.3 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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6. 6.

   In a triangle, a = 7, b = 15 and the included angle C = 110°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

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

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7. 7.

   A population of 2,300 grows 5% per year. Find its size after 7 years (nearest whole number).

   Formula:Exponential Growth

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

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8. 8.

   In a triangle, a = 9, b = 7 and the included angle C = 40°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

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

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9. 9.

   A population of 7,400 grows 5% per year. Find its size after 2 years (nearest whole number).

   Formula:Exponential Growth

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

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10. 10.

    Find the force needed to accelerate a 11 kg mass at 6 m/s².

    Formula:Newton's Second Law

    $F = ma$

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11. 11.

    Find the momentum of a 11 kg object moving at 22 m/s.

    Formula:Momentum

    $p = mv$

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12. 12.

    A body starts at 6 m/s and accelerates at 5.5 m/s² for 4 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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13. 13.

    Find the sum of the first 3 terms of a geometric series with first term a = 3 and common ratio r = 4.

    Formula:Sum of a Geometric Series

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

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14. 14.

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

    Formula:Kinetic Energy

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

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15. 15.

    Find the momentum of a 32 kg object moving at 16 m/s.

    Formula:Momentum

    $p = mv$

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16. 16.

    Two masses 3,500 kg and 390 kg are 14 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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17. 17.

    A cone has base radius 2 cm and height 19 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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18. 18.

    An object has mass 30.8 g and volume 22 cm³. Find its density.

    Formula:Density

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

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19. 19.

    Find the population standard deviation of: 20, 14, 4, 5, 2 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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20. 20.

    A force of 7 N moves an object 3 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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