Ethiopia · Grade 11 · Practice Sheet 30

1. 1.

   Find the gravitational potential energy of a 8 kg object raised 20 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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2. 2.

   Solve using the quadratic formula: x² − 4x + 3 = 0.

   Formula:Quadratic Formula

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

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3. 3.

   Find the sum of the first 6 terms of a geometric series with first term a = 7 and common ratio r = 2.

   Formula:Sum of a Geometric Series

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

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4. 4.

   Find the momentum of a 30 kg object moving at 19 m/s.

   Formula:Momentum

   $p = mv$

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5. 5.

   Find the sum of the first 15 terms of an arithmetic series with first term a = 7 and common difference d = 2.

   Formula:Sum of an Arithmetic Series

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

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6. 6.

   A body starts at 3 m/s and accelerates at 2.6 m/s² for 12 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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7. 7.

   A force of 304 N acts on an area of 6.8 m². Find the pressure.

   Formula:Pressure

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

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8. 8.

   A wave has frequency 784 Hz and wavelength 3.79 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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9. 9.

   Find the momentum of a 16 kg object moving at 30 m/s.

   Formula:Momentum

   $p = mv$

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10. 10.

    A triangle has sides a = 20 cm and b = 11 cm with an included angle C = 60°. 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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11. 11.

    A force of 64 N moves an object 2 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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12. 12.

    A device runs at 45 V drawing 1.8 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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13. 13.

    Solve using the quadratic formula: x² + 2x − 8 = 0.

    Formula:Quadratic Formula

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

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14. 14.

    Br 3,800 is invested at 6% compound interest per annum for 5 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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15. 15.

    Find the gravitational potential energy of a 48 kg object raised 28 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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16. 16.

    An object with initial velocity 9 m/s accelerates at 4.4 m/s² for 8 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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17. 17.

    Find the force needed to accelerate a 7 kg mass at 7.9 m/s².

    Formula:Newton's Second Law

    $F = ma$

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18. 18.

    An object has mass 71.5 g and volume 11 cm³. Find its density.

    Formula:Density

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

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19. 19.

    Find the sum of the first 10 terms of an arithmetic series with first term a = 1 and common difference d = 3.

    Formula:Sum of an Arithmetic Series

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

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20. 20.

    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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