Lebanon · Grade 11 · Practice Sheet 41

1. 1.

   Find the sum of the first 8 terms of an arithmetic series with first term a = 7 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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2. 2.

   LL 1,200 is invested at 4% 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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3. 3.

   A force of 34 N moves an object 36 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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4. 4.

   Two masses 7,100 kg and 140 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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5. 5.

   A device runs at 205 V drawing 8.7 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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6. 6.

   A population of 9,000 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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7. 7.

   Find the momentum of a 31 kg object moving at 27 m/s.

   Formula:Momentum

   $p = mv$

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8. 8.

   Find the force needed to accelerate a 31 kg mass at 8.4 m/s².

   Formula:Newton's Second Law

   $F = ma$

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9. 9.

   A cylinder has radius 8 cm and height 19 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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10. 10.

    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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11. 11.

    Find the gravitational potential energy of a 6 kg object raised 22 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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12. 12.

    A body starts at 19 m/s and accelerates at 3.5 m/s² for 11 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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13. 13.

    A device runs at 200 V drawing 1.2 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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14. 14.

    A 3 kg object moves at 19 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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15. 15.

    A wave has frequency 490 Hz and wavelength 2.35 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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16. 16.

    A force of 475 N acts on an area of 2.9 m². Find the pressure.

    Formula:Pressure

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

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17. 17.

    A 12 kg object moves at 8 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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18. 18.

    Find the population standard deviation of: 16, 14, 18, 19, 11 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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19. 19.

    A triangle has sides a = 18 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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20. 20.

    An object with initial velocity 2 m/s accelerates at 4.8 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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