Ethiopia · Grade 12 · Practice Sheet 16

1. 1.

   Br 2,800 is invested at 6% compound interest per annum for 3 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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2. 2.

   Find the gravitational potential energy of a 23 kg object raised 6 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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3. 3.

   Solve using the quadratic formula: x² + 11x + 30 = 0.

   Formula:Quadratic Formula

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

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4. 4.

   Find the sum of the first 6 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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5. 5.

   A current of 6.7 A flows through a 51 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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6. 6.

   Find the sum of the first 17 terms of an arithmetic series with first term a = 9 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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7. 7.

   A device runs at 47 V drawing 3.9 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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8. 8.

   A wave has frequency 436 Hz and wavelength 1.36 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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9. 9.

   Find the momentum of a 7 kg object moving at 14 m/s.

   Formula:Momentum

   $p = mv$

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10. 10.

    A force of 230 N acts on an area of 9.2 m². Find the pressure.

    Formula:Pressure

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

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11. 11.

    A body starts at 13 m/s and accelerates at 4.4 m/s² for 11 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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12. 12.

    Find the sum of the first 5 terms of an arithmetic series with first term a = 6 and common difference d = 5.

    Formula:Sum of an Arithmetic Series

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

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13. 13.

    Find the volume of a sphere of radius 6 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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14. 14.

    Find the momentum of a 40 kg object moving at 18 m/s.

    Formula:Momentum

    $p = mv$

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15. 15.

    A force of 57 N moves an object 4 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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16. 16.

    A device runs at 102 V drawing 0.6 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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17. 17.

    A force of 22 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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18. 18.

    A cone has base radius 7 cm and height 13 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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19. 19.

    Find the force needed to accelerate a 14 kg mass at 2.7 m/s².

    Formula:Newton's Second Law

    $F = ma$

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20. 20.

    A device runs at 11 V drawing 8.1 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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